LMFDB - Embedded newform 45.4.e.c.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 $ x^14 - 2x^13 + 48x^12 - 60x^11 + 1605x^10 - 1800x^9 + 23232x^8 - 2346x^7 + 209529x^6 - 55412x^5 + 765088x^4 + 276096x^3 + 1572480x^2 - 345600*x + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.5
Root			$1.09722 - 1.90044i$ of defining polynomial
Character	$\chi$	$=$	45.31
Dual form			45.4.e.c.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09722 + 1.90044i) q^{2} +(0.206141 - 5.19206i) q^{3} +(1.59221 - 2.75778i) q^{4} +(2.50000 - 4.33013i) q^{5} +(10.0934 - 5.30509i) q^{6} +(-1.38302 - 2.39547i) q^{7} +24.5436 q^{8} +(-26.9150 - 2.14059i) q^{9} +O(q^{10})$	\(q+(1.09722 + 1.90044i) q^{2} +(0.206141 - 5.19206i) q^{3} +(1.59221 - 2.75778i) q^{4} +(2.50000 - 4.33013i) q^{5} +(10.0934 - 5.30509i) q^{6} +(-1.38302 - 2.39547i) q^{7} +24.5436 q^{8} +(-26.9150 - 2.14059i) q^{9} +10.9722 q^{10} +(26.3295 + 45.6040i) q^{11} +(-13.9904 - 8.83533i) q^{12} +(-10.2267 + 17.7132i) q^{13} +(3.03497 - 5.25672i) q^{14} +(-21.9669 - 13.8728i) q^{15} +(14.1921 + 24.5814i) q^{16} +3.66084 q^{17} +(-25.4637 - 53.4992i) q^{18} -95.6705 q^{19} +(-7.96104 - 13.7889i) q^{20} +(-12.7225 + 6.68694i) q^{21} +(-57.7786 + 100.075i) q^{22} +(44.9206 - 77.8047i) q^{23} +(5.05943 - 127.432i) q^{24} +(-12.5000 - 21.6506i) q^{25} -44.8840 q^{26} +(-16.6623 + 139.303i) q^{27} -8.80825 q^{28} +(113.890 + 197.264i) q^{29} +(2.26182 - 56.9684i) q^{30} +(-139.569 + 241.741i) q^{31} +(67.0306 - 116.100i) q^{32} +(242.206 - 127.303i) q^{33} +(4.01675 + 6.95722i) q^{34} -13.8302 q^{35} +(-48.7576 + 70.8175i) q^{36} +273.725 q^{37} +(-104.972 - 181.816i) q^{38} +(89.8599 + 56.7492i) q^{39} +(61.3589 - 106.277i) q^{40} +(-32.4323 + 56.1744i) q^{41} +(-26.6676 - 16.8414i) q^{42} +(-209.381 - 362.658i) q^{43} +167.688 q^{44} +(-76.5566 + 111.194i) q^{45} +197.151 q^{46} +(-69.3544 - 120.125i) q^{47} +(130.554 - 68.6190i) q^{48} +(167.674 - 290.421i) q^{49} +(27.4306 - 47.5111i) q^{50} +(0.754647 - 19.0073i) q^{51} +(32.5661 + 56.4062i) q^{52} -197.063 q^{53} +(-283.020 + 121.181i) q^{54} +263.295 q^{55} +(-33.9444 - 58.7934i) q^{56} +(-19.7216 + 496.727i) q^{57} +(-249.926 + 432.884i) q^{58} +(-370.552 + 641.814i) q^{59} +(-73.2340 + 38.4917i) q^{60} +(-244.234 - 423.026i) q^{61} -612.554 q^{62} +(32.0964 + 67.4346i) q^{63} +521.263 q^{64} +(51.1336 + 88.5660i) q^{65} +(507.687 + 320.620i) q^{66} +(205.734 - 356.341i) q^{67} +(5.82882 - 10.0958i) q^{68} +(-394.707 - 249.269i) q^{69} +(-15.1748 - 26.2836i) q^{70} -310.343 q^{71} +(-660.591 - 52.5377i) q^{72} -51.0260 q^{73} +(300.338 + 520.200i) q^{74} +(-114.988 + 60.4377i) q^{75} +(-152.327 + 263.839i) q^{76} +(72.8286 - 126.143i) q^{77} +(-9.25240 + 233.040i) q^{78} +(-603.999 - 1046.16i) q^{79} +141.921 q^{80} +(719.836 + 115.228i) q^{81} -142.342 q^{82} +(-452.611 - 783.945i) q^{83} +(-1.81574 + 45.7330i) q^{84} +(9.15210 - 15.8519i) q^{85} +(459.475 - 795.833i) q^{86} +(1047.68 - 550.661i) q^{87} +(646.220 + 1119.29i) q^{88} +663.633 q^{89} +(-295.317 - 23.4870i) q^{90} +56.5752 q^{91} +(-143.046 - 247.763i) q^{92} +(1226.36 + 774.485i) q^{93} +(152.194 - 263.608i) q^{94} +(-239.176 + 414.265i) q^{95} +(-588.982 - 371.960i) q^{96} +(362.668 + 628.159i) q^{97} +735.905 q^{98} +(-611.039 - 1283.79i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.09722	+	1.90044i	0.387927	+	0.671909i	0.992170	−	0.124891i	$-0.0398581\pi$
$2$	1.09722	+	1.90044i	0.387927	+	0.671909i	−0.604244	+	0.796799i	$0.706525\pi$
$3$	0.206141	−	5.19206i	0.0396718	−	0.999213i
$3$	0.206141	−	5.19206i	0.0396718	−	0.999213i
