LMFDB - Embedded newform 105.4.s.a.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(26,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("105.26");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	105.101
Dual form			105.4.s.a.26.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.64936 - 2.10696i) q^{2} +(4.80130 + 1.98684i) q^{3} +(4.87855 - 8.44990i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(21.7079 - 2.86543i) q^{6} +(16.7999 + 7.79504i) q^{7} -7.40430i q^{8} +(19.1049 + 19.0788i) q^{9} +O(q^{10})$	\(q+(3.64936 - 2.10696i) q^{2} +(4.80130 + 1.98684i) q^{3} +(4.87855 - 8.44990i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(21.7079 - 2.86543i) q^{6} +(16.7999 + 7.79504i) q^{7} -7.40430i q^{8} +(19.1049 + 19.0788i) q^{9} +(-18.2468 - 10.5348i) q^{10} +(-50.2115 - 28.9896i) q^{11} +(40.2120 - 30.8776i) q^{12} -47.9765i q^{13} +(77.7328 - 6.94984i) q^{14} +(-3.39996 - 25.7573i) q^{15} +(23.4279 + 40.5782i) q^{16} +(-11.9134 + 20.6345i) q^{17} +(109.919 + 29.3723i) q^{18} +(-116.533 + 67.2802i) q^{19} -48.7855 q^{20} +(65.1739 + 70.8051i) q^{21} -244.320 q^{22} +(84.9135 - 49.0248i) q^{23} +(14.7112 - 35.5503i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-101.084 - 175.083i) q^{26} +(53.8217 + 129.562i) q^{27} +(147.827 - 103.929i) q^{28} +57.6971i q^{29} +(-66.6773 - 86.8342i) q^{30} +(-124.065 - 71.6288i) q^{31} +(222.292 + 128.340i) q^{32} +(-183.482 - 238.950i) q^{33} +100.404i q^{34} +(-8.24630 - 92.2334i) q^{35} +(254.419 - 68.3574i) q^{36} +(-0.379630 - 0.657539i) q^{37} +(-283.513 + 491.059i) q^{38} +(95.3217 - 230.349i) q^{39} +(-32.0616 + 18.5108i) q^{40} -518.431 q^{41} +(387.026 + 121.075i) q^{42} +201.904 q^{43} +(-489.919 + 282.855i) q^{44} +(34.8516 - 130.424i) q^{45} +(206.587 - 357.819i) q^{46} +(140.594 + 243.516i) q^{47} +(31.8615 + 241.376i) q^{48} +(221.475 + 261.912i) q^{49} +105.348i q^{50} +(-98.1972 + 75.4026i) q^{51} +(-405.397 - 234.056i) q^{52} +(168.453 + 97.2564i) q^{53} +(469.396 + 359.417i) q^{54} +289.896i q^{55} +(57.7168 - 124.392i) q^{56} +(-693.183 + 91.5000i) q^{57} +(121.565 + 210.558i) q^{58} +(244.533 - 423.544i) q^{59} +(-234.234 - 96.9292i) q^{60} +(159.081 - 91.8453i) q^{61} -603.676 q^{62} +(172.241 + 469.447i) q^{63} +706.785 q^{64} +(-207.744 + 119.941i) q^{65} +(-1173.05 - 485.425i) q^{66} +(452.293 - 783.394i) q^{67} +(116.240 + 201.333i) q^{68} +(505.100 - 66.6730i) q^{69} +(-224.426 - 319.218i) q^{70} -524.004i q^{71} +(141.266 - 141.459i) q^{72} +(-110.969 - 64.0683i) q^{73} +(-2.77082 - 1.59973i) q^{74} +(-103.033 + 79.1156i) q^{75} +1312.92i q^{76} +(-617.574 - 878.424i) q^{77} +(-137.473 - 1041.47i) q^{78} +(120.336 + 208.428i) q^{79} +(117.139 - 202.891i) q^{80} +(0.995105 + 728.999i) q^{81} +(-1891.94 + 1092.31i) q^{82} -607.116 q^{83} +(916.251 - 205.287i) q^{84} +119.134 q^{85} +(736.821 - 425.404i) q^{86} +(-114.635 + 277.021i) q^{87} +(-214.648 + 371.781i) q^{88} +(436.983 + 756.876i) q^{89} +(-147.612 - 549.394i) q^{90} +(373.979 - 806.001i) q^{91} -956.681i q^{92} +(-453.356 - 590.408i) q^{93} +(1026.16 + 592.451i) q^{94} +(582.664 + 336.401i) q^{95} +(812.298 + 1057.86i) q^{96} -1292.71i q^{97} +(1360.08 + 489.173i) q^{98} +(-406.198 - 1511.82i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) $ 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	3.64936	−	2.10696i	1.29024	−	0.744923i	0.311546	−	0.950231i	$-0.399153\pi$
$2$	3.64936	−	2.10696i	1.29024	−	0.744923i	0.978697	+	0.205308i	$0.0658197\pi$
$3$	4.80130	+	1.98684i	0.924010	+	0.382368i
$3$	4.80130	+	1.98684i	0.924010	+	0.382368i
$4$	4.87855	−	8.44990i	0.609819	−	1.05624i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	21.7079	−	2.86543i	1.47703	−	0.194968i
$7$	16.7999	+	7.79504i	0.907111	+	0.420893i
$7$	16.7999	+	7.79504i	0.907111	+	0.420893i
$8$		−	7.40430i		−	0.327227i
$9$	19.1049	+	19.0788i	0.707589	+	0.706624i
$10$	−18.2468	−	10.5348i	−0.577015	−	0.333139i
$11$	−50.2115	−	28.9896i	−1.37630	−	0.794609i	−0.384591	−	0.923087i	$-0.625657\pi$
$11$	−50.2115	−	28.9896i	−1.37630	−	0.794609i	−0.991712	+	0.128478i	$0.958991\pi$
$12$	40.2120	−	30.8776i	0.967351	−	0.742799i
$13$		−	47.9765i		−	1.02356i	−0.859117	−	0.511780i	$-0.828986\pi$
$13$		−	47.9765i		−	1.02356i	0.859117	−	0.511780i	$-0.171014\pi$
$14$	77.7328	−	6.94984i	1.48393	−	0.132673i
$15$	−3.39996	−	25.7573i	−0.0585244	−	0.443368i
$16$	23.4279	+	40.5782i	0.366060	+	0.634035i
$17$	−11.9134	+	20.6345i	−0.169966	+	0.294389i	−0.938407	−	0.345531i	$-0.887699\pi$
$17$	−11.9134	+	20.6345i	−0.169966	+	0.294389i	0.768442	+	0.639919i	$0.221032\pi$
$18$	109.919	+	29.3723i	1.43934	+	0.384618i
$19$	−116.533	+	67.2802i	−1.40708	+	0.812375i	−0.995105	−	0.0988217i	$-0.968493\pi$
$19$	−116.533	+	67.2802i	−1.40708	+	0.812375i	−0.411970	+	0.911197i	$0.635159\pi$
$20$	−48.7855			−0.545439
$21$	65.1739	+	70.8051i	0.677243	+	0.735759i
$22$	−244.320			−2.36769
$23$	84.9135	−	49.0248i	0.769813	−	0.444452i	−0.0629951	−	0.998014i	$-0.520065\pi$
$23$	84.9135	−	49.0248i	0.769813	−	0.444452i	0.832808	+	0.553562i	$0.186732\pi$
$24$	14.7112	−	35.5503i	0.125121	−	0.302361i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−101.084	−	175.083i	−0.762473	−	1.32064i
$27$	53.8217	+	129.562i	0.383629	+	0.923487i
$28$	147.827	−	103.929i	0.997736	−	0.701456i
$29$			57.6971i			0.369451i	0.982790	+	0.184726i	$0.0591396\pi$
$29$			57.6971i			0.369451i	−0.982790	+	0.184726i	$0.940860\pi$
$30$	−66.6773	−	86.8342i	−0.405785	−	0.528456i
$31$	−124.065	−	71.6288i	−0.718796	−	0.414997i	0.0955135	−	0.995428i	$-0.469551\pi$
$31$	−124.065	−	71.6288i	−0.718796	−	0.414997i	−0.814309	+	0.580431i	$0.802884\pi$
$32$	222.292	+	128.340i	1.22800	+	0.708987i
$33$	−183.482	−	238.950i	−0.967885	−	1.26048i
$34$			100.404i			0.506445i
$35$	−8.24630	−	92.2334i	−0.0398251	−	0.445437i
$36$	254.419	−	68.3574i	1.17786	−	0.316470i
$37$	−0.379630	−	0.657539i	−0.00168678	−	0.00292159i	0.865181	−	0.501460i	$-0.167204\pi$
$37$	−0.379630	−	0.657539i	−0.00168678	−	0.00292159i	−0.866868	+	0.498538i	$0.833870\pi$
$38$	−283.513	+	491.059i	−1.21031	+	2.09632i
$39$	95.3217	−	230.349i	0.391377	−	0.945780i
$40$	−32.0616	+	18.5108i	−0.126735	+	0.0731702i
$41$	−518.431			−1.97477			−0.987383	−	0.158351i	$-0.949382\pi$
$41$	−518.431			−1.97477			−0.987383	+	0.158351i	$0.949382\pi$
$42$	387.026	+	121.075i	1.42189	+	0.444815i
$43$	201.904			0.716049			0.358025	−	0.933712i	$-0.383450\pi$
$43$	201.904			0.716049			0.358025	+	0.933712i	$0.383450\pi$
$44$	−489.919	+	282.855i	−1.67859	+	0.969136i
$45$	34.8516	−	130.424i	0.115453	−	0.432054i
$46$	206.587	−	357.819i	0.662164	−	1.14690i
$47$	140.594	+	243.516i	0.436335	+	0.755754i	0.997404	−	0.0720155i	$-0.0229431\pi$
$47$	140.594	+	243.516i	0.436335	+	0.755754i	−0.561069	+	0.827769i	$0.689610\pi$
$48$	31.8615	+	241.376i	0.0958086	+	0.725825i
$49$	221.475	+	261.912i	0.645699	+	0.763592i
$50$			105.348i			0.297969i
$51$	−98.1972	+	75.4026i	−0.269615	+	0.207029i
$52$	−405.397	−	234.056i	−1.08112	−	0.624187i
$53$	168.453	+	97.2564i	0.436581	+	0.252060i	0.702146	−	0.712033i	$-0.252225\pi$
$53$	168.453	+	97.2564i	0.436581	+	0.252060i	−0.265565	+	0.964093i	$0.585559\pi$
$54$	469.396	+	359.417i	1.18290	+	0.905750i
$55$			289.896i			0.710720i
$56$	57.7168	−	124.392i	0.137727	−	0.296831i
$57$	−693.183	+	91.5000i	−1.61078	+	0.212622i
$58$	121.565	+	210.558i	0.275212	+	0.476682i
$59$	244.533	−	423.544i	0.539586	−	0.934590i	−0.459341	−	0.888260i	$-0.651914\pi$
$59$	244.533	−	423.544i	0.539586	−	0.934590i	0.998926	−	0.0463294i	$-0.0147524\pi$
$60$	−234.234	−	96.9292i	−0.503991	−	0.208558i
$61$	159.081	−	91.8453i	0.333905	−	0.192780i	−0.323669	−	0.946171i	$-0.604916\pi$
$61$	159.081	−	91.8453i	0.333905	−	0.192780i	0.657573	+	0.753390i	$0.271583\pi$
$62$	−603.676			−1.23656
$63$	172.241	+	469.447i	0.344449	+	0.938805i
$64$	706.785			1.38044
$65$	−207.744	+	119.941i	−0.396423	+	0.228875i
$66$	−1173.05	−	485.425i	−2.18777	−	0.905329i
$67$	452.293	−	783.394i	0.824722	−	1.42846i	−0.0774103	−	0.996999i	$-0.524665\pi$
$67$	452.293	−	783.394i	0.824722	−	1.42846i	0.902132	−	0.431460i	$-0.142002\pi$
$68$	116.240	+	201.333i	0.207296	+	0.359048i
$69$	505.100	−	66.6730i	0.881259	−	0.116326i
$70$	−224.426	−	319.218i	−0.383200	−	0.545055i
$71$		−	524.004i		−	0.875886i	−0.899003	−	0.437943i	$-0.855707\pi$
$71$		−	524.004i		−	0.875886i	0.899003	−	0.437943i	$-0.144293\pi$
$72$	141.266	−	141.459i	0.231227	−	0.231542i
$73$	−110.969	−	64.0683i	−0.177918	−	0.102721i	0.408396	−	0.912805i	$-0.366088\pi$
$73$	−110.969	−	64.0683i	−0.177918	−	0.102721i	−0.586314	+	0.810084i	$0.699422\pi$
$74$	−2.77082	−	1.59973i	−0.00435271	−	0.00251304i
$75$	−103.033	+	79.1156i	−0.158629	+	0.121806i
$76$			1312.92i			1.98161i