$4$	1.59221	−	2.75778i	0.199026	−	0.344723i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	10.0934	−	5.30509i	0.686769	−	0.360965i
$7$	−1.38302	−	2.39547i	−0.0746763	−	0.129343i	0.826269	−	0.563275i	$-0.190459\pi$
$7$	−1.38302	−	2.39547i	−0.0746763	−	0.129343i	−0.900945	+	0.433932i	$0.857126\pi$
$8$	24.5436			1.08468
$9$	−26.9150	−	2.14059i	−0.996852	−	0.0792811i
$10$	10.9722			0.346972
$11$	26.3295	+	45.6040i	0.721694	+	1.25001i	0.960320	+	0.278900i	$0.0899698\pi$
$11$	26.3295	+	45.6040i	0.721694	+	1.25001i	−0.238626	+	0.971112i	$0.576697\pi$
$12$	−13.9904	−	8.83533i	−0.336556	−	0.212545i
$13$	−10.2267	+	17.7132i	−0.218183	+	0.377905i	−0.954253	−	0.299002i	$-0.903346\pi$
$13$	−10.2267	+	17.7132i	−0.218183	+	0.377905i	0.736069	+	0.676906i	$0.236680\pi$
$14$	3.03497	−	5.25672i	0.0579378	−	0.100351i
$15$	−21.9669	−	13.8728i	−0.378123	−	0.238796i
$16$	14.1921	+	24.5814i	0.221751	+	0.384085i
$17$	3.66084			0.0522285			0.0261142	−	0.999659i	$-0.491687\pi$
$17$	3.66084			0.0522285			0.0261142	+	0.999659i	$0.491687\pi$
$18$	−25.4637	−	53.4992i	−0.333436	−	0.700549i
$19$	−95.6705			−1.15517			−0.577587	−	0.816329i	$-0.696006\pi$
$19$	−95.6705			−1.15517			−0.577587	+	0.816329i	$0.696006\pi$
$20$	−7.96104	−	13.7889i	−0.0890071	−	0.154165i
$21$	−12.7225	+	6.68694i	−0.132204	+	0.0694862i
$22$	−57.7786	+	100.075i	−0.559929	+	0.969825i
$23$	44.9206	−	77.8047i	0.407243	−	0.705365i	−0.587337	−	0.809343i	$-0.699824\pi$
$23$	44.9206	−	77.8047i	0.407243	−	0.705365i	0.994580	+	0.103977i	$0.0331569\pi$
$24$	5.05943	−	127.432i	0.0430313	−	1.08383i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−44.8840			−0.338556
$27$	−16.6623	+	139.303i	−0.118766	+	0.992922i
$28$	−8.80825			−0.0594501
$29$	113.890	+	197.264i	0.729272	+	1.26314i	0.957191	+	0.289456i	$0.0934744\pi$
$29$	113.890	+	197.264i	0.729272	+	1.26314i	−0.227919	+	0.973680i	$0.573192\pi$
$30$	2.26182	−	56.9684i	0.0137650	−	0.346699i
$31$	−139.569	+	241.741i	−0.808625	+	1.40058i	0.105191	+	0.994452i	$0.466455\pi$
$31$	−139.569	+	241.741i	−0.808625	+	1.40058i	−0.913816	+	0.406128i	$0.866879\pi$
$32$	67.0306	−	116.100i	0.370295	−	0.641370i
$33$	242.206	−	127.303i	1.27766	−	0.671536i
$34$	4.01675	+	6.95722i	0.0202608	+	0.0350928i
$35$	−13.8302			−0.0667925
$36$	−48.7576	+	70.8175i	−0.225730	+	0.327859i
$37$	273.725			1.21622			0.608110	−	0.793852i	$-0.291928\pi$
$37$	273.725			1.21622			0.608110	+	0.793852i	$0.291928\pi$
$38$	−104.972	−	181.816i	−0.448123	−	0.776172i
$39$	89.8599	+	56.7492i	0.368951	+	0.233004i
$40$	61.3589	−	106.277i	0.242542	−	0.420096i
$41$	−32.4323	+	56.1744i	−0.123539	+	0.213975i	−0.921161	−	0.389182i	$-0.872758\pi$
$41$	−32.4323	+	56.1744i	−0.123539	+	0.213975i	0.797622	+	0.603157i	$0.206091\pi$
$42$	−26.6676	−	16.8414i	−0.0979738	−	0.0618733i
$43$	−209.381	−	362.658i	−0.742565	−	1.28616i	−0.951324	−	0.308193i	$-0.900276\pi$
$43$	−209.381	−	362.658i	−0.742565	−	1.28616i	0.208759	−	0.977967i	$-0.433057\pi$
$44$	167.688			0.574544
$45$	−76.5566	+	111.194i	−0.253608	+	0.368351i
$46$	197.151			0.631921
$47$	−69.3544	−	120.125i	−0.215242	−	0.372810i	0.738105	−	0.674685i	$-0.235721\pi$
$47$	−69.3544	−	120.125i	−0.215242	−	0.372810i	−0.953347	+	0.301875i	$0.902387\pi$
$48$	130.554	−	68.6190i	0.392580	−	0.206339i
$49$	167.674	−	290.421i	0.488847	−	0.846708i
$50$	27.4306	−	47.5111i	0.0775853	−	0.134382i
$51$	0.754647	−	19.0073i	0.00207200	−	0.0521874i
$52$	32.5661	+	56.4062i	0.0868483	+	0.150426i
$53$	−197.063			−0.510730			−0.255365	−	0.966845i	$-0.582196\pi$
$53$	−197.063			−0.510730			−0.255365	+	0.966845i	$0.582196\pi$
$54$	−283.020	+	121.181i	−0.713225	+	0.305381i
$55$	263.295			0.645503