$77$	−617.574	−	878.424i	−0.914014	−	1.30007i
$78$	−137.473	−	1041.47i	−0.199561	−	1.51183i
$79$	120.336	+	208.428i	0.171378	+	0.296835i	0.938902	−	0.344185i	$-0.111845\pi$
$79$	120.336	+	208.428i	0.171378	+	0.296835i	−0.767524	+	0.641020i	$0.778511\pi$
$80$	117.139	−	202.891i	0.163707	−	0.283549i
$81$	0.995105	+	728.999i	0.00136503	+	0.999999i
$82$	−1891.94	+	1092.31i	−2.54793	+	1.47105i
$83$	−607.116			−0.802887			−0.401443	−	0.915884i	$-0.631491\pi$
$83$	−607.116			−0.802887			−0.401443	+	0.915884i	$0.631491\pi$
$84$	916.251	−	205.287i	1.19013	−	0.266650i
$85$	119.134			0.152022
$86$	736.821	−	425.404i	0.923878	−	0.533401i
$87$	−114.635	+	277.021i	−0.141266	+	0.341377i
$88$	−214.648	+	371.781i	−0.260018	+	0.450364i
$89$	436.983	+	756.876i	0.520450	+	0.901446i	0.999717	+	0.0237771i	$0.00756920\pi$
$89$	436.983	+	756.876i	0.520450	+	0.901446i	−0.479267	+	0.877669i	$0.659097\pi$
$90$	−147.612	−	549.394i	−0.172885	−	0.643458i
$91$	373.979	−	806.001i	0.430809	−	0.928482i
$92$		−	956.681i		−	1.08414i
$93$	−453.356	−	590.408i	−0.505493	−	0.658306i
$94$	1026.16	+	592.451i	1.12596	+	0.650071i
$95$	582.664	+	336.401i	0.629263	+	0.363305i
$96$	812.298	+	1057.86i	0.863591	+	1.12466i
$97$		−	1292.71i		−	1.35315i	−0.736375	−	0.676573i	$-0.763464\pi$
$97$		−	1292.71i		−	1.35315i	0.736375	−	0.676573i	$-0.236536\pi$
$98$	1360.08	+	489.173i	1.40193	+	0.504224i
$99$	−406.198	−	1511.82i	−0.412368	−	1.53479i
$100$	121.964	+	211.248i	0.121964	+	0.211248i
$101$	−111.663	+	193.406i	−0.110009	+	0.190541i	−0.915774	−	0.401695i	$-0.868421\pi$
$101$	−111.663	+	193.406i	−0.110009	+	0.190541i	0.805765	+	0.592236i	$0.201755\pi$
$102$	−199.487	+	482.069i	−0.193648	+	0.467960i
$103$	720.483	−	415.971i	0.689236	−	0.397931i	−0.114090	−	0.993470i	$-0.536395\pi$
$103$	720.483	−	415.971i	0.689236	−	0.397931i	0.803326	+	0.595540i	$0.203062\pi$
$104$	−355.232			−0.334937
$105$	143.660	−	459.224i	0.133522	−	0.426816i
$106$	819.661			0.751061
$107$	748.609	−	432.210i	0.676362	−	0.390498i	−0.122121	−	0.992515i	$-0.538970\pi$
$107$	748.609	−	432.210i	0.676362	−	0.390498i	0.798483	+	0.602017i	$0.205636\pi$
$108$	1357.36	+	177.286i	1.20937	+	0.157957i
$109$	813.647	−	1409.28i	0.714984	−	1.23839i	−0.247981	−	0.968765i	$-0.579767\pi$
$109$	813.647	−	1409.28i	0.714984	−	1.23839i	0.962966	−	0.269624i	$-0.0868995\pi$
$110$	610.799	+	1057.94i	0.529431	+	0.917002i
$111$	−0.516291	−	3.91131i	−0.000441479	−	0.00334455i
$112$	77.2772	+	864.332i	0.0651965	+	0.729212i
$113$			756.786i			0.630021i	0.949088	+	0.315011i	$0.102008\pi$
$113$			756.786i			0.630021i	−0.949088	+	0.315011i	$0.897992\pi$
$114$	−2336.89	+	1794.43i	−1.91991	+	1.47424i
$115$	−424.568	−	245.124i	−0.344271	−	0.198765i
$116$	487.535	+	281.478i	0.390228	+	0.225298i
$117$	915.336	−	916.586i	0.723272	−	0.724260i
$118$		−	2060.89i		−	1.60780i
$119$	−360.991	+	253.794i	−0.278084	+	0.195506i
$120$	−190.715	+	25.1743i	−0.145082	+	0.0191508i
$121$	1015.30	+	1758.54i	0.762807	+	1.32122i
$122$	387.029	−	670.353i	0.287213	−	0.497467i
$123$	−2489.14	−	1030.04i	−1.82470	−	0.755087i
$124$	−1210.51	+	698.890i	−0.876671	+	0.506146i
$125$	125.000			0.0894427
$126$	1617.67	+	1350.28i	1.14376	+	0.954700i
$127$	−1423.41			−0.994544			−0.497272	−	0.867595i	$-0.665665\pi$
$127$	−1423.41			−0.994544			−0.497272	+	0.867595i	$0.665665\pi$
$128$	800.979	−	462.445i	0.553103	−	0.319334i
$129$	969.403	+	401.152i	0.661637	+	0.273794i
$130$	−505.422	+	875.417i	−0.340988	+	0.590609i
$131$	−3.54194	−	6.13481i	−0.00236229	−	0.00409161i	0.864842	−	0.502044i	$-0.167419\pi$
$131$	−3.54194	−	6.13481i	−0.00236229	−	0.00409161i	−0.867204	+	0.497953i	$0.834085\pi$
$132$	−2914.23	+	384.678i	−1.92160	+	0.253651i
$133$	−2482.19	+	221.925i	−1.61830	+	0.144687i
$134$		−	3811.85i		−	2.45741i
$135$	426.464	−	556.959i	0.271883	−	0.355077i
$136$	152.784	+	88.2101i	0.0963320	+	0.0556173i
$137$	2.00839	+	1.15955i	0.00125247	+	0.000723114i	0.500626	−	0.865664i	$-0.333103\pi$
$137$	2.00839	+	1.15955i	0.00125247	+	0.000723114i	−0.499374	+	0.866387i	$0.666436\pi$
$138$	1702.81	−	1307.54i	1.05038	−	0.806558i
$139$		−	331.436i		−	0.202245i	−0.994874	−	0.101122i	$-0.967757\pi$
$139$		−	331.436i		−	0.202245i	0.994874	−	0.101122i	$-0.0322434\pi$
$140$	−819.593	−	380.285i	−0.494773	−	0.229571i
$141$	191.205	+	1448.53i	0.114201	+	0.865164i
$142$	−1104.06	−	1912.28i	−0.652467	−	1.13011i
$143$	−1390.82	+	2408.97i	−0.813330	+	1.40873i
$144$	−326.599	+	1222.22i	−0.189004	+	0.707303i
$145$	249.836	−	144.243i	0.143088	−	0.0826118i
$146$	−539.957			−0.306076
$147$	542.988	+	1697.55i	0.304659	+	0.952461i
$148$	−7.40819			−0.00411452
$149$	1404.05	−	810.630i	0.771977	−	0.445701i	−0.0616027	−	0.998101i	$-0.519621\pi$
$149$	1404.05	−	810.630i	0.771977	−	0.445701i	0.833579	+	0.552400i	$0.186288\pi$
$150$	−209.310	+	505.807i	−0.113934	+	0.275326i
$151$	−803.303	+	1391.36i	−0.432926	+	0.749850i	−0.997124	−	0.0757895i	$-0.975852\pi$
$151$	−803.303	+	1391.36i	−0.432926	+	0.749850i	0.564198	+	0.825640i	$0.309186\pi$
$152$	498.163	+	862.844i	0.265831	+	0.460433i
$153$	−621.287	+	166.928i	−0.328288	+	0.0882047i
$154$	−4104.55	−	1904.48i	−2.14776	−	0.996543i
$155$			716.288i			0.371185i
$156$	−1481.40	−	1929.23i	−0.760299	−	0.990142i
$157$	1045.97	+	603.892i	0.531705	+	0.306980i	0.741710	−	0.670720i	$-0.234015\pi$
$157$	1045.97	+	603.892i	0.531705	+	0.306980i	−0.210006	+	0.977700i	$0.567348\pi$
$158$	878.299	+	507.086i	0.442239	+	0.255327i
$159$	615.560	+	801.646i	0.307026	+	0.399841i
$160$		−	1283.40i		−	0.634137i
$161$	1808.69	−	161.709i	0.885371	−	0.0791583i
$162$	1539.60	+	2658.28i	0.746683	+	1.28923i
$163$	1017.79	+	1762.86i	0.489076	+	0.847105i	0.999921	−	0.0125679i	$-0.00400060\pi$
$163$	1017.79	+	1762.86i	0.489076	+	0.847105i	−0.510845	+	0.859673i	$0.670667\pi$
$164$	−2529.20	+	4380.70i	−1.20425	+	2.08582i
$165$	−575.978	+	1391.88i	−0.271757	+	0.656712i
$166$	−2215.58	+	1279.17i	−1.03592	+	0.598088i
$167$	−3172.20			−1.46990			−0.734948	−	0.678124i	$-0.762793\pi$
$167$	−3172.20			−1.46990			−0.734948	+	0.678124i	$0.762793\pi$
$168$	524.263	−	482.567i	0.240760	−	0.221612i
$169$	−104.742			−0.0476752
$170$	434.761	−	251.010i	0.196145	−	0.113244i
$171$	−3509.98	−	937.928i	−1.56968	−	0.419445i
$172$	985.001	−	1706.07i	0.436661	−	0.756318i
$173$	643.213	+	1114.08i	0.282674	+	0.489605i	0.972042	−	0.234805i	$-0.0754453\pi$
$173$	643.213	+	1114.08i	0.282674	+	0.489605i	−0.689369	+	0.724411i	$0.742112\pi$
$174$	165.327	+	1252.48i	0.0720311	+	0.545691i
$175$	−378.767	+	266.291i	−0.163612	+	0.115027i
$176$		−	2716.66i		−	1.16350i
$177$	2015.59	−	1547.71i	0.855940	−	0.657250i
$178$	3189.41	+	1841.41i	1.34302	+	0.775390i
$179$	559.016	+	322.748i	0.233424	+	0.134767i	0.612150	−	0.790741i	$-0.290305\pi$
$179$	559.016	+	322.748i	0.233424	+	0.134767i	−0.378727	+	0.925509i	$0.623638\pi$
$180$	−932.043	−	930.772i	−0.385947	−	0.385420i
$181$		−	1807.48i		−	0.742260i	−0.928581	−	0.371130i	$-0.878970\pi$
$181$		−	1807.48i		−	0.742260i	0.928581	−	0.371130i	$-0.121030\pi$
$182$	−333.429	−	3729.35i	−0.135799	−	1.51889i
$183$	946.276	−	124.908i	0.382245	−	0.0504562i
$184$	−362.995	−	628.726i	−0.145437	−	0.251904i
$185$	−1.89815	+	3.28770i	−0.000754351	+	0.00130657i
$186$	−2898.43	−	1199.41i	−1.14260	−	0.472822i
$187$	1196.38	−	690.727i	0.467848	−	0.270112i
$188$	2743.58			1.06434
$189$	−105.738	+	2596.17i	−0.0406949	+	0.999172i
$190$	2835.13			1.08254
$191$	−2884.10	+	1665.14i	−1.09260	+	0.630812i	−0.934267	−	0.356574i	$-0.883945\pi$
$191$	−2884.10	+	1665.14i	−1.09260	+	0.630812i	−0.158332	+	0.987386i	$0.550612\pi$
$192$	3393.49	+	1404.27i	1.27554	+	0.527836i
$193$	−2263.14	+	3919.88i	−0.844066	+	1.46196i	0.0423643	+	0.999102i	$0.486511\pi$
$193$	−2263.14	+	3919.88i	−0.844066	+	1.46196i	−0.886430	+	0.462863i	$0.846822\pi$
$194$	−2723.70	−	4717.58i	−1.00799	−	1.74589i
$195$	−1235.75	+	163.118i	−0.453813	+	0.0599032i
$196$	3293.61	−	593.688i	1.20029	−	0.216359i
$197$			4938.99i			1.78624i	0.449823	+	0.893118i	$0.351487\pi$
$197$			4938.99i			1.78624i	−0.449823	+	0.893118i	$0.648513\pi$
$198$	−4667.71	−	4661.34i	−1.67535	−	1.67307i
$199$	−1487.84	−	859.007i	−0.530002	−	0.305997i	0.211015	−	0.977483i	$-0.432323\pi$
$199$	−1487.84	−	859.007i	−0.530002	−	0.305997i	−0.741017	+	0.671486i	$0.765656\pi$
$200$	160.308	+	92.5538i	0.0566774	+	0.0327227i
$201$	3728.07	−	2862.67i	1.30825	−	1.00456i
$202$			941.078i			0.327792i
$203$	−449.751	+	969.307i	−0.155499	+	0.335133i
$204$	158.084	+	1197.61i	0.0542555	+	0.411028i
$205$	1296.08	+	2244.87i	0.441571	+	0.764823i
$206$	1752.87	−	3036.06i	0.592855	−	1.02686i
$207$	2557.60	+	683.437i	0.858771	+	0.229479i
$208$	1946.80	−	1123.99i	0.648973	−	0.374685i
$209$	7801.71			2.58208