$56$	−33.9444	−	58.7934i	−0.0810001	−	0.140296i
$57$	−19.7216	+	496.727i	−0.0458278	+	1.15427i
$58$	−249.926	+	432.884i	−0.565808	+	0.980008i
$59$	−370.552	+	641.814i	−0.817656	+	1.41622i	0.0897490	+	0.995964i	$0.471394\pi$
$59$	−370.552	+	641.814i	−0.817656	+	1.41622i	−0.907405	+	0.420257i	$0.861940\pi$
$60$	−73.2340	+	38.4917i	−0.157575	+	0.0828211i
$61$	−244.234	−	423.026i	−0.512639	−	0.887916i	−0.999893	−	0.0146560i	$-0.995335\pi$
$61$	−244.234	−	423.026i	−0.512639	−	0.887916i	0.487254	−	0.873260i	$-0.337999\pi$
$62$	−612.554			−1.25475
$63$	32.0964	+	67.4346i	0.0641868	+	0.134856i
$64$	521.263			1.01809
$65$	51.1336	+	88.5660i	0.0975746	+	0.169004i
$66$	507.687	+	320.620i	0.946848	+	0.597963i
$67$	205.734	−	356.341i	0.375140	−	0.649762i	−0.615208	−	0.788365i	$-0.710928\pi$
$67$	205.734	−	356.341i	0.375140	−	0.649762i	0.990348	+	0.138603i	$0.0442613\pi$
$68$	5.82882	−	10.0958i	0.0103948	−	0.0180044i
$69$	−394.707	−	249.269i	−0.688654	−	0.434905i
$70$	−15.1748	−	26.2836i	−0.0259106	−	0.0448785i
$71$	−310.343			−0.518746			−0.259373	−	0.965777i	$-0.583516\pi$
$71$	−310.343			−0.518746			−0.259373	+	0.965777i	$0.583516\pi$
$72$	−660.591	−	52.5377i	−1.08127	−	0.0859948i
$73$	−51.0260			−0.0818101			−0.0409051	−	0.999163i	$-0.513024\pi$
$73$	−51.0260			−0.0818101			−0.0409051	+	0.999163i	$0.513024\pi$
$74$	300.338	+	520.200i	0.471804	+	0.817189i
$75$	−114.988	+	60.4377i	−0.177036	+	0.0930499i
$76$	−152.327	+	263.839i	−0.229910	+	0.398215i
$77$	72.8286	−	126.143i	0.107787	−	0.186692i
$78$	−9.25240	+	233.040i	−0.0134311	+	0.338290i
$79$	−603.999	−	1046.16i	−0.860193	−	1.48990i	−0.871742	−	0.489964i	$-0.837010\pi$
$79$	−603.999	−	1046.16i	−0.860193	−	1.48990i	0.0115496	−	0.999933i	$-0.496324\pi$
$80$	141.921			0.198340
$81$	719.836	+	115.228i	0.987429	+	0.158063i
$82$	−142.342			−0.191695
$83$	−452.611	−	783.945i	−0.598560	−	1.03674i	−0.993034	−	0.117829i	$-0.962406\pi$
$83$	−452.611	−	783.945i	−0.598560	−	1.03674i	0.394474	−	0.918907i	$-0.370927\pi$
$84$	−1.81574	+	45.7330i	−0.00235849	+	0.0594033i
$85$	9.15210	−	15.8519i	0.0116786	−	0.0202280i
$86$	459.475	−	795.833i	0.576121	−	0.997871i
$87$	1047.68	−	550.661i	1.29107	−	0.678587i
$88$	646.220	+	1119.29i	0.782810	+	1.35587i
$89$	663.633			0.790393			0.395197	−	0.918597i	$-0.370676\pi$
$89$	663.633			0.790393			0.395197	+	0.918597i	$0.370676\pi$
$90$	−295.317	−	23.4870i	−0.345880	−	0.0275083i
$91$	56.5752			0.0651725
$92$	−143.046	−	247.763i	−0.162104	−	0.280772i
$93$	1226.36	+	774.485i	1.36740	+	0.863552i
$94$	152.194	−	263.608i	0.166996	−	0.289246i
$95$	−239.176	+	414.265i	−0.258305	+	0.447397i
$96$	−588.982	−	371.960i	−0.626175	−	0.395448i
$97$	362.668	+	628.159i	0.379622	+	0.657525i	0.991007	−	0.133809i	$-0.0427207\pi$
$97$	362.668	+	628.159i	0.379622	+	0.657525i	−0.611385	+	0.791333i	$0.709387\pi$
$98$	735.905			0.758547
$99$	−611.039	−	1283.79i	−0.620321	−	1.30329i
$100$	−79.6104			−0.0796104
$101$	−488.891	−	846.784i	−0.481648	−	0.834239i	0.518130	−	0.855302i	$-0.326628\pi$
$101$	−488.891	−	846.784i	−0.481648	−	0.834239i	−0.999778	+	0.0210629i	$0.993295\pi$
$102$	36.9503	−	19.4211i	0.0358689	−	0.0188527i
$103$	−793.852	+	1374.99i	−0.759423	+	1.31536i	0.183722	+	0.982978i	$0.441185\pi$
$103$	−793.852	+	1374.99i	−0.759423	+	1.31536i	−0.943145	+	0.332381i	$0.892148\pi$
$104$	−251.000	+	434.745i	−0.236660	+	0.409907i
$105$	−2.85097	+	71.8075i	−0.00264978	+	0.0667399i
$106$	−216.222	−	374.507i	−0.198126	−	0.343164i
$107$	897.731			0.811093			0.405546	−	0.914074i	$-0.367081\pi$
$107$	897.731			0.811093			0.405546	+	0.914074i	$0.367081\pi$
$108$	357.638	+	267.751i	0.318646	+	0.238559i