$210$	−443.298	−	1978.56i	−0.145669	−	0.650160i
$211$	4061.55			1.32516			0.662580	−	0.748991i	$-0.269462\pi$
$211$	4061.55			1.32516			0.662580	+	0.748991i	$0.269462\pi$
$212$	1643.61	−	948.941i	0.532471	−	0.307422i
$213$	1041.11	−	2515.90i	0.334911	−	0.809327i
$214$	1821.30	−	3154.58i	0.581781	−	1.00767i
$215$	−504.761	−	874.271i	−0.160113	−	0.277325i
$216$	959.314	−	398.512i	0.302190	−	0.125534i
$217$	−1525.93	−	2170.45i	−0.477358	−	0.678984i
$218$		−	6857.29i		−	2.13043i
$219$	−405.504	−	528.090i	−0.125121	−	0.162945i
$220$	2449.59	+	1414.27i	0.750689	+	0.433411i
$221$	989.973	+	571.561i	0.301325	+	0.173970i
$222$	−10.1251	−	13.1860i	−0.00306104	−	0.00398641i
$223$		−	1188.19i		−	0.356803i	−0.983958	−	0.178402i	$-0.942907\pi$
$223$		−	1188.19i		−	0.356803i	0.983958	−	0.178402i	$-0.0570926\pi$
$224$	2734.07	+	3888.88i	0.815525	+	1.15999i
$225$	−651.881	+	175.148i	−0.193150	+	0.0518956i
$226$	1594.52	+	2761.78i	0.469317	+	0.812881i
$227$	257.244	−	445.560i	0.0752153	−	0.130277i	−0.825965	−	0.563722i	$-0.809369\pi$
$227$	257.244	−	445.560i	0.0752153	−	0.130277i	0.901180	+	0.433445i	$0.142702\pi$
$228$	−2608.57	+	6303.72i	−0.757704	+	1.83103i
$229$	−2143.89	+	1237.78i	−0.618656	+	0.357181i	−0.776346	−	0.630307i	$-0.782929\pi$
$229$	−2143.89	+	1237.78i	−0.618656	+	0.357181i	0.157689	+	0.987489i	$0.449596\pi$
$230$	−2065.87			−0.592257
$231$	−1219.87	−	5444.60i	−0.347451	−	1.55077i
$232$	427.207			0.120894
$233$	−3117.05	+	1799.63i	−0.876414	+	0.505998i	−0.869474	−	0.493978i	$-0.835542\pi$
$233$	−3117.05	+	1799.63i	−0.876414	+	0.505998i	−0.00693988	+	0.999976i	$0.502209\pi$
$234$	1409.18	−	5273.53i	0.393680	−	1.47325i
$235$	702.969	−	1217.58i	0.195135	−	0.337983i
$236$	−2385.94	−	4132.57i	−0.658099	−	1.13986i
$237$	163.655	+	1239.81i	0.0448546	+	0.339808i
$238$	−782.652	+	1686.78i	−0.213159	+	0.459401i
$239$		−	694.947i		−	0.188085i	−0.995568	−	0.0940427i	$-0.970021\pi$
$239$		−	694.947i		−	0.188085i	0.995568	−	0.0940427i	$-0.0299790\pi$
$240$	965.534	−	741.404i	0.259687	−	0.199406i
$241$	−1672.78	−	965.781i	−0.447109	−	0.258139i	0.259499	−	0.965743i	$-0.416442\pi$
$241$	−1672.78	−	965.781i	−0.447109	−	0.258139i	−0.706609	+	0.707605i	$0.749776\pi$
$242$	7410.36	+	4278.38i	1.96841	+	1.13646i
$243$	−1443.63	+	3502.12i	−0.381106	+	0.924531i
$244$		−	1792.29i		−	0.470244i
$245$	580.426	−	1613.79i	0.151355	−	0.420823i
$246$	−11254.0	+	1485.53i	−2.91679	+	0.385016i
$247$	3227.87	+	5590.83i	0.831515	+	1.44023i
$248$	−530.361	+	918.613i	−0.135798	+	0.235210i
$249$	−2914.94	−	1206.24i	−0.741875	−	0.306998i
$250$	456.170	−	263.370i	0.115403	−	0.0666279i
$251$	−856.279			−0.215330			−0.107665	−	0.994187i	$-0.534337\pi$
$251$	−856.279			−0.215330			−0.107665	+	0.994187i	$0.534337\pi$
$252$	4807.06	+	834.804i	1.20165	+	0.208681i
$253$	−5684.85			−1.41266
$254$	−5194.53	+	2999.06i	−1.28320	+	0.740858i
$255$	571.996	+	236.700i	0.140470	+	0.0581283i
$256$	−878.434	+	1521.49i	−0.214462	+	0.371458i
$257$	2258.12	+	3911.17i	0.548083	+	0.949308i	0.998406	+	0.0564420i	$0.0179756\pi$
$257$	2258.12	+	3911.17i	0.548083	+	0.949308i	−0.450323	+	0.892866i	$0.648691\pi$
$258$	4382.91	−	578.543i	1.05763	−	0.139607i
$259$	−1.25222	−	14.0058i	−0.000300421	−	0.00336016i
$260$			2340.56i			0.558289i
$261$	−1100.79	+	1102.30i	−0.261063	+	0.261420i
$262$	−25.8516	−	14.9254i	−0.00609587	−	0.00351945i
$263$	−3860.66	−	2228.95i	−0.905166	−	0.522598i	−0.0262934	−	0.999654i	$-0.508370\pi$
$263$	−3860.66	−	2228.95i	−0.905166	−	0.522598i	−0.878873	+	0.477056i	$0.841704\pi$
$264$	−1769.26	+	1358.56i	−0.412464	+	0.316718i
$265$		−	972.564i		−	0.225449i
$266$	−8590.83	+	6039.76i	−1.98022	+	1.39219i
$267$	594.289	+	4502.20i	0.136217	+	1.03195i
$268$	−4413.07	−	7643.66i	−1.00586	−	1.74220i
$269$	−2224.18	+	3852.39i	−0.504128	+	0.873175i	0.495861	+	0.868402i	$0.334853\pi$
$269$	−2224.18	+	3852.39i	−0.504128	+	0.873175i	−0.999989	+	0.00477314i	$0.998481\pi$
$270$	382.832	−	2931.09i	0.0862905	−	0.660668i
$271$	231.231	−	133.501i	0.0518312	−	0.0299248i	−0.473860	−	0.880600i	$-0.657140\pi$
$271$	231.231	−	133.501i	0.0518312	−	0.0299248i	0.525692	+	0.850675i	$0.323807\pi$
$272$	−1116.42			−0.248870
$273$	3396.98	−	3126.81i	0.753094	−	0.693199i
$274$	9.77246			0.00215466
$275$	1255.29	−	724.741i	0.275261	−	0.158922i
$276$	1900.78	−	4593.31i	0.414541	−	1.00176i
$277$	1095.20	−	1896.95i	0.237561	−	0.411468i	−0.722453	−	0.691420i	$-0.756985\pi$
$277$	1095.20	−	1896.95i	0.237561	−	0.411468i	0.960014	+	0.279952i	$0.0903187\pi$
$278$	−698.322	−	1209.53i	−0.150657	−	0.260945i
$279$	−1003.65	−	3735.47i	−0.215365	−	0.801566i
$280$	−682.924	+	61.0581i	−0.145759	+	0.0130319i
$281$		−	4484.62i		−	0.952064i	−0.879428	−	0.476032i	$-0.842075\pi$
$281$		−	4484.62i		−	0.952064i	0.879428	−	0.476032i	$-0.157925\pi$
$282$	3749.77	+	4883.34i	0.791828	+	1.03120i
$283$	−4428.40	−	2556.74i	−0.930181	−	0.537040i	−0.0433120	−	0.999062i	$-0.513791\pi$
$283$	−4428.40	−	2556.74i	−0.930181	−	0.537040i	−0.886869	+	0.462022i	$0.847124\pi$
$284$	−4427.79	−	2556.38i	−0.925144	−	0.534132i
$285$	2129.16	+	2772.82i	0.442529	+	0.576308i
$286$			11721.6i			2.42347i
$287$	−8709.61	−	4041.19i	−1.79133	−	0.831164i
$288$	1798.28	+	6693.00i	0.367933	+	1.36941i
$289$	2172.64	+	3763.13i	0.442223	+	0.765953i
$290$	607.827	−	1052.79i	0.123079	−	0.213179i
$291$	2568.42	−	6206.70i	0.517400	−	1.25032i
$292$	−1082.74	+	625.121i	−0.216995	+	0.125282i
$293$	7533.12			1.50201			0.751007	−	0.660295i	$-0.229569\pi$
$293$	7533.12			1.50201			0.751007	+	0.660295i	$0.229569\pi$
$294$	5558.23	+	5050.93i	1.10259	+	1.00196i
$295$	−2445.33			−0.482620
$296$	−4.86862	+	2.81090i	−0.000956023	+	0.000551960i
$297$	1053.48	−	8065.76i	0.205821	−	1.57583i
$298$	3415.93	−	5916.57i	0.664025	−	1.15013i
$299$	−2352.04	−	4073.85i	−0.454923	−	0.787949i
$300$	165.869	+	1256.59i	0.0319215	+	0.241830i
$301$	3391.98	+	1573.85i	0.649536	+	0.301380i
$302$			6770.11i			1.28999i
$303$	−920.395	+	706.743i	−0.174506	+	0.133998i
$304$	−5460.22	−	3152.46i	−1.03015	−	0.594757i
$305$	−795.404	−	459.227i	−0.149327	−	0.0862139i
$306$	−1915.59	+	1918.21i	−0.357866	+	0.358355i
$307$			176.870i			0.0328811i	0.999865	+	0.0164405i	$0.00523342\pi$
$307$			176.870i			0.0328811i	−0.999865	+	0.0164405i	$0.994767\pi$
$308$	−10435.5	+	933.002i	−1.93057	+	0.172606i
$309$	4285.72	−	565.714i	0.789017	−	0.104150i
$310$	1509.19	+	2613.99i	0.276504	+	0.478919i
$311$	−4560.64	+	7899.27i	−0.831545	+	1.44028i	0.0652681	+	0.997868i	$0.479210\pi$
$311$	−4560.64	+	7899.27i	−0.831545	+	1.44028i	−0.896813	+	0.442410i	$0.854124\pi$
$312$	−1705.58	−	705.791i	−0.309485	−	0.128069i
$313$	1906.84	−	1100.92i	0.344348	−	0.198810i	−0.317845	−	0.948143i	$-0.602959\pi$
$313$	1906.84	−	1100.92i	0.344348	−	0.198810i	0.662193	+	0.749333i	$0.269626\pi$
$314$	5089.51			0.914705
$315$	1602.16	−	1919.44i	0.286577	−	0.343328i
$316$	2348.26			0.418038
$317$	4772.59	−	2755.45i	0.845600	−	0.488207i	−0.0135639	−	0.999908i	$-0.504318\pi$
$317$	4772.59	−	2755.45i	0.845600	−	0.488207i	0.859164	+	0.511701i	$0.170984\pi$
$318$	3935.44	+	1628.54i	0.693988	+	0.287182i
$319$	1672.62	−	2897.06i	0.293569	−	0.508477i
$320$	−1766.96	−	3060.47i	−0.308676	−	0.534642i
$321$	4453.03	−	587.798i	0.774279	−	0.102205i
$322$	6259.85	−	4400.97i	1.08338	−	0.761667i
$323$		−	3206.13i		−	0.552303i
$324$	6164.83	+	3548.05i	1.05707	+	0.608377i
$325$	1038.72	+	599.706i	0.177286	+	0.102356i
$326$	7428.56	+	4288.88i	1.26206	+	0.728648i
$327$	6706.58	−	5149.78i	1.13417	−	0.870897i
$328$			3838.62i			0.646197i
$329$	463.751	+	5186.98i	0.0777126	+	0.869202i
$330$	830.678	+	6293.03i	0.138568	+	1.04976i
$331$	−5645.88	−	9778.95i	−0.937540	−	1.62387i	−0.770042	−	0.637994i	$-0.779765\pi$
$331$	−5645.88	−	9778.95i	−0.937540	−	1.62387i	−0.167498	−	0.985872i	$-0.553569\pi$
$332$	−2961.85	+	5130.07i	−0.489616	+	0.848039i
$333$	5.29229	−	19.8051i	0.000870917	−	0.00325920i
$334$	−11576.5	+	6683.71i	−1.89652	+	1.09496i
$335$	−4522.93			−0.737653
$336$	−1346.26	+	4303.45i	−0.218585	+	0.698728i
$337$	−320.299			−0.0517739			−0.0258869	−	0.999665i	$-0.508241\pi$
$337$	−320.299			−0.0517739			−0.0258869	+	0.999665i	$0.508241\pi$
$338$	−382.242	+	220.688i	−0.0615126	+	0.0355143i
$339$	−1503.61	+	3633.55i	−0.240900	+	0.582146i
$340$	581.199	−	1006.67i	0.0927058	−	0.160571i
$341$	4152.98	+	7193.18i	0.659521	+	1.14232i
$342$	−14785.3	+	3972.54i	−2.33772	+	0.628100i
$343$	1679.14	+	6126.51i	0.264330	+	0.964432i
$344$		−	1494.96i		−	0.234311i
$345$	−1551.45	−	2020.46i	−0.242108	−	0.315299i
$346$	4694.63	+	2710.45i	0.729436	+	0.421140i
$347$	−9651.95	−	5572.56i	−1.49321	−	0.862106i	−0.493241	−	0.869893i	$-0.664188\pi$
$347$	−9651.95	−	5572.56i	−1.49321	−	0.862106i	−0.999970	+	0.00778724i	$0.997521\pi$