$109$	855.492			0.751754			0.375877	−	0.926669i	$-0.377341\pi$
$109$	855.492			0.751754			0.375877	+	0.926669i	$0.377341\pi$
$110$	288.893	+	500.377i	0.250408	+	0.433719i
$111$	56.4259	−	1421.20i	0.0482496	−	1.21526i
$112$	39.2560	−	67.9934i	0.0331191	−	0.0573640i
$113$	−455.121	+	788.292i	−0.378886	+	0.656250i	−0.990900	−	0.134597i	$-0.957026\pi$
$113$	−455.121	+	788.292i	−0.378886	+	0.656250i	0.612014	+	0.790847i	$0.290359\pi$
$114$	−965.641	+	507.540i	−0.793339	+	0.416978i
$115$	−224.603	−	389.024i	−0.182125	−	0.315449i
$116$	725.348			0.580576
$117$	313.169	−	454.860i	0.247457	−	0.359417i
$118$	−1626.31			−1.26876
$119$	−5.06303	−	8.76943i	−0.00390023	−	0.00675539i
$120$	−539.147	−	340.487i	−0.410143	−	0.259017i
$121$	−720.984	+	1248.78i	−0.541686	+	0.938227i
$122$	535.958	−	928.306i	0.397732	−	0.688893i
$123$	284.976	+	179.971i	0.208906	+	0.131930i
$124$	444.447	+	769.804i	0.321875	+	0.557504i
$125$	−125.000			−0.0894427
$126$	−92.9387	+	134.988i	−0.0657114	+	0.0954420i
$127$	−2038.25			−1.42414			−0.712068	−	0.702111i	$-0.752241\pi$
$127$	−2038.25			−1.42414			−0.712068	+	0.702111i	$0.752241\pi$
$128$	35.6968	+	61.8287i	0.0246499	+	0.0426948i
$129$	−1926.11	+	1012.36i	−1.31461	+	0.690956i
$130$	−112.210	+	194.353i	−0.0757035	+	0.131122i
$131$	−117.823	+	204.075i	−0.0785817	+	0.136108i	−0.902638	−	0.430400i	$-0.858372\pi$
$131$	−117.823	+	204.075i	−0.0785817	+	0.136108i	0.824057	+	0.566508i	$0.191706\pi$
$132$	34.5673	−	870.647i	0.0227932	−	0.574091i
$133$	132.315	+	229.176i	0.0862642	+	0.149414i
$134$	902.942			0.582107
$135$	561.544	+	420.408i	0.358000	+	0.268022i
$136$	89.8501			0.0566513
$137$	1486.45	+	2574.60i	0.926975	+	1.60557i	0.788354	+	0.615222i	$0.210934\pi$
$137$	1486.45	+	2574.60i	0.926975	+	1.60557i	0.138621	+	0.990345i	$0.455733\pi$
$138$	40.6409	−	1023.62i	0.0250694	−	0.631424i
$139$	1047.32	−	1814.00i	0.639080	−	1.10692i	−0.346555	−	0.938030i	$-0.612648\pi$
$139$	1047.32	−	1814.00i	0.639080	−	1.10692i	0.985635	−	0.168890i	$-0.0540182\pi$
$140$	−22.0206	+	38.1408i	−0.0132934	+	0.0230249i
$141$	−637.995	+	335.330i	−0.381056	+	0.200283i
$142$	−340.515	−	589.790i	−0.201235	−	0.348550i
$143$	−1077.06			−0.629847
$144$	−329.362	−	691.989i	−0.190603	−	0.400456i
$145$	1138.90			0.652281
$146$	−55.9868	−	96.9720i	−0.0317363	−	0.0549689i
$147$	−1473.32	−	930.444i	−0.826648	−	0.522052i
$148$	435.828	−	754.876i	0.242060	−	0.419259i
$149$	−136.969	+	237.237i	−0.0753081	+	0.130437i	−0.901220	−	0.433361i	$-0.857327\pi$
$149$	−136.969	+	237.237i	−0.0753081	+	0.130437i	0.825912	+	0.563799i	$0.190661\pi$
$150$	−241.026	−	152.215i	−0.131198	−	0.0828554i
$151$	468.422	+	811.331i	0.252448	+	0.437253i	0.964199	−	0.265179i	$-0.0854310\pi$
$151$	468.422	+	811.331i	0.252448	+	0.437253i	−0.711751	+	0.702432i	$0.752098\pi$
$152$	−2348.10			−1.25300
$153$	−98.5315	−	7.83635i	−0.0520641	−	0.00414073i
$154$	319.637			0.167254
$155$	697.846	+	1208.71i	0.361628	+	0.626358i
$156$	299.578	−	157.458i	0.153753	−	0.0808123i
$157$	−199.218	+	345.055i	−0.101269	+	0.175404i	−0.912208	−	0.409728i	$-0.865624\pi$
$157$	−199.218	+	345.055i	−0.101269	+	0.175404i	0.810938	+	0.585131i	$0.198957\pi$
$158$	1325.44	−	2295.73i	0.667383	−	1.15594i
$159$	−40.6227	+	1023.16i	−0.0202616	+	0.510328i
$160$	−335.153	−	580.502i	−0.165601	−	0.286829i
$161$	−248.505			−0.121646
$162$	570.835	+	1494.44i	0.276846	+	0.724779i
$163$	478.154			0.229766			0.114883	−	0.993379i	$-0.463351\pi$
$163$	478.154			0.229766			0.114883	+	0.993379i	$0.463351\pi$
$164$	103.278	+	178.883i	0.0491747	+	0.0851732i
$165$	54.2757	−	1367.04i	0.0256082	−	0.644995i
$166$	993.229	−	1720.32i	0.464395	−	0.804355i