$348$	1781.55	+	2320.12i	0.274428	+	0.357389i
$349$			3927.05i			0.602322i	0.953573	+	0.301161i	$0.0973742\pi$
$349$			3927.05i			0.602322i	−0.953573	+	0.301161i	$0.902626\pi$
$350$	−821.191	+	1769.84i	−0.125413	+	0.270291i
$351$	6215.91	−	2582.17i	0.945245	−	0.392667i
$352$	−7441.07	−	12888.3i	−1.12673	−	1.95156i
$353$	3705.89	−	6418.79i	0.558767	−	0.967812i	−0.438833	−	0.898569i	$-0.644608\pi$
$353$	3705.89	−	6418.79i	0.558767	−	0.967812i	0.997600	−	0.0692435i	$-0.0220585\pi$
$354$	4094.66	−	9894.94i	0.614771	−	1.48562i
$355$	−2269.01	+	1310.01i	−0.339229	+	0.195854i
$356$	8527.37			1.26952
$357$	−2237.47	+	501.307i	−0.331707	+	0.0743193i
$358$	2720.07			0.401565
$359$	940.710	−	543.119i	0.138297	−	0.0798460i	−0.429255	−	0.903183i	$-0.641224\pi$
$359$	940.710	−	543.119i	0.138297	−	0.0798460i	0.567552	+	0.823337i	$0.307890\pi$
$360$	−965.698	−	258.052i	−0.141380	−	0.0377792i
$361$	5623.75	−	9740.62i	0.819908	−	1.42012i
$362$	−3808.29	−	6596.15i	−0.552926	−	0.957696i
$363$	1380.79	+	10460.5i	0.199649	+	1.51249i
$364$	−4986.16	−	7092.20i	−0.717982	−	1.02124i
$365$			640.683i			0.0918763i
$366$	3190.13	−	2449.60i	0.455603	−	0.349843i
$367$	−7481.40	−	4319.39i	−1.06410	−	0.614360i	−0.137538	−	0.990496i	$-0.543919\pi$
$367$	−7481.40	−	4319.39i	−1.06410	−	0.614360i	−0.926564	+	0.376136i	$0.877252\pi$
$368$	3978.68	+	2297.09i	0.563596	+	0.325392i
$369$	−9904.59	−	9891.07i	−1.39732	−	1.39542i
$370$			15.9973i			0.00224773i
$371$	2071.88	+	2947.00i	0.289937	+	0.412400i
$372$	−7200.61	+	950.479i	−1.00359	+	0.132473i
$373$	2347.14	+	4065.36i	0.325818	+	0.564334i	0.981678	−	0.190549i	$-0.0610269\pi$
$373$	2347.14	+	4065.36i	0.325818	+	0.564334i	−0.655859	+	0.754883i	$0.727694\pi$
$374$	2910.67	−	5041.43i	0.402425	−	0.697021i
$375$	600.162	+	248.355i	0.0826460	+	0.0342000i
$376$	1803.06	−	1041.00i	0.247303	−	0.142780i
$377$	2768.10			0.378155
$378$	5084.14	+	9697.14i	0.691799	+	1.31949i
$379$	−5794.79			−0.785378			−0.392689	−	0.919671i	$-0.628455\pi$
$379$	−5794.79			−0.785378			−0.392689	+	0.919671i	$0.628455\pi$
$380$	5685.11	−	3282.30i	0.767474	−	0.443101i
$381$	−6834.21	−	2828.09i	−0.918969	−	0.380282i
$382$	−7016.76	+	12153.4i	−0.939813	+	1.62780i
$383$	−3919.80	−	6789.30i	−0.522957	−	0.905788i	−0.999643	−	0.0267146i	$-0.991495\pi$
$383$	−3919.80	−	6789.30i	−0.522957	−	0.905788i	0.476686	−	0.879074i	$-0.341838\pi$
$384$	4764.54	−	628.918i	0.633176	−	0.0835790i
$385$	−2259.75	+	4870.23i	−0.299137	+	0.644702i
$386$			19073.4i			2.51505i
$387$	3857.36	+	3852.10i	0.506669	+	0.505978i
$388$	−10923.3	−	6306.57i	−1.42924	−	0.825175i
$389$	−5808.72	−	3353.67i	−0.757105	−	0.437115i	0.0711505	−	0.997466i	$-0.477333\pi$
$389$	−5808.72	−	3353.67i	−0.757105	−	0.437115i	−0.828255	+	0.560351i	$0.810666\pi$
$390$	−4166.00	+	3198.94i	−0.540907	+	0.415346i
$391$			2336.20i			0.302166i
$392$	1939.28	−	1639.87i	0.249868	−	0.211290i
$393$	−4.81698	−	36.4923i	−0.000618281	−	0.00468396i
$394$	10406.3	+	18024.2i	1.33061	+	2.30468i
$395$	601.680	−	1042.14i	0.0766425	−	0.132749i
$396$	−14756.4	−	3943.17i	−1.87257	−	0.500384i
$397$	−4544.79	+	2623.94i	−0.574551	+	0.331717i	−0.758965	−	0.651132i	$-0.774295\pi$
$397$	−4544.79	+	2623.94i	−0.574551	+	0.331717i	0.184414	+	0.982849i	$0.440961\pi$
$398$	−7239.57			−0.911776
$399$	−12358.7	−	3866.20i	−1.55065	−	0.485093i
$400$	−1171.39			−0.146424
$401$	10311.6	−	5953.38i	1.28413	−	0.741390i	0.306526	−	0.951862i	$-0.400833\pi$
$401$	10311.6	−	5953.38i	1.28413	−	0.741390i	0.977600	+	0.210472i	$0.0675001\pi$
$402$	7573.55	−	18301.8i	0.939637	−	2.27068i
$403$	−3436.50	+	5952.19i	−0.424774	+	0.735731i
$404$	1089.51	+	1887.08i	0.134171	+	0.232391i
$405$	3154.17	−	1826.81i	0.386993	−	0.224135i
$406$	400.986	+	4484.96i	0.0490162	+	0.548238i
$407$			44.0214i			0.00536132i
$408$	558.304	+	727.082i	0.0677455	+	0.0882253i
$409$	8219.74	+	4745.67i	0.993740	+	0.573736i	0.906390	−	0.422441i	$-0.138827\pi$
$409$	8219.74	+	4745.67i	0.993740	+	0.573736i	0.0873501	+	0.996178i	$0.472160\pi$
$410$	9459.72	+	5461.57i	1.13947	+	0.657872i
$411$	7.33905	+	9.55768i	0.000880799	+	0.00114707i
$412$		−	8117.35i		−	0.970663i
$413$	7409.69	−	5209.37i	0.882826	−	0.620669i
$414$	10773.6	−	2894.66i	1.27897	−	0.343634i
$415$	1517.79	+	2628.89i	0.179531	+	0.310957i
$416$	6157.32	−	10664.8i	0.725690	−	1.25693i
$417$	658.511	−	1591.32i	0.0773320	−	0.186876i
$418$	28471.2	−	16437.9i	3.33152	−	1.92345i
$419$	6972.32			0.812936			0.406468	−	0.913665i	$-0.366760\pi$
$419$	6972.32			0.812936			0.406468	+	0.913665i	$0.366760\pi$
$420$	−3179.54	−	3454.26i	−0.369395	−	0.401312i
$421$	−11795.0			−1.36545			−0.682723	−	0.730677i	$-0.739205\pi$
$421$	−11795.0			−1.36545			−0.682723	+	0.730677i	$0.739205\pi$
$422$	14822.1	−	8557.52i	1.70978	−	0.987141i
$423$	−1959.97	+	7334.71i	−0.225288	+	0.843088i
$424$	720.116	−	1247.28i	0.0824809	−	0.142861i
$425$	−297.834	−	515.863i	−0.0339931	−	0.0588778i
$426$	−1501.50	−	11375.0i	−0.170770	−	1.29371i
$427$	3388.48	−	302.953i	0.384028	−	0.0343348i
$428$		−	8434.23i		−	0.952532i
$429$	−11464.0	+	8802.84i	−1.29018	+	0.990688i
$430$	−3684.11	−	2127.02i	−0.413171	−	0.238544i
$431$	11447.4	+	6609.16i	1.27936	+	0.738636i	0.976730	−	0.214473i	$-0.0688034\pi$
$431$	11447.4	+	6609.16i	1.27936	+	0.738636i	0.302626	+	0.953109i	$0.402137\pi$
$432$	−3996.46	+	5219.34i	−0.445092	+	0.581286i
$433$			3173.13i			0.352173i	0.984375	+	0.176087i	$0.0563439\pi$
$433$			3173.13i			0.352173i	−0.984375	+	0.176087i	$0.943656\pi$
$434$	−10141.7	−	4705.67i	−1.12170	−	0.520460i
$435$	1486.12	−	196.168i	0.163803	−	0.0216219i
$436$	−7938.85	−	13750.5i	−0.872022	−	1.51039i
$437$	−6596.80	+	11426.0i	−0.722123	+	1.25075i
$438$	−2592.49	−	1072.81i	−0.282818	−	0.117034i
$439$	10432.8	−	6023.36i	1.13423	−	0.654850i	0.189237	−	0.981931i	$-0.439399\pi$
$439$	10432.8	−	6023.36i	1.13423	−	0.654850i	0.944996	+	0.327082i	$0.106065\pi$
$440$	2146.48			0.232567
$441$	−765.726	+	9229.29i	−0.0826829	+	0.996576i
$442$	4817.02			0.518376
$443$	3956.84	−	2284.48i	0.424368	−	0.245009i	−0.272576	−	0.962134i	$-0.587876\pi$
$443$	3956.84	−	2284.48i	0.424368	−	0.245009i	0.696944	+	0.717125i	$0.254542\pi$
$444$	−35.5689	−	14.7189i	−0.00380186	−	0.00157326i
$445$	2184.91	−	3784.38i	0.232752	−	0.403139i
$446$	−2503.47	−	4336.13i	−0.265791	−	0.460363i
$447$	8351.87	−	1102.44i	0.883736	−	0.116653i
$448$	11873.9	+	5509.42i	1.25221	+	0.581017i
$449$		−	6215.10i		−	0.653248i	−0.945154	−	0.326624i	$-0.894089\pi$
$449$		−	6215.10i		−	0.653248i	0.945154	−	0.326624i	$-0.105911\pi$
$450$	−2009.92	+	2012.66i	−0.210552	+	0.210840i
$451$	26031.2	+	15029.1i	2.71788	+	1.56917i
$452$	6394.77	+	3692.02i	0.665452	+	0.384199i
$453$	−6621.31	+	5084.30i	−0.686747	+	0.527332i
$454$		−	2168.01i		−	0.224118i
$455$	−4425.03	+	395.628i	−0.455931	+	0.0407634i
$456$	677.494	+	5132.54i	0.0695758	+	0.527090i
$457$	787.087	+	1363.28i	0.0805654	+	0.139543i	0.903493	−	0.428603i	$-0.140994\pi$
$457$	787.087	+	1363.28i	0.0805654	+	0.139543i	−0.822928	+	0.568146i	$0.807661\pi$
$458$	−5215.89	+	9034.18i	−0.532145	+	0.921702i
$459$	−3314.64	−	432.929i	−0.337068	−	0.0440248i
$460$	−4142.55	+	2391.70i	−0.419886	+	0.242421i
$461$	−10611.4			−1.07206			−0.536032	−	0.844198i	$-0.680077\pi$
$461$	−10611.4			−1.07206			−0.536032	+	0.844198i	$0.680077\pi$
$462$	−15923.3	−	17299.1i	−1.60350	−	1.74205i
$463$	−8273.06			−0.830414			−0.415207	−	0.909727i	$-0.636291\pi$
$463$	−8273.06			−0.830414			−0.415207	+	0.909727i	$0.636291\pi$
$464$	−2341.25	+	1351.72i	−0.234245	+	0.135241i
$465$	−1423.15	+	3439.11i	−0.141929	+	0.342978i
$466$	−7583.49	+	13135.0i	−0.753859	+	1.30572i
$467$	−2740.57	−	4746.80i	−0.271560	−	0.470355i	0.697702	−	0.716388i	$-0.254206\pi$
$467$	−2740.57	−	4746.80i	−0.271560	−	0.470355i	−0.969261	+	0.246033i	$0.920873\pi$
$468$	−3279.55	−	12206.1i	−0.323926	−	1.20562i
$469$	13705.1	−	9635.32i	1.34934	−	0.948652i
$470$		−	5924.51i		−	0.581441i
$471$	3822.18	+	4977.65i	0.373921	+	0.486960i
$472$	−3136.05	−	1810.60i	−0.305823	−	0.176567i
$473$	−10137.9	−	5853.13i	−0.985501	−	0.568979i
$474$	3209.47	+	4179.71i	0.311004	+	0.405022i
$475$		−	3364.01i		−	0.324950i
$476$	383.419	+	4288.48i	0.0369202	+	0.412946i
$477$	1362.74	+	5071.96i	0.130808	+	0.486854i
$478$	−1464.23	−	2536.11i	−0.140109	−	0.242676i
$479$	−5140.25	+	8903.18i	−0.490322	+	0.849262i	−0.999938	−	0.0111398i	$-0.996454\pi$
$479$	−5140.25	+	8903.18i	−0.490322	+	0.849262i	0.509616	+	0.860402i	$0.329787\pi$
$480$	2549.92	−	6162.00i	0.242474	−	0.585949i
$481$	−31.5464	+	18.2133i	−0.00299042	+	0.00172652i
$482$	−8139.44			−0.769173
$483$	9005.35	+	2817.17i	0.848360	+	0.265395i
$484$	19812.7			1.86070
$485$	−5597.62	+	3231.78i	−0.524071	+	0.302573i