$167$	170.181	−	294.763i	0.0788564	−	0.136583i	−0.823900	−	0.566735i	$-0.808206\pi$
$167$	170.181	−	294.763i	0.0788564	−	0.136583i	0.902757	+	0.430151i	$0.141540\pi$
$168$	−312.256	+	164.122i	−0.143399	+	0.0753705i
$169$	889.328	+	1540.36i	0.404792	+	0.701120i
$170$	40.1675			0.0181218
$171$	2574.97	+	204.791i	1.15154	+	0.0915835i
$172$	−1333.51			−0.591159
$173$	−1888.03	−	3270.17i	−0.829738	−	1.43715i	−0.898244	−	0.439497i	$-0.855157\pi$
$173$	−1888.03	−	3270.17i	−0.829738	−	1.43715i	0.0685065	−	0.997651i	$-0.478177\pi$
$174$	2196.04	+	1386.87i	0.956790	+	0.604241i
$175$	−34.5756	+	59.8867i	−0.0149353	+	0.0258686i
$176$	−747.341	+	1294.43i	−0.320073	+	0.554384i
$177$	3255.95	+	2056.23i	1.38267	+	0.873196i
$178$	728.153	+	1261.20i	0.306615	+	0.531072i
$179$	186.652			0.0779385			0.0389693	−	0.999240i	$-0.487593\pi$
$179$	186.652			0.0779385			0.0389693	+	0.999240i	$0.487593\pi$
$180$	184.755	+	388.170i	0.0765046	+	0.160736i
$181$	1438.75			0.590837			0.295418	−	0.955368i	$-0.404541\pi$
$181$	1438.75			0.590837			0.295418	+	0.955368i	$0.404541\pi$
$182$	62.0756	+	107.518i	0.0252821	+	0.0437900i
$183$	−2246.72	+	1180.88i	−0.907555	+	0.477010i
$184$	1102.51	−	1909.61i	0.441729	−	0.765098i
$185$	684.313	−	1185.27i	0.271955	−	0.471040i
$186$	−126.272	+	3180.42i	−0.0497781	+	1.25376i
$187$	96.3880	+	166.949i	0.0376930	+	0.0652862i
$188$	−441.706			−0.171355
$189$	356.741	−	152.746i	0.137297	−	0.0587863i
$190$	−1049.72			−0.400813
$191$	195.218	+	338.127i	0.0739552	+	0.128094i	0.900631	−	0.434584i	$-0.143104\pi$
$191$	195.218	+	338.127i	0.0739552	+	0.128094i	−0.826676	+	0.562678i	$0.809771\pi$
$192$	107.453	−	2706.43i	0.0403895	−	1.01729i
$193$	1957.52	−	3390.53i	0.730081	−	1.26454i	−0.226767	−	0.973949i	$-0.572816\pi$
$193$	1957.52	−	3390.53i	0.730081	−	1.26454i	0.956848	−	0.290588i	$-0.0938510\pi$
$194$	−795.854	+	1378.46i	−0.294531	+	0.510143i
$195$	470.381	−	247.232i	0.172742	−	0.0907930i
$196$	−533.945	−	924.820i	−0.194586	−	0.337034i
$197$	−892.680			−0.322847			−0.161423	−	0.986885i	$-0.551608\pi$
$197$	−892.680			−0.322847			−0.161423	+	0.986885i	$0.551608\pi$
$198$	1769.33	−	2569.85i	0.635055	−	0.922381i
$199$	−2770.50			−0.986913			−0.493457	−	0.869770i	$-0.664267\pi$
$199$	−2770.50			−0.986913			−0.493457	+	0.869770i	$0.664267\pi$
$200$	−306.795	−	531.384i	−0.108468	−	0.187873i
$201$	−1807.74	−	1141.64i	−0.634368	−	0.400622i
$202$	1072.84	−	1858.22i	0.373688	−	0.647247i
$203$	315.026	−	545.641i	0.108919	−	0.188653i
$204$	−51.2165	−	32.3447i	−0.0175778	−	0.0111009i
$205$	162.162	+	280.872i	0.0552481	+	0.0956925i
$206$	−3484.13			−1.17840
$207$	−1375.59	+	1997.96i	−0.461883	+	0.670859i
$208$	−580.554			−0.193530
$209$	−2518.96	−	4362.96i	−0.833683	−	1.44398i
$210$	−139.594	+	73.3706i	−0.0458710	+	0.0241098i
$211$	−2291.25	+	3968.57i	−0.747566	+	1.29482i	0.201420	+	0.979505i	$0.435444\pi$
$211$	−2291.25	+	3968.57i	−0.747566	+	1.29482i	−0.948986	+	0.315318i	$0.897889\pi$
$212$	−313.765	+	543.458i	−0.101649	+	0.176060i
$213$	−63.9743	+	1611.32i	−0.0205796	+	0.518338i
$214$	985.010	+	1706.09i	0.314644	+	0.544980i
$215$	−2093.81			−0.664170
$216$	−408.953	+	3419.00i	−0.128823	+	1.07701i
$217$	772.111			0.241541
$218$	938.664	+	1625.81i	0.291626	+	0.505110i
$219$	−10.5185	+	264.930i	−0.00324555	+	0.0817457i
$220$	419.220	−	726.111i	0.128472	−	0.222520i
$221$	−37.4384	+	64.8452i	−0.0113954	+	0.0197374i
$222$	2762.82	−	1452.14i	0.835263	−	0.439014i
$223$	−2047.67	−	3546.66i	−0.614897	−	1.06503i	−0.990403	−	0.138212i	$-0.955864\pi$
$223$	−2047.67	−	3546.66i	−0.614897	−	1.06503i	0.375506	−	0.926820i	$-0.377469\pi$
$224$	−370.820			−0.110609
$225$	290.093	+	609.484i	0.0859533	+	0.180588i
$226$	−1997.47			−0.587920
$227$	1934.68	+	3350.96i	0.565678	+	0.979784i	0.996986	+	0.0775789i	$0.0247190\pi$
$227$	1934.68	+	3350.96i	0.565678	+	0.979784i	−0.431308	+	0.902205i	$0.641948\pi$
$228$	1338.47	+	845.281i	0.388781	+	0.245527i
$229$	−618.006	+	1070.42i	−0.178336	+	0.308887i	−0.941311	−	0.337541i	$-0.890405\pi$
$229$	−618.006	+	1070.42i	−0.178336	+	0.308887i	0.762975	+	0.646429i	$0.223738\pi$
$230$	492.878	−	853.690i	0.141302	−	0.244742i
$231$	−639.929	−	404.134i	−0.182269	−	0.115109i
$232$	2795.27	+	4841.56i	0.791029	+	1.37010i
$233$	2207.05			0.620552			0.310276	−	0.950647i	$-0.399579\pi$
$233$	2207.05			0.620552			0.310276	+	0.950647i	$0.399579\pi$
$234$	1208.05	+	96.0781i	0.337491	+	0.0268411i
$235$	−693.544			−0.192518
$236$	1179.99	+	2043.80i	0.325470	+	0.563730i
$237$	−5556.22	+	2920.35i	−1.52285	+	0.800409i
$238$	11.1105	−	19.2440i	0.00302600	−	0.00524119i
$239$	−438.324	+	759.199i	−0.118631	+	0.205475i	−0.919225	−	0.393732i	$-0.871184\pi$
$239$	−438.324	+	759.199i	−0.118631	+	0.205475i	0.800594	+	0.599207i	$0.204517\pi$
$240$	29.2556	−	736.862i	0.00786852	−	0.198184i
$241$	238.931	+	413.840i	0.0638626	+	0.110613i	0.896189	−	0.443673i	$-0.146325\pi$
$241$	238.931	+	413.840i	0.0638626	+	0.110613i	−0.832326	+	0.554286i	$0.812991\pi$
$242$	−3164.32			−0.840537
$243$	746.658	−	3713.68i	0.197112	−	0.980381i
$244$	−1555.49			−0.408114
$245$	−838.372	−	1452.10i	−0.218619	−	0.378659i
$246$	−29.3424	+	739.048i	−0.00760490	+	0.191545i
$247$	978.396	−	1694.63i	0.252040	−	0.436546i
$248$	−3425.53	+	5933.19i	−0.877102	+	1.51919i
$249$	−4163.59	+	2188.38i	−1.05967	+	0.556960i
$250$	−137.153	−	237.556i	−0.0346972	−	0.0600973i
$251$	6892.28			1.73322			0.866608	−	0.498990i	$-0.166296\pi$
$251$	6892.28			1.73322			0.866608	+	0.498990i	$0.166296\pi$
$252$	237.074	+	18.8548i	0.0592630	+	0.00471327i
$253$	4730.94			1.17562
$254$	−2236.41	−	3873.57i	−0.552460	−	0.956889i
$255$	−80.4174	−	50.7860i	−0.0197488	−	0.0124719i
$256$	2006.72	−	3475.74i	0.489921	−	0.848568i
$257$	3628.35	−	6284.49i	0.880664	−	1.52535i	0.0300589	−	0.999548i	$-0.490431\pi$
$257$	3628.35	−	6284.49i	0.880664	−	1.52535i	0.850605	−	0.525806i	$-0.176236\pi$
$258$	−4037.30	−	2549.67i	−0.974230	−	0.615255i
$259$	−378.569	−	655.701i	−0.0908229	−	0.157310i
$260$	325.661			0.0776795
$261$	−2643.10	−	5553.15i	−0.626834	−	1.31698i
$262$	−517.110			−0.121936
$263$	3158.78	+	5471.16i	0.740603	+	1.28276i	0.952221	+	0.305409i	$0.0987933\pi$
$263$	3158.78	+	5471.16i	0.740603	+	1.28276i	−0.211618	+	0.977352i	$0.567873\pi$
$264$	5944.61	−	3124.48i	1.38585	−	0.728404i
$265$	−492.658	+	853.308i	−0.114203	+	0.197805i
$266$	−290.357	+	502.913i	−0.0669283	+	0.115923i
$267$	136.802	−	3445.63i	0.0313563	−	0.789771i
$268$	−655.142	−	1134.74i	−0.149325	−	0.258639i
$269$	5746.22			1.30243			0.651214	−	0.758894i	$-0.274260\pi$
$269$	5746.22			1.30243			0.651214	+	0.758894i	$0.274260\pi$
$270$	−182.823	+	1528.46i	−0.0412083	+	0.344516i
$271$	4925.20			1.10400			0.552001	−	0.833844i	$-0.313865\pi$
$271$	4925.20			1.10400			0.552001	+	0.833844i	$0.313865\pi$
$272$	51.9550	+	89.9886i	0.0115817	+	0.0200602i
$273$	11.6625	−	293.742i	0.00258551	−	0.0651212i
$274$	−3261.92	+	5649.81i	−0.719196	+	1.24568i
$275$	658.237	−	1140.10i	0.144339	−	0.250002i
$276$	−1315.89	+	691.629i	−0.286982	+	0.150837i
$277$	−1162.94	−	2014.27i	−0.252254	−	0.436917i	0.711892	−	0.702289i	$-0.247839\pi$
$277$	−1162.94	−	2014.27i	−0.252254	−	0.436917i	−0.964146	+	0.265372i	$0.914505\pi$
$278$	4596.55			0.991665
$279$	4273.98	−	6207.70i	0.917119	−	1.33206i