$486$	2110.50	+	15822.2i	0.196984	+	1.47677i
$487$	−9139.28	+	15829.7i	−0.850391	+	1.47292i	0.0304657	+	0.999536i	$0.490301\pi$
$487$	−9139.28	+	15829.7i	−0.850391	+	1.47292i	−0.880856	+	0.473384i	$0.843032\pi$
$488$	−680.051	−	1177.88i	−0.0630829	−	0.109263i
$489$	1384.18	+	10486.2i	0.128005	+	0.969741i
$490$	−1282.02	−	7112.25i	−0.118195	−	0.655712i
$491$		−	19670.0i		−	1.80793i	−0.427605	−	0.903966i	$-0.640643\pi$
$491$		−	19670.0i		−	1.80793i	0.427605	−	0.903966i	$-0.359357\pi$
$492$	−20847.2	+	16007.9i	−1.91029	+	1.46685i
$493$	−1190.55	−	687.366i	−0.108762	−	0.0627940i
$494$	23559.3	+	13602.0i	2.14571	+	1.23883i
$495$	−5530.89	+	5538.44i	−0.502212	+	0.502898i
$496$		−	6712.43i		−	0.607656i
$497$	4084.63	−	8803.23i	0.368654	−	0.794525i
$498$	−13179.2	+	1739.65i	−1.18589	+	0.156537i
$499$	−8198.23	−	14199.8i	−0.735477	−	1.27388i	−0.954514	−	0.298167i	$-0.903625\pi$
$499$	−8198.23	−	14199.8i	−0.735477	−	1.27388i	0.219036	−	0.975717i	$-0.429709\pi$
$500$	609.819	−	1056.24i	0.0545439	−	0.0944728i
$501$	−15230.7	−	6302.67i	−1.35820	−	0.562041i
$502$	−3124.87	+	1804.15i	−0.277828	+	0.160404i
$503$	16646.4			1.47560			0.737798	−	0.675022i	$-0.235866\pi$
$503$	16646.4			1.47560			0.737798	+	0.675022i	$0.235866\pi$
$504$	3475.93	−	1275.32i	0.307203	−	0.112713i
$505$	1116.63			0.0983949
$506$	−20746.1	+	11977.7i	−1.82268	+	1.05232i
$507$	−502.899	−	208.107i	−0.0440523	−	0.0182295i
$508$	−6944.18	+	12027.7i	−0.606492	+	1.05048i
$509$	11075.3	+	19183.0i	0.964448	+	1.67047i	0.711091	+	0.703100i	$0.248202\pi$
$509$	11075.3	+	19183.0i	0.964448	+	1.67047i	0.253357	+	0.967373i	$0.418465\pi$
$510$	2586.13	−	341.369i	0.224541	−	0.0296394i
$511$	−1364.86	−	1941.35i	−0.118157	−	0.168063i
$512$			14802.4i			1.27770i
$513$	−14988.9	−	11477.0i	−1.29001	−	0.987766i
$514$	16481.4	+	9515.51i	1.41432	+	0.816559i
$515$	−3602.42	−	2079.86i	−0.308236	−	0.177960i
$516$	8118.98	−	6234.31i	0.692671	−	0.531881i
$517$		−	16303.1i		−	1.38686i
$518$	−34.0795	−	48.4740i	−0.00289067	−	0.00411163i
$519$	874.759	+	6626.98i	0.0739839	+	0.560486i
$520$	888.081	+	1538.20i	0.0748941	+	0.129720i
$521$	1940.15	−	3360.43i	0.163147	−	0.282578i	−0.772849	−	0.634590i	$-0.781169\pi$
$521$	1940.15	−	3360.43i	0.163147	−	0.282578i	0.935996	+	0.352012i	$0.114502\pi$
$522$	−1694.70	+	6342.01i	−0.142098	+	0.531767i
$523$	3636.80	−	2099.70i	0.304065	−	0.175552i	−0.340203	−	0.940352i	$-0.610496\pi$
$523$	3636.80	−	2099.70i	0.304065	−	0.175552i	0.644268	+	0.764800i	$0.277162\pi$
$524$	−69.1181			−0.00576229
$525$	−2347.65	+	525.992i	−0.195162	+	0.0437261i
$526$	−18785.3			−1.55718
$527$	2956.05	−	1706.68i	0.244341	−	0.141070i
$528$	5397.58	−	13043.5i	0.444885	−	1.07509i
$529$	−1276.63	+	2211.19i	−0.104926	+	0.181737i
$530$	−2049.15	−	3549.24i	−0.167942	−	0.290885i
$531$	12752.5	−	3426.36i	1.04221	−	0.280021i
$532$	−10234.3	+	22057.0i	−0.834044	+	1.79754i
$533$			24872.5i			2.02129i
$534$	11654.7	+	15178.0i	0.944475	+	1.22999i
$535$	−3743.04	−	2161.05i	−0.302478	−	0.174636i
$536$	−5800.49	−	3348.91i	−0.467431	−	0.269871i
$537$	2042.75	+	2660.29i	0.164155	+	0.213780i
$538$			18745.0i			1.50215i
$539$	−3527.85	−	19571.5i	−0.281920	−	1.56401i
$540$	−2625.72	−	6320.74i	−0.209246	−	0.503706i
$541$	−6361.95	−	11019.2i	−0.505585	−	0.875699i	−0.999979	−	0.00646086i	$-0.997943\pi$
$541$	−6361.95	−	11019.2i	−0.505585	−	0.875699i	0.494394	−	0.869238i	$-0.335390\pi$
$542$	562.562	−	974.386i	0.0445832	−	0.0772204i
$543$	3591.18	−	8678.26i	0.283817	−	0.685856i
$544$	−5296.49	+	3057.93i	−0.417436	+	0.241007i
$545$	−8136.47			−0.639501
$546$	5808.73	−	18568.2i	0.455295	−	1.45539i
$547$	3657.00			0.285854			0.142927	−	0.989733i	$-0.454349\pi$
$547$	3657.00			0.285854			0.142927	+	0.989733i	$0.454349\pi$
$548$	19.5961	−	11.3138i	0.00152756	−	0.000881938i
$549$	4791.53	+	1280.38i	0.372491	+	0.0995361i
$550$	3054.00	−	5289.68i	0.236769	−	0.410096i
$551$	−3881.87	−	6723.60i	−0.300133	−	0.519846i
$552$	−493.667	−	3739.91i	−0.0380650	−	0.288372i
$553$	396.931	+	4439.60i	0.0305230	+	0.341394i
$554$		−	9230.20i		−	0.707858i
$555$	−15.6457	+	12.0139i	−0.00119662	+	0.000918848i
$556$	−2800.60	−	1616.93i	−0.213619	−	0.123333i
$557$	−3806.68	−	2197.79i	−0.289576	−	0.167187i	0.348174	−	0.937430i	$-0.386802\pi$
$557$	−3806.68	−	2197.79i	−0.289576	−	0.167187i	−0.637751	+	0.770243i	$0.720135\pi$
$558$	−11533.2	−	11517.4i	−0.874978	−	0.873785i
$559$		−	9686.66i		−	0.732919i
$560$	3549.48	−	2495.45i	0.267844	−	0.188307i
$561$	7116.52	−	939.378i	0.535579	−	0.0706962i
$562$	−9448.91	−	16366.0i	−0.709214	−	1.22839i
$563$	4278.35	−	7410.33i	0.320268	−	0.554721i	−0.660275	−	0.751024i	$-0.729560\pi$
$563$	4278.35	−	7410.33i	0.320268	−	0.554721i	0.980543	+	0.196303i	$0.0628936\pi$
$564$	13172.7	+	5451.06i	0.983461	+	0.406970i
$565$	3276.98	−	1891.96i	0.244006	−	0.140877i
$566$	−21547.8			−1.60021
$567$	−5665.86	+	12254.9i	−0.419654	+	0.907684i
$568$	−3879.89			−0.286614
$569$	−15109.4	+	8723.41i	−1.11321	+	0.642714i	−0.939660	−	0.342110i	$-0.888858\pi$
$569$	−15109.4	+	8723.41i	−1.11321	+	0.642714i	−0.173554	+	0.984824i	$0.555525\pi$
$570$	13612.3	+	5632.96i	1.00028	+	0.413928i
$571$	−8895.75	+	15407.9i	−0.651971	+	1.12925i	0.330673	+	0.943745i	$0.392724\pi$
$571$	−8895.75	+	15407.9i	−0.651971	+	1.12925i	−0.982644	+	0.185502i	$0.940609\pi$
$572$	13570.4	+	23504.6i	0.991969	+	1.71814i
$573$	−17155.8	+	2264.56i	−1.25078	+	0.165102i
$574$	−40299.1	+	3603.02i	−2.93041	+	0.261998i
$575$			2451.24i			0.177781i
$576$	13503.1	+	13484.7i	0.976785	+	0.975452i
$577$	−1074.10	−	620.130i	−0.0774960	−	0.0447423i	0.460751	−	0.887529i	$-0.347580\pi$
$577$	−1074.10	−	620.130i	−0.0774960	−	0.0447423i	−0.538247	+	0.842787i	$0.680913\pi$
$578$	15857.5	+	9155.34i	1.14115	+	0.658844i
$579$	−18654.2	+	14324.0i	−1.33893	+	1.02813i
$580$		−	2814.78i		−	0.201513i
$581$	−10199.5	−	4732.49i	−0.728307	−	0.337929i
$582$	−3704.18	−	28062.1i	−0.263820	−	1.99864i
$583$	−5638.85	−	9766.78i	−0.400579	−	0.693823i
$584$	−474.381	+	821.652i	−0.0336131	+	0.0582195i
$585$	−6257.27	−	1672.06i	−0.442233	−	0.118173i
$586$	27491.1	−	15872.0i	1.93796	−	1.11888i
$587$	18161.7			1.27702			0.638512	−	0.769612i	$-0.279550\pi$
$587$	18161.7			1.27702			0.638512	+	0.769612i	$0.279550\pi$
$588$	16993.2	+	3693.41i	1.19181	+	0.259037i
$589$	19276.8			1.34853
$590$	−8923.91	+	5152.22i	−0.622697	+	0.359515i
$591$	−9813.00	+	23713.6i	−0.683000	+	1.65050i
$592$	17.7879	−	30.8095i	0.00123493	−	0.00213896i
$593$	7291.15	+	12628.6i	0.504910	+	0.874530i	0.999984	+	0.00567914i	$0.00180774\pi$
$593$	7291.15	+	12628.6i	0.504910	+	0.874530i	−0.495074	+	0.868851i	$0.664859\pi$
$594$	−13149.7	−	31654.5i	−0.908314	−	2.18653i
$595$	2001.43	+	928.651i	0.137901	+	0.0639848i
$596$		−	15818.8i		−	1.08719i
$597$	−5436.87	−	7080.46i	−0.372724	−	0.485400i
$598$	−17166.9	−	9911.30i	−1.17392	−	0.677765i
$599$	−196.122	−	113.231i	−0.0133778	−	0.00772370i	0.493296	−	0.869861i	$-0.335792\pi$
$599$	−196.122	−	113.231i	−0.0133778	−	0.00772370i	−0.506674	+	0.862138i	$0.669125\pi$
$600$	585.796	+	762.885i	0.0398584	+	0.0519078i
$601$		−	6930.86i		−	0.470409i	−0.971946	−	0.235204i	$-0.924424\pi$
$601$		−	6930.86i		−	0.470409i	0.971946	−	0.235204i	$-0.0755759\pi$
$602$	15694.6	−	1403.20i	1.06256	−	0.0950005i
$603$	23587.3	−	6337.45i	1.59295	−	0.427995i
$604$	7837.91	+	13575.7i	0.528013	+	0.914546i
$605$	5076.48	−	8792.72i	0.341138	−	0.590868i
$606$	−1869.78	+	4518.40i	−0.125337	+	0.302883i
$607$	16733.0	−	9660.77i	1.11890	−	0.645995i	0.177777	−	0.984071i	$-0.443110\pi$
$607$	16733.0	−	9660.77i	1.11890	−	0.645995i	0.941119	+	0.338076i	$0.109776\pi$
$608$	−34539.0			−2.30385
$609$	−4085.25	+	3760.35i	−0.271827	+	0.250208i
$610$	−3870.29			−0.256891
$611$	11683.0	−	6745.20i	0.773559	−	0.446615i
$612$	−1620.46	+	6064.18i	−0.107031	+	0.400539i
$613$	−2191.99	+	3796.64i	−0.144427	+	0.250155i	−0.929159	−	0.369680i	$-0.879467\pi$
$613$	−2191.99	+	3796.64i	−0.144427	+	0.250155i	0.784732	+	0.619835i	$0.212801\pi$
$614$	372.658	+	645.462i	0.0244939	+	0.0424246i
$615$	1762.65	+	13353.4i	0.115572	+	0.875547i
$616$	−6504.12	+	4572.71i	−0.425420	+	0.299090i
$617$		−	15673.4i		−	1.02267i	−0.859381	−	0.511336i	$-0.829151\pi$
$617$		−	15673.4i		−	1.02267i	0.859381	−	0.511336i	$-0.170849\pi$
$618$	14448.2	−	11094.3i	0.940441	−	0.722136i
$619$	−1966.30	−	1135.25i	−0.127678	−	0.0737147i	0.434801	−	0.900527i	$-0.356819\pi$
$619$	−1966.30	−	1135.25i	−0.127678	−	0.0737147i	−0.562478	+	0.826812i	$0.690152\pi$
$620$	6052.56	+	3494.45i	0.392059	+	0.226355i
$621$	10921.9	+	8362.94i	0.705768	+	0.540408i
$622$			38436.4i			2.47775i
$623$	1441.40	+	16121.8i	0.0926939	+	1.03676i
$624$	11580.4	−	1528.60i	0.742925	−	0.0980659i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	4639.17	−	8035.27i	0.296196	−	0.513026i