$280$	−339.444			−0.0724487
$281$	−1641.71	−	2843.52i	−0.348527	−	0.603667i	0.637461	−	0.770483i	$-0.279985\pi$
$281$	−1641.71	−	2843.52i	−0.348527	−	0.603667i	−0.985988	+	0.166816i	$0.946652\pi$
$282$	−1337.30	−	844.543i	−0.282393	−	0.178340i
$283$	−1007.11	+	1744.36i	−0.211541	+	0.366400i	−0.952197	−	0.305484i	$-0.901182\pi$
$283$	−1007.11	+	1744.36i	−0.211541	+	0.366400i	0.740656	+	0.671885i	$0.234515\pi$
$284$	−494.131	+	855.860i	−0.103244	+	0.178824i
$285$	2101.59	+	1327.21i	0.436798	+	0.275851i
$286$	−1181.77	−	2046.89i	−0.244334	−	0.423199i
$287$	179.419			0.0369016
$288$	−2052.65	+	2981.36i	−0.419978	+	0.609994i
$289$	−4899.60			−0.997272
$290$	1249.63	+	2164.42i	0.253037	+	0.438273i
$291$	3336.20	−	1753.50i	0.672067	−	0.353238i
$292$	−81.2440	+	140.719i	−0.0162823	+	0.0282018i
$293$	−240.348	+	416.295i	−0.0479225	+	0.0830042i	−0.888992	−	0.457923i	$-0.848593\pi$
$293$	−240.348	+	416.295i	−0.0479225	+	0.0830042i	0.841069	+	0.540928i	$0.181927\pi$
$294$	151.700	−	3820.86i	0.0300929	−	0.757950i
$295$	1852.76	+	3209.07i	0.365667	+	0.633354i
$296$	6718.20			1.31921
$297$	−6791.49	+	2907.91i	−1.32688	+	0.568128i
$298$	−601.140			−0.116856
$299$	918.781	+	1591.37i	0.177707	+	0.307798i
$300$	−16.4109	+	413.342i	−0.00315828	+	0.0795477i
$301$	−579.158	+	1003.13i	−0.110904	+	0.192091i
$302$	−1027.93	+	1780.42i	−0.195863	+	0.339244i
$303$	−4497.33	+	2363.79i	−0.852690	+	0.448173i
$304$	−1357.76	−	2351.72i	−0.256162	−	0.443685i
$305$	−2442.34			−0.458518
$306$	−93.2184	−	195.852i	−0.0174148	−	0.0365886i
$307$	3222.21			0.599026			0.299513	−	0.954092i	$-0.403176\pi$
$307$	3222.21			0.599026			0.299513	+	0.954092i	$0.403176\pi$
$308$	−231.917	−	401.691i	−0.0429048	−	0.0743133i
$309$	6975.40	+	4405.17i	1.28420	+	0.811008i
$310$	−1531.38	+	2652.44i	−0.280570	+	0.485962i
$311$	−1207.00	+	2090.59i	−0.220074	+	0.381179i	−0.954830	−	0.297152i	$-0.903963\pi$
$311$	−1207.00	+	2090.59i	−0.220074	+	0.381179i	0.734757	+	0.678331i	$0.237296\pi$
$312$	2205.48	+	1392.83i	0.400195	+	0.252735i
$313$	1253.47	+	2171.07i	0.226359	+	0.392065i	0.956726	−	0.290990i	$-0.0939846\pi$
$313$	1253.47	+	2171.07i	0.226359	+	0.392065i	−0.730368	+	0.683054i	$0.760651\pi$
$314$	−874.344			−0.157140
$315$	372.241	+	29.6049i	0.0665823	+	0.00529538i
$316$	−3846.77			−0.684803
$317$	−1853.56	−	3210.46i	−0.328411	−	0.568825i	0.653786	−	0.756680i	$-0.273180\pi$
$317$	−1853.56	−	3210.46i	−0.328411	−	0.568825i	−0.982197	+	0.187855i	$0.939846\pi$
$318$	−1989.04	+	1045.44i	−0.350754	+	0.184356i
$319$	−5997.34	+	10387.7i	−1.05262	+	1.82320i
$320$	1303.16	−	2257.13i	0.227652	−	0.394305i
$321$	185.059	−	4661.07i	0.0321775	−	0.810454i
$322$	−272.665	−	472.270i	−0.0471895	−	0.0817347i
$323$	−350.234			−0.0603330
$324$	1463.90	−	1801.69i	0.251012	−	0.308931i
$325$	511.336			0.0872733
$326$	524.641	+	908.704i	0.0891324	+	0.154382i
$327$	176.352	−	4441.77i	0.0298234	−	0.751163i
$328$	−796.005	+	1378.72i	−0.134000	+	0.232095i
$329$	−191.838	+	332.272i	−0.0321470	+	0.0556802i
$330$	2657.54	−	1396.80i	0.443312	−	0.233004i
$331$	−1276.72	−	2211.35i	−0.212009	−	0.367211i	0.740334	−	0.672239i	$-0.234667\pi$
$331$	−1276.72	−	2211.35i	−0.212009	−	0.367211i	−0.952343	+	0.305029i	$0.901334\pi$
$332$	−2882.60			−0.476516
$333$	−7367.32	−	585.933i	−1.21239	−	0.0964233i
$334$	746.906			0.122362
$335$	−1028.67	−	1781.71i	−0.167768	−	0.290582i
$336$	−344.934	−	217.836i	−0.0560050	−	0.0353688i
$337$	−1776.44	+	3076.89i	−0.287148	+	0.497356i	−0.973128	−	0.230265i	$-0.926041\pi$
$337$	−1776.44	+	3076.89i	−0.287148	+	0.497356i	0.685979	+	0.727621i	$0.259374\pi$
$338$	−1951.58	+	3380.24i	−0.314059	+	0.543966i