$627$	37458.3	+	15500.8i	2.38587	+	0.987307i
$628$	10205.7	−	5892.24i	0.648488	−	0.374405i
$629$	18.0907			0.00114678
$630$	1802.68	−	10380.4i	0.114001	−	0.656454i
$631$	2432.81			0.153485			0.0767423	−	0.997051i	$-0.475548\pi$
$631$	2432.81			0.153485			0.0767423	+	0.997051i	$0.475548\pi$
$632$	1543.26	−	891.004i	0.0971326	−	0.0560795i
$633$	19500.7	+	8069.67i	1.22446	+	0.506699i
$634$	11611.3	−	20111.3i	0.727353	−	1.25981i
$635$	3558.52	+	6163.54i	0.222387	+	0.385185i
$636$	9776.87	−	1290.54i	0.609557	−	0.0804613i
$637$	12565.6	−	10625.6i	0.781582	−	0.660912i
$638$		−	14096.5i		−	0.874745i
$639$	9997.40	−	10011.1i	0.618922	−	0.619767i
$640$	−4004.89	−	2312.23i	−0.247355	−	0.142811i
$641$	11020.4	+	6362.62i	0.679063	+	0.392057i	0.799502	−	0.600664i	$-0.205097\pi$
$641$	11020.4	+	6362.62i	0.679063	+	0.392057i	−0.120439	+	0.992721i	$0.538430\pi$
$642$	15012.2	−	11527.4i	0.922874	−	0.708647i
$643$			114.877i			0.00704558i	0.999994	+	0.00352279i	$0.00112134\pi$
$643$			114.877i			0.00704558i	−0.999994	+	0.00352279i	$0.998879\pi$
$644$	7457.37	−	16072.2i	0.456307	−	0.983435i
$645$	−686.467	−	5200.52i	−0.0419063	−	0.317473i
$646$	−6755.19	−	11700.3i	−0.411423	−	0.712606i
$647$	−12704.9	+	22005.6i	−0.771998	+	1.33714i	0.164469	+	0.986382i	$0.447409\pi$
$647$	−12704.9	+	22005.6i	−0.771998	+	1.33714i	−0.936467	+	0.350757i	$0.885924\pi$
$648$	5397.73	−	7.36806i	0.327227	−	0.000446674i
$649$	−24556.8	+	14177.9i	−1.48527	+	0.857519i
$650$	5054.22			0.304989
$651$	−3014.10	−	13452.7i	−0.181462	−	0.809914i
$652$	19861.4			1.19299
$653$	26049.1	−	15039.5i	1.56107	−	0.901287i	0.563926	−	0.825825i	$-0.309290\pi$
$653$	26049.1	−	15039.5i	1.56107	−	0.901287i	0.997149	−	0.0754614i	$-0.0240430\pi$
$654$	13624.4	−	32923.9i	0.814609	−	1.96854i
$655$	−17.7097	+	30.6741i	−0.00105645	+	0.00182982i
$656$	−12145.7	−	21037.0i	−0.722883	−	1.25207i
$657$	−897.713	−	3341.19i	−0.0533077	−	0.198405i
$658$	12621.1	+	17952.1i	0.747756	+	1.06359i
$659$			17922.7i			1.05944i	0.848173	+	0.529720i	$0.177703\pi$
$659$			17922.7i			1.05944i	−0.848173	+	0.529720i	$0.822297\pi$
$660$	8951.29	+	11657.3i	0.527922	+	0.687515i
$661$	−21121.9	−	12194.8i	−1.24289	−	0.717581i	−0.273205	−	0.961956i	$-0.588084\pi$
$661$	−21121.9	−	12194.8i	−1.24289	−	0.717581i	−0.969681	+	0.244375i	$0.921417\pi$
$662$	−41207.7	−	23791.3i	−2.41931	−	1.39679i
$663$	3617.55	+	4711.15i	0.211907	+	0.275967i
$664$			4495.27i			0.262726i
$665$	7166.44	+	10193.4i	0.417899	+	0.594410i
$666$	−22.4152	−	83.4267i	−0.00130416	−	0.00485393i
$667$	2828.59	+	4899.26i	0.164203	+	0.284408i
$668$	−15475.8	+	26804.8i	−0.896371	+	1.55256i
$669$	2360.75	−	5704.85i	0.136430	−	0.329690i
$670$	−16505.8	+	9529.62i	−0.951753	+	0.549495i
$671$	−10650.2			−0.612739
$672$	5400.48	+	24103.8i	0.310012	+	1.38367i
$673$	−10681.1			−0.611780			−0.305890	−	0.952067i	$-0.598954\pi$
$673$	−10681.1			−0.611780			−0.305890	+	0.952067i	$0.598954\pi$
$674$	−1168.89	+	674.857i	−0.0668009	+	0.0385675i
$675$	−3477.86	−	454.248i	−0.198316	−	0.0259022i
$676$	−510.991	+	885.062i	−0.0290732	+	0.0503563i
$677$	−7803.32	−	13515.8i	−0.442993	−	0.767286i	0.554917	−	0.831906i	$-0.312750\pi$
$677$	−7803.32	−	13515.8i	−0.442993	−	0.767286i	−0.997910	+	0.0646196i	$0.979417\pi$
$678$	2168.52	+	16428.2i	0.122834	+	0.930562i
$679$	10076.8	−	21717.5i	0.569529	−	1.22745i
$680$		−	882.101i		−	0.0497456i
$681$	2120.36	−	1628.16i	0.119313	−	0.0916171i
$682$	30311.5	+	17500.3i	1.70188	+	0.982584i
$683$	−10611.4	−	6126.48i	−0.594485	−	0.343226i	0.172384	−	0.985030i	$-0.444853\pi$
$683$	−10611.4	−	6126.48i	−0.594485	−	0.343226i	−0.766869	+	0.641804i	$0.778186\pi$
$684$	−25049.0	+	25083.2i	−1.40025	+	1.40216i
$685$		−	11.5955i		−	0.000646773i
$686$	19036.1	+	18819.9i	1.05948	+	1.04745i
$687$	−12752.7	+	1683.36i	−0.708220	+	0.0934848i
$688$	4730.19	+	8192.92i	0.262117	+	0.454000i
$689$	4666.02	−	8081.78i	0.257999	−	0.446867i
$690$	−9918.84	−	4104.55i	−0.547252	−	0.226460i
$691$	−22287.0	+	12867.4i	−1.22697	+	0.708393i	−0.966395	−	0.257061i	$-0.917246\pi$
$691$	−22287.0	+	12867.4i	−1.22697	+	0.708393i	−0.260577	+	0.965453i	$0.583913\pi$
$692$	12551.8			0.689519
$693$	4960.62	−	28564.8i	0.271917	−	1.56578i
$694$	−46964.6			−2.56881
$695$	−1435.16	+	828.590i	−0.0783291	+	0.0452233i
$696$	2051.15	+	848.793i	0.111708	+	0.0462262i
$697$	6176.26	−	10697.6i	0.335642	−	0.581349i
$698$	8274.14	+	14331.2i	0.448683	+	0.777142i
$699$	−18541.4	+	2447.47i	−1.00329	+	0.132434i
$700$	402.300	+	4499.66i	0.0217222	+	0.242959i
$701$		−	6403.56i		−	0.345020i	−0.985008	−	0.172510i	$-0.944812\pi$
$701$		−	6403.56i		−	0.345020i	0.985008	−	0.172510i	$-0.0551878\pi$
$702$	17243.6	−	22520.0i	0.927089	−	1.21077i
$703$	88.4787	+	51.0832i	0.00474685	+	0.00274060i
$704$	−35488.8	−	20489.4i	−1.89990	−	1.09691i
$705$	5794.30	−	4449.27i	0.309540	−	0.237687i
$706$		−	31232.6i		−	1.66495i
$707$	−3383.54	+	2378.79i	−0.179987	+	0.126540i
$708$	−3244.84	−	24582.2i	−0.172244	−	1.30488i
$709$	13148.4	+	22773.7i	0.696472	+	1.20632i	0.969682	+	0.244370i	$0.0785811\pi$
$709$	13148.4	+	22773.7i	0.696472	+	1.20632i	−0.273210	+	0.961954i	$0.588086\pi$
$710$	−5520.28	+	9561.40i	−0.291792	+	0.505399i
$711$	−1677.56	+	6277.87i	−0.0884858	+	0.331137i
$712$	5604.14	−	3235.55i	0.294978	−	0.170305i
$713$	−14046.4			−0.737784
$714$	−7109.10	+	6543.71i	−0.372621	+	0.342986i
$715$	13908.2			0.727465
$716$	5454.38	−	3149.09i	0.284692	−	0.164367i
$717$	1380.75	−	3336.65i	0.0719179	−	0.173793i
$718$	2288.66	−	3964.07i	0.118958	−	0.206042i
$719$	−2265.71	−	3924.32i	−0.117520	−	0.203550i	0.801265	−	0.598310i	$-0.204161\pi$
$719$	−2265.71	−	3924.32i	−0.117520	−	0.203550i	−0.918784	+	0.394760i	$0.870828\pi$
$720$	6108.87	−	1641.34i	0.316200	−	0.0849569i
$721$	15346.6	−	1372.09i	0.792700	−	0.0708728i
$722$		−	47396.0i		−	2.44307i
$723$	−6112.67	−	7960.56i	−0.314429	−	0.409483i
$724$	−15273.0	−	8817.89i	−0.784003	−	0.452644i
$725$	−1249.18	−	721.214i	−0.0639908	−	0.0369451i
$726$	27078.9	+	35265.0i	1.38429	+	1.80276i
$727$			6125.91i			0.312513i	0.987716	+	0.156257i	$0.0499427\pi$
$727$			6125.91i			0.312513i	−0.987716	+	0.156257i	$0.950057\pi$
$728$	−5967.88	−	2769.05i	−0.303825	−	0.140972i
$729$	−13889.5	+	13946.5i	−0.705657	+	0.708553i
$730$	1349.89	+	2338.08i	0.0684408	+	0.118543i
$731$	−2405.36	+	4166.20i	−0.121704	+	0.210797i
$732$	3561.00	−	8605.31i	0.179806	−	0.434510i
$733$	−5841.32	+	3372.49i	−0.294344	+	0.169939i	−0.639899	−	0.768459i	$-0.721024\pi$
$733$	−5841.32	+	3372.49i	−0.294344	+	0.169939i	0.345555	+	0.938398i	$0.387691\pi$
$734$	−36403.1			−1.83060
$735$	5993.15	−	6595.09i	0.300763	−	0.330971i
$736$	25167.5			1.26044
$737$	−45420.6	+	26223.6i	−2.27013	+	1.31066i
$738$	−56985.5	−	15227.5i	−2.84236	−	0.759530i
$739$	431.566	−	747.493i	0.0214823	−	0.0372084i	−0.855084	−	0.518489i	$-0.826495\pi$
$739$	431.566	−	747.493i	0.0214823	−	0.0372084i	0.876567	+	0.481280i	$0.159828\pi$
$740$	18.5205	+	32.0784i	0.000920035	+	0.00159355i
$741$	4389.85	+	33256.5i	0.217632	+	1.64873i
$742$	13770.2	+	6389.29i	0.681296	+	0.316116i
$743$			5381.32i			0.265708i	0.991136	+	0.132854i	$0.0424142\pi$
$743$			5381.32i			0.265708i	−0.991136	+	0.132854i	$0.957586\pi$
$744$	−4371.56	+	3356.79i	−0.215416	+	0.165411i
$745$	−7020.27	−	4053.15i	−0.345238	−	0.199324i
$746$	17131.1	+	9890.65i	0.840770	+	0.485419i
$747$	−11598.9	−	11583.1i	−0.568114	−	0.567339i
$748$		−	13479.0i		−	0.658879i
$749$	15945.7	−	1425.65i	0.777893	−	0.0695489i
$750$	2713.48	−	358.179i	0.132110	−	0.0174385i
$751$	4598.53	+	7964.88i	0.223439	+	0.387008i	0.955850	−	0.293855i	$-0.0949384\pi$
$751$	4598.53	+	7964.88i	0.223439	+	0.387008i	−0.732411	+	0.680863i	$0.761605\pi$
$752$	−6587.63	+	11410.1i	−0.319450	+	0.553303i
$753$	−4111.25	−	1701.29i	−0.198967	−	0.0823354i
$754$	10101.8	−	5832.28i	0.487913	−	0.281697i
$755$	8033.03			0.387221
$756$	21421.5	+	13559.0i	1.03055	+	0.652298i
$757$	−14977.7			−0.719120			−0.359560	−	0.933122i	$-0.617073\pi$
$757$	−14977.7			−0.719120			−0.359560	+	0.933122i	$0.617073\pi$
$758$	−21147.3	+	12209.4i	−1.01333	+	0.585046i
$759$	−27294.6	−	11294.9i	−1.30531	−	0.540157i
$760$	2490.82	−	4314.22i	0.118883	−	0.205912i
$761$	8289.68	+	14358.2i	0.394876	+	0.683946i	0.993085	−	0.117394i	$-0.0374542\pi$
$761$	8289.68	+	14358.2i	0.394876	+	0.683946i	−0.598209	+	0.801340i	$0.704121\pi$
$762$	−30899.2	+	4078.68i	−1.46897	+	0.193904i
$763$	24654.6	−	17333.4i	1.16980	−	0.822424i
$764$			32493.9i			1.53873i
$765$	2276.04	+	2272.93i	0.107569	+	0.107422i
$766$	−28609.5	−	16517.7i	−1.34948	−	0.779125i
$767$	−20320.2	−	11731.9i	−0.956609	−	0.552298i
$768$	−7240.59	+	5559.83i	−0.340198	+	0.261228i
$769$			14006.6i			0.656813i	0.944536	+	0.328406i	$0.106512\pi$
$769$			14006.6i			0.656813i	−0.944536	+	0.328406i	$0.893488\pi$
$770$	2014.73	+	22534.4i	0.0942934	+	1.05466i
$771$	3071.00	+	23265.2i	0.143449	+	1.08674i
$772$	22081.7	+	38246.7i	1.02945	+	1.78307i
$773$	4386.23	−	7597.17i	0.204090	−	0.353495i	−0.745752	−	0.666223i	$-0.767910\pi$
$773$	4386.23	−	7597.17i	0.204090	−	0.353495i	0.949842	+	0.312729i	$0.101243\pi$
$774$	22193.1	+	5930.40i	1.03064	+	0.275405i
$775$	3101.62	−	1790.72i	0.143759	−	0.0829994i
$776$	−9571.65			−0.442786
$777$	21.8151	−	69.7342i	0.00100722	−	0.00321969i
$778$	−28264.1			−1.30247
$779$	60414.2	−	34880.2i	2.77864	−	1.60425i
$780$	−4650.32	+	11237.7i	−0.213472	+	0.515865i
$781$	−15190.7	+	26311.0i	−0.695987	+	1.20548i
$782$	4922.28	+	8525.64i	0.225090	+	0.389867i
$783$	−7475.33	+	3105.35i	−0.341183	+	0.141732i
$784$	−5439.25	+	15123.1i	−0.247779	+	0.688917i
$785$		−	6038.92i		−	0.274571i
$786$	−94.4667	−	123.025i	−0.00428692	−	0.00558287i
$787$	17834.6	+	10296.8i	0.807795	+	0.466381i	0.846189	−	0.532882i	$-0.178891\pi$
$787$	17834.6	+	10296.8i	0.807795	+	0.466381i	−0.0383947	+	0.999263i	$0.512224\pi$
$788$	41734.0	+	24095.1i	1.88669	+	1.08928i
$789$	−14107.6	−	18372.4i	−0.636558	−	0.828992i
$790$		−	5070.86i		−	0.228371i
$791$	−5899.17	+	12713.9i	−0.265171	+	0.571499i
$792$	−11194.0	+	3007.61i	−0.502224	+	0.134938i
$793$	−4406.41	−	7632.13i	−0.197322	−	0.341772i
$794$	−11057.1	+	19151.4i	−0.494207	+	0.855991i
$795$	1932.33	−	4669.57i	0.0862047	−	0.208318i
$796$	−14517.1	+	8381.43i	−0.646411	+	0.373206i
$797$	19451.5			0.864501			0.432251	−	0.901754i	$-0.357720\pi$
$797$	19451.5			0.864501			0.432251	+	0.901754i	$0.357720\pi$
$798$	−53247.2	+	11930.1i	−2.36207	+	0.529223i
$799$	−6699.78			−0.296647
$800$	−5557.30	+	3208.51i	−0.245600	+	0.141797i
$801$	−6091.81	+	22797.2i	−0.268719	+	1.00562i
$802$	25087.0	−	43452.0i	1.10456	−	1.91315i
$803$	3714.63	+	6433.93i	0.163246	+	0.282750i
$804$	−6001.70	−	45467.5i	−0.263263	−	1.99442i
$805$	−5221.95	−	7427.59i	−0.228633	−	0.325203i
$806$			28962.2i			1.26570i
$807$	−18333.0	+	14077.4i	−0.799694	+	0.614060i
$808$	1432.04	+	826.788i	0.0623502	+	0.0359979i
$809$	−953.045	−	550.241i	−0.0414181	−	0.0239128i	0.479148	−	0.877734i	$-0.340946\pi$
$809$	−953.045	−	550.241i	−0.0414181	−	0.0239128i	−0.520566	+	0.853821i	$0.674279\pi$
$810$	7661.70	−	13312.4i	0.332352	−	0.577469i
$811$			23525.7i			1.01862i	0.860583	+	0.509310i	$0.170099\pi$
$811$			23525.7i			1.01862i	−0.860583	+	0.509310i	$0.829901\pi$
$812$	5996.41	+	8529.17i	0.259154	+	0.368615i
$813$	1375.45	−	181.559i	0.0593348	−	0.00783218i
$814$	92.7512	+	160.650i	0.00399377	+	0.00691741i
$815$	5088.95	−	8814.32i	0.218722	−	0.378837i
$816$	−5360.25	−	2218.15i	−0.229959	−	0.0951601i
$817$	−23528.5	+	13584.2i	−1.00754	+	0.581701i
$818$	39995.7			1.70956
$819$	22522.4	−	8263.50i	0.960923	−	0.352564i
$820$	25292.0			1.07711
$821$	−14795.9	+	8542.41i	−0.628965	+	0.363133i	−0.780351	−	0.625342i	$-0.784960\pi$
$821$	−14795.9	+	8542.41i	−0.628965	+	0.363133i	0.151386	+	0.988475i	$0.451626\pi$
$822$	46.9205	+	19.4163i	0.00199092	+	0.000823872i
$823$	12590.3	−	21807.1i	0.533257	−	0.923629i	−0.465988	−	0.884791i	$-0.654301\pi$
$823$	12590.3	−	21807.1i	0.533257	−	0.923629i	0.999246	−	0.0388377i	$-0.0123655\pi$
$824$	−3079.98	−	5334.68i	−0.130214	−	0.225537i
$825$	7466.95	−	985.636i	0.315110	−	0.0415945i
$826$	16064.7	−	34622.8i	0.676710	−	1.45845i
$827$		−	36551.0i		−	1.53688i	−0.639919	−	0.768442i	$-0.721032\pi$
$827$		−	36551.0i		−	1.53688i	0.639919	−	0.768442i	$-0.278968\pi$
$828$	18252.4	−	18277.3i	0.766080	−	0.767126i
$829$	38029.3	+	21956.2i	1.59326	+	0.919870i	0.992743	+	0.120258i	$0.0383723\pi$
$829$	38029.3	+	21956.2i	1.59326	+	0.919870i	0.600518	+	0.799611i	$0.294961\pi$
$830$	11077.9	+	6395.84i	0.463277	+	0.267473i
$831$	9027.34	−	6931.82i	0.376841	−	0.289365i
$832$		−	33909.1i		−	1.41296i
$833$	−8042.94	+	1449.78i	−0.334540	+	0.0603023i
$834$	−949.707	−	7194.77i	−0.0394312	−	0.298722i
$835$	7930.51	+	13736.1i	0.328679	+	0.569288i
$836$	38061.1	−	65923.7i	1.57460	−	2.72729i
$837$	2602.98	−	19929.2i	0.107493	−	0.823004i
$838$	25444.5	−	14690.4i	1.04889	−	0.605574i
$839$	−35210.1			−1.44885			−0.724427	−	0.689352i	$-0.757895\pi$
$839$	−35210.1			−1.44885			−0.724427	+	0.689352i	$0.757895\pi$
$840$	−3400.23	−	1063.71i	−0.139666	−	0.0436920i
$841$	21060.0			0.863506
$842$	−43044.2	+	24851.6i	−1.76176	+	1.01715i
$843$	8910.23	−	21532.0i	0.364039	−	0.879717i
$844$	19814.5	−	34319.7i	0.808108	−	1.39968i
$845$	261.856	+	453.548i	0.0106605	+	0.0184645i
$846$	8301.32	+	30896.6i	0.337358	+	1.25561i
$847$	3348.97	+	37457.7i	0.135858	+	1.51955i
$848$			9114.04i			0.369077i
$849$	−16182.2	−	21074.2i	−0.654149	−	0.851902i
$850$	−2173.81	−	1255.05i	−0.0877188	−	0.0506445i
$851$	−64.4715	−	37.2226i	−0.00259701	−	0.00149938i
$852$	−16180.0	−	21071.3i	−0.650607	−	0.847289i
$853$		−	1117.20i		−	0.0448445i	−0.999749	−	0.0224223i	$-0.992862\pi$
$853$		−	1117.20i		−	0.0448445i	0.999749	−	0.0224223i	$-0.00713782\pi$
$854$	11727.5	−	8244.98i	0.469914	−	0.330372i
$855$	4713.59	+	17543.5i	0.188540	+	0.701724i
$856$	−3200.21	−	5542.93i	−0.127781	−	0.221324i
$857$	8656.41	−	14993.3i	0.345038	−	0.597623i	−0.640323	−	0.768106i	$-0.721199\pi$
$857$	8656.41	−	14993.3i	0.345038	−	0.597623i	0.985361	+	0.170483i	$0.0545328\pi$
$858$	−23289.0	+	56278.9i	−0.926658	+	2.23931i
$859$	−9058.20	+	5229.75i	−0.359792	+	0.207726i	−0.668990	−	0.743272i	$-0.733273\pi$
$859$	−9058.20	+	5229.75i	−0.359792	+	0.207726i	0.309197	+	0.950998i	$0.399940\pi$
$860$	−9850.01			−0.390561
$861$	−33788.2	−	36707.6i	−1.33740	−	1.45295i
$862$	55701.0			2.20091
$863$	−18215.6	+	10516.8i	−0.718501	+	0.414827i	−0.814201	−	0.580584i	$-0.802824\pi$
$863$	−18215.6	+	10516.8i	−0.718501	+	0.414827i	0.0957000	+	0.995410i	$0.469491\pi$
$864$	−4663.86	+	35708.0i	−0.183643	+	1.40603i
$865$	3216.06	−	5570.38i	0.126416	−	0.218958i
$866$	6685.66	+	11579.9i	0.262342	+	0.454390i
$867$	2954.76	+	22384.6i	0.115743	+	0.876841i
$868$	−25784.4	+	2305.30i	−1.00827	+	0.0901463i
$869$		−	13954.0i		−	0.544714i
$870$	5010.08	−	3847.09i	0.195239	−	0.149918i
$871$	−37584.5	−	21699.4i	−1.46211	−	0.844152i
$872$	−10434.7	−	6024.49i	−0.405235	−	0.233962i
$873$	24663.5	−	24697.2i	0.956166	−	0.957472i
$874$			55596.8i			2.15170i
$875$	2099.99	+	974.380i	0.0811344	+	0.0376458i
$876$	−6440.58	+	850.154i	−0.248410	+	0.0327900i
$877$	5290.02	+	9162.59i	0.203685	+	0.352792i	0.949713	−	0.313122i	$-0.101375\pi$
$877$	5290.02	+	9162.59i	0.203685	+	0.352792i	−0.746028	+	0.665914i	$0.768042\pi$
$878$	25381.9	−	43962.8i	0.975625	−	1.68983i
$879$	36168.8	+	14967.1i	1.38788	+	0.574322i
$880$	−11763.5	+	6791.65i	−0.450621	+	0.260166i
$881$	−15511.1			−0.593168			−0.296584	−	0.955007i	$-0.595847\pi$
$881$	−15511.1			−0.593168			−0.296584	+	0.955007i	$0.595847\pi$
$882$	16651.3	+	35294.4i	0.635691	+	1.34742i
$883$	−35432.9			−1.35041			−0.675205	−	0.737630i	$-0.735945\pi$
$883$	−35432.9			−1.35041			−0.675205	+	0.737630i	$0.735945\pi$
$884$	9659.27	−	5576.78i	0.367507	−	0.212180i
$885$	−11740.8	−	4858.50i	−0.445946	−	0.184539i
$886$	9626.62	−	16673.8i	0.365025	−	0.632242i
$887$	13040.3	+	22586.4i	0.493630	+	0.854991i	0.999973	−	0.00734044i	$-0.00233655\pi$
$887$	13040.3	+	22586.4i	0.493630	+	0.854991i	−0.506344	+	0.862332i	$0.669003\pi$
$888$	−28.9605	+	3.82278i	−0.00109443	+	0.000144464i
$889$	−23913.2	−	11095.5i	−0.902161	−	0.418596i
$890$		−	18414.1i		−	0.693530i
$891$	21083.4	−	36633.0i	0.792730	−	1.37739i
$892$	−10040.1	−	5796.65i	−0.376869	−	0.217585i
$893$	−32767.6	−	18918.4i	−1.22791	−	0.708935i
$894$	28156.2	−	21620.3i	1.05334	−	0.808826i
$895$		−	3227.48i		−	0.120539i
$896$	17061.2	−	1525.38i	0.636131	−	0.0568745i
$897$	−3198.74	−	24232.9i	−0.119067	−	0.902021i
$898$	−13095.0	−	22681.1i	−0.486620	−	0.842850i
$899$	4132.77	−	7158.17i	0.153321	−	0.265560i
$900$	−1700.25	+	6362.79i	−0.0629723	+	0.235659i
$901$	−4013.68	+	2317.30i	−0.148407	+	0.0856831i
$902$	126663.			4.67563
$903$	13158.9	+	14295.9i	0.484940	+	0.526840i
$904$	5603.47			0.206160
$905$	−7826.62	+	4518.70i	−0.287476	+	0.165974i
$906$	−13451.1	+	32505.3i	−0.493250	+	1.19196i
$907$	−13467.2	+	23325.8i	−0.493021	+	0.853938i	−0.999968	−	0.00803986i	$-0.997441\pi$
$907$	−13467.2	+	23325.8i	−0.493021	+	0.853938i	0.506947	+	0.861977i	$0.330774\pi$
$908$	−2509.96	−	4347.37i	−0.0917355	−	0.158891i
$909$	−5823.28	+	1564.60i	−0.212482	+	0.0570898i
$910$	−15315.0	+	10767.2i	−0.557897	+	0.392228i
$911$		−	17794.2i		−	0.647146i	−0.946203	−	0.323573i	$-0.895116\pi$
$911$		−	17794.2i		−	0.647146i	0.946203	−	0.323573i	$-0.104884\pi$
$912$	−19952.7	−	25984.5i	−0.724452	−	0.943457i
$913$	30484.2	+	17600.1i	1.10502	+	0.637981i
$914$	5744.73	+	3316.72i	0.207898	+	0.120030i
$915$	−2906.56	−	3785.23i	−0.105014	−	0.136760i
$916$			24154.2i			0.871265i
$917$	−11.6831	−	130.674i	−0.000420732	−	0.00470582i
$918$	−13008.5	+	5403.90i	−0.467695	+	0.194287i
$919$	6772.91	+	11731.0i	0.243109	+	0.421078i	0.961598	−	0.274460i	$-0.0884993\pi$
$919$	6772.91	+	11731.0i	0.243109	+	0.421078i	−0.718489	+	0.695538i	$0.755166\pi$
$920$	−1814.97	+	3143.63i	−0.0650412	+	0.112655i
$921$	−351.413	+	849.205i	−0.0125727	+	0.0303825i
$922$	−38724.7	+	22357.7i	−1.38322	+	0.798604i
$923$	−25139.9			−0.896522
$924$	−51957.5	−	16254.0i	−1.84987	−	0.578699i
$925$	18.9815			0.000674712
$926$	−30191.4	+	17431.0i	−1.07144	+	0.618594i
$927$	21701.0	+	5798.90i	0.768884	+	0.205459i
$928$	−7404.86	+	12825.6i	−0.261936	+	0.453686i
$929$	1592.82	+	2758.85i	0.0562528	+	0.0974327i	0.892780	−	0.450492i	$-0.148751\pi$
$929$	1592.82	+	2758.85i	0.0562528	+	0.0974327i	−0.836528	+	0.547925i	$0.815418\pi$
$930$	2052.47	+	15549.1i	0.0723691	+	0.548252i
$931$	−43430.5	−	15620.5i	−1.52887	−	0.549882i
$932$			35118.3i			1.23427i
$933$	−37591.6	+	28865.4i	−1.31907	+	1.01287i
$934$	−20002.6	−	11548.5i	−0.700756	−	0.404582i
$935$	−5981.88	−	3453.64i	−0.209228	−	0.120798i
$936$	−6786.68	−	6777.43i	−0.236998	−	0.236674i
$937$		−	40146.1i		−	1.39970i	−0.714291	−	0.699849i	$-0.753251\pi$
$937$		−	40146.1i		−	1.39970i	0.714291	−	0.699849i	$-0.246749\pi$
$938$	29713.5	−	64038.8i	1.03431	−	2.22915i
$939$	11342.7	−	1497.23i	0.394200	−	0.0520343i
$940$	−6858.95	−	11880.0i	−0.237994	−	0.412217i
$941$	17633.0	−	30541.3i	0.610861	−	1.05804i	−0.380234	−	0.924890i	$-0.624157\pi$
$941$	17633.0	−	30541.3i	0.610861	−	1.05804i	0.991096	−	0.133153i	$-0.0425101\pi$
$942$	24436.2	+	10112.0i	0.845197	+	0.349754i
$943$	−44021.8	+	25416.0i	−1.52020	+	0.877688i
$944$	22915.6			0.790083
$945$	11506.1	−	6032.56i	0.396077	−	0.207660i
$946$	−49329.2			−1.69538
$947$	47225.1	−	27265.4i	1.62050	−	0.935594i	0.633710	−	0.773571i	$-0.281531\pi$
$947$	47225.1	−	27265.4i	1.62050	−	0.935594i	0.986787	−	0.162024i	$-0.0518021\pi$
$948$	11274.7	+	4665.63i	0.386272	+	0.159845i
$949$	−3073.77	+	5323.93i	−0.105141	+	0.182110i
$950$	−7087.83	−	12276.5i	−0.242063	−	0.419265i
$951$	28389.3	−	3747.37i	0.968018	−	0.127778i
$952$	1879.16	+	2672.88i	0.0639749	+	0.0909965i
$953$			55150.2i			1.87460i	0.348530	+	0.937298i	$0.386681\pi$
$953$			55150.2i			1.87460i	−0.348530	+	0.937298i	$0.613319\pi$
$954$	15659.5	+	15638.2i	0.531443	+	0.530718i
$955$	14420.5	+	8325.69i	0.488625	+	0.282108i
$956$	−5872.24	−	3390.34i	−0.198663	−	0.114698i
$957$	13786.7	−	10586.4i	0.465686	−	0.357586i
$958$			43321.2i			1.46101i
$959$	24.7021	+	35.1358i	0.000831776	+	0.00118310i
$960$	−2403.04	−	18204.9i	−0.0807894	−	0.612043i
$961$	−4634.14	−	8026.57i	−0.155555	−	0.269429i
$962$	−76.7495	+	132.934i	−0.00257225	+	0.00445526i
$963$	22548.2	+	6025.27i	0.754522	+	0.201622i
$964$	−16321.5	+	9423.23i	−0.545312	+	0.314836i
$965$	22631.4			0.754955
$966$	38799.4	−	8693.04i	1.29229	−	0.289538i
$967$	−10213.0			−0.339637			−0.169819	−	0.985475i	$-0.554318\pi$
$967$	−10213.0			−0.339637			−0.169819	+	0.985475i	$0.554318\pi$
$968$	13020.8	−	7517.56i	0.432339	−	0.249611i
$969$	6370.08	−	15393.6i	0.211183	−	0.510334i
$970$	−13618.5	+	23587.9i	−0.450787	+	0.780785i
$971$	−26921.2	−	46628.9i	−0.889744	−	1.54108i	−0.840177	−	0.542312i	$-0.817549\pi$
$971$	−26921.2	−	46628.9i	−0.889744	−	1.54108i	−0.0495672	−	0.998771i	$-0.515784\pi$
$972$	22549.7	+	29283.8i	0.744119	+	0.966336i
$973$	2583.56	−	5568.10i	0.0851234	−	0.183458i
$974$			77024.3i			2.53390i
$975$	3795.69	+	4943.14i	0.124676	+	0.162366i
$976$	7453.84	+	4303.48i	0.244459	+	0.141138i
$977$	20488.2	+	11828.9i	0.670906	+	0.387348i	0.796420	−	0.604744i	$-0.206725\pi$
$977$	20488.2	+	11828.9i	0.670906	+	0.387348i	−0.125514	+	0.992092i	$0.540058\pi$
$978$	27145.4	+	35351.6i	0.887540	+	1.15585i
$979$		−	50671.8i		−	1.65422i
$980$	−10804.8	−	12777.5i	−0.352189	−	0.416493i
$981$	42432.1	−	11400.7i	1.38099	−	0.371046i
$982$	−41443.9	−	71782.9i	−1.34677	−	2.33267i
$983$	130.336	−	225.748i	0.00422896	−	0.00732477i	−0.863903	−	0.503658i	$-0.831987\pi$
$983$	130.336	−	225.748i	0.00422896	−	0.00732477i	0.868132	+	0.496333i	$0.165321\pi$
$984$	−7626.74	+	18430.4i	−0.247085	+	0.597092i
$985$	21386.5	−	12347.5i	0.691806	−	0.399414i
$986$	−5793.01			−0.187107
$987$	−8079.11	+	25825.6i	−0.260548	+	0.832866i
$988$	62989.3			2.02830
$989$	17144.4	−	9898.33i	0.551224	−	0.318249i
$990$	−8514.93	+	31865.1i	−0.273356	+	1.02297i
$991$	25256.8	−	43746.0i	0.809594	−	1.40226i	−0.103551	−	0.994624i	$-0.533020\pi$
$991$	25256.8	−	43746.0i	0.809594	−	1.40226i	0.913145	−	0.407635i	$-0.133646\pi$
$992$	−18385.7	−	31845.0i	−0.588455	−	1.01923i
$993$	−7678.31	−	58169.1i	−0.245381	−	1.85895i
$994$	−3641.75	−	40732.3i	−0.116206	−	1.29975i
$995$			8590.07i			0.273692i
$996$	−24413.3	+	18746.3i	−0.776673	+	0.596383i
$997$	−38905.8	−	22462.3i	−1.23587	−	0.713529i	−0.267621	−	0.963524i	$-0.586237\pi$
$997$	−38905.8	−	22462.3i	−1.23587	−	0.713529i	−0.968247	+	0.249996i	$0.919571\pi$
$998$	−59836.6	−	34546.7i	−1.89789	−	1.09575i
$999$	64.7595	−	84.5754i	0.00205095	−	0.00267853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.s.a.101.14	yes	32
3.2	odd	2		105.4.s.b.101.3	yes	32
7.5	odd	6		105.4.s.b.26.3	yes	32
21.5	even	6	inner	105.4.s.a.26.14	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.s.a.26.14	✓	32	21.5	even	6	inner
105.4.s.a.101.14	yes	32	1.1	even	1	trivial
105.4.s.b.26.3	yes	32	7.5	odd	6
105.4.s.b.101.3	yes	32	3.2	odd	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.64936 - 2.10696i) q^{2} +(4.80130 + 1.98684i) q^{3} +(4.87855 - 8.44990i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(21.7079 - 2.86543i) q^{6} +(16.7999 + 7.79504i) q^{7} -7.40430i q^{8} +(19.1049 + 19.0788i) q^{9} +O(q^{10})\)	\(q+(3.64936 - 2.10696i) q^{2} +(4.80130 + 1.98684i) q^{3} +(4.87855 - 8.44990i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(21.7079 - 2.86543i) q^{6} +(16.7999 + 7.79504i) q^{7} -7.40430i q^{8} +(19.1049 + 19.0788i) q^{9} +(-18.2468 - 10.5348i) q^{10} +(-50.2115 - 28.9896i) q^{11} +(40.2120 - 30.8776i) q^{12} -47.9765i q^{13} +(77.7328 - 6.94984i) q^{14} +(-3.39996 - 25.7573i) q^{15} +(23.4279 + 40.5782i) q^{16} +(-11.9134 + 20.6345i) q^{17} +(109.919 + 29.3723i) q^{18} +(-116.533 + 67.2802i) q^{19} -48.7855 q^{20} +(65.1739 + 70.8051i) q^{21} -244.320 q^{22} +(84.9135 - 49.0248i) q^{23} +(14.7112 - 35.5503i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-101.084 - 175.083i) q^{26} +(53.8217 + 129.562i) q^{27} +(147.827 - 103.929i) q^{28} +57.6971i q^{29} +(-66.6773 - 86.8342i) q^{30} +(-124.065 - 71.6288i) q^{31} +(222.292 + 128.340i) q^{32} +(-183.482 - 238.950i) q^{33} +100.404i q^{34} +(-8.24630 - 92.2334i) q^{35} +(254.419 - 68.3574i) q^{36} +(-0.379630 - 0.657539i) q^{37} +(-283.513 + 491.059i) q^{38} +(95.3217 - 230.349i) q^{39} +(-32.0616 + 18.5108i) q^{40} -518.431 q^{41} +(387.026 + 121.075i) q^{42} +201.904 q^{43} +(-489.919 + 282.855i) q^{44} +(34.8516 - 130.424i) q^{45} +(206.587 - 357.819i) q^{46} +(140.594 + 243.516i) q^{47} +(31.8615 + 241.376i) q^{48} +(221.475 + 261.912i) q^{49} +105.348i q^{50} +(-98.1972 + 75.4026i) q^{51} +(-405.397 - 234.056i) q^{52} +(168.453 + 97.2564i) q^{53} +(469.396 + 359.417i) q^{54} +289.896i q^{55} +(57.7168 - 124.392i) q^{56} +(-693.183 + 91.5000i) q^{57} +(121.565 + 210.558i) q^{58} +(244.533 - 423.544i) q^{59} +(-234.234 - 96.9292i) q^{60} +(159.081 - 91.8453i) q^{61} -603.676 q^{62} +(172.241 + 469.447i) q^{63} +706.785 q^{64} +(-207.744 + 119.941i) q^{65} +(-1173.05 - 485.425i) q^{66} +(452.293 - 783.394i) q^{67} +(116.240 + 201.333i) q^{68} +(505.100 - 66.6730i) q^{69} +(-224.426 - 319.218i) q^{70} -524.004i q^{71} +(141.266 - 141.459i) q^{72} +(-110.969 - 64.0683i) q^{73} +(-2.77082 - 1.59973i) q^{74} +(-103.033 + 79.1156i) q^{75} +1312.92i q^{76} +(-617.574 - 878.424i) q^{77} +(-137.473 - 1041.47i) q^{78} +(120.336 + 208.428i) q^{79} +(117.139 - 202.891i) q^{80} +(0.995105 + 728.999i) q^{81} +(-1891.94 + 1092.31i) q^{82} -607.116 q^{83} +(916.251 - 205.287i) q^{84} +119.134 q^{85} +(736.821 - 425.404i) q^{86} +(-114.635 + 277.021i) q^{87} +(-214.648 + 371.781i) q^{88} +(436.983 + 756.876i) q^{89} +(-147.612 - 549.394i) q^{90} +(373.979 - 806.001i) q^{91} -956.681i q^{92} +(-453.356 - 590.408i) q^{93} +(1026.16 + 592.451i) q^{94} +(582.664 + 336.401i) q^{95} +(812.298 + 1057.86i) q^{96} -1292.71i q^{97} +(1360.08 + 489.173i) q^{98} +(-406.198 - 1511.82i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

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