$339$	3999.04	+	2525.51i	0.640702	+	0.404623i
$340$	−29.1441	−	50.4790i	−0.00464871	−	0.00805179i
$341$	−14699.2			−2.33432
$342$	2436.12	+	5118.29i	0.385177	+	0.809256i
$343$	−1876.35			−0.295374
$344$	−5138.95	−	8900.93i	−0.805447	−	1.39508i
$345$	−2066.13	+	1085.96i	−0.322426	+	0.169467i
$346$	4143.19	−	7176.21i	0.643754	−	1.11502i
$347$	3884.01	−	6727.30i	0.600878	−	1.04075i	−0.391811	−	0.920046i	$-0.628151\pi$
$347$	3884.01	−	6727.30i	0.600878	−	1.04075i	0.992688	−	0.120705i	$-0.0385155\pi$
$348$	149.524	−	3766.05i	0.0230325	−	0.580119i
$349$	−348.003	−	602.760i	−0.0533759	−	0.0924498i	0.838103	−	0.545512i	$-0.183665\pi$
$349$	−348.003	−	602.760i	−0.0533759	−	0.0924498i	−0.891479	+	0.453062i	$0.850331\pi$
$350$	−151.748			−0.0231751
$351$	−2297.10	−	1719.76i	−0.349317	−	0.261521i
$352$	7059.52			1.06896
$353$	2725.94	+	4721.46i	0.411011	+	0.711892i	0.995001	−	0.0998692i	$-0.0318424\pi$
$353$	2725.94	+	4721.46i	0.411011	+	0.711892i	−0.583990	+	0.811761i	$0.698509\pi$
$354$	−335.248	+	8443.90i	−0.0503340	+	1.26776i
$355$	−775.858	+	1343.83i	−0.115995	+	0.200909i
$356$	1056.64	−	1830.16i	0.157309	−	0.272467i
$357$	−46.5751	+	24.4798i	−0.00690481	+	0.00362916i
$358$	204.798	+	354.721i	0.0302344	+	0.0523675i
$359$	4036.41			0.593408			0.296704	−	0.954969i	$-0.404113\pi$
$359$	4036.41			0.593408			0.296704	+	0.954969i	$0.404113\pi$
$360$	−1878.97	+	2729.10i	−0.275085	+	0.399545i
$361$	2293.85			0.334429
$362$	1578.63	+	2734.26i	0.229201	+	0.396988i
$363$	6335.12	+	4000.82i	0.915999	+	0.578481i
$364$	90.0795	−	156.022i	0.0129710	−	0.0224665i
$365$	−127.565	+	220.949i	−0.0182933	+	0.0316849i
$366$	−4709.34	−	2974.09i	−0.672572	−	0.424749i
$367$	−5619.96	−	9734.06i	−0.799345	−	1.38451i	−0.920043	−	0.391817i	$-0.871847\pi$
$367$	−5619.96	−	9734.06i	−0.799345	−	1.38451i	0.120698	−	0.992689i	$-0.461487\pi$
$368$	2550.07			0.361227
$369$	993.163	−	1442.51i	0.140114	−	0.203507i
$370$	3003.38			0.421995
$371$	272.543	+	472.059i	0.0381394	+	0.0660595i
$372$	4088.49	−	2148.91i	0.569834	−	0.299504i
$373$	3160.36	−	5473.90i	0.438706	−	0.759860i	−0.558884	−	0.829246i	$-0.688770\pi$
$373$	3160.36	−	5473.90i	0.438706	−	0.759860i	0.997590	+	0.0693853i	$0.0221038\pi$
$374$	−211.518	+	366.360i	−0.0292442	+	0.0506525i
$375$	−25.7676	+	649.008i	−0.00354835	+	0.0893723i
$376$	−1702.20	−	2948.30i	−0.233469	−	0.404381i
$377$	−4658.90			−0.636460
$378$	681.708	+	510.370i	0.0927600	+	0.0694460i
$379$	9325.49			1.26390			0.631950	−	0.775009i	$-0.282255\pi$
$379$	9325.49			1.26390			0.631950	+	0.775009i	$0.282255\pi$
$380$	761.637	+	1319.19i	0.102819	+	0.178087i
$381$	−420.165	+	10582.7i	−0.0564980	+	1.42301i
$382$	−428.394	+	742.000i	−0.0573784	+	0.0993823i
$383$	−5574.01	+	9654.47i	−0.743652	+	1.28804i	0.207170	+	0.978305i	$0.433575\pi$
$383$	−5574.01	+	9654.47i	−0.743652	+	1.28804i	−0.950822	+	0.309738i	$0.899759\pi$
$384$	328.377	−	172.595i	0.0436391	−	0.0229367i
$385$	−364.143	−	630.715i	−0.0482038	−	0.0834914i
$386$	8591.35			1.13287
$387$	4859.19	+	10209.1i	0.638259	+	1.34098i
$388$	2309.77			0.302219
$389$	−3285.41	−	5690.49i	−0.428218	−	0.741695i	0.568497	−	0.822685i	$-0.307525\pi$
$389$	−3285.41	−	5690.49i	−0.428218	−	0.741695i	−0.996715	+	0.0809902i	$0.974192\pi$
$390$	985.963	+	622.665i	0.128016	+	0.0808458i
$391$	164.447	−	284.831i	0.0212697	−	0.0368402i
$392$	4115.33	−	7127.96i	0.530244	−	0.918409i
$393$	1035.28	+	653.810i	0.132883	+	0.0839195i
$394$	−979.469	−	1696.49i	−0.125241	−	0.216924i
$395$	−6039.99			−0.769380
$396$	−4513.33	−	358.951i	−0.572735	−	0.0455504i
$397$	3969.33			0.501800			0.250900	−	0.968013i	$-0.419273\pi$
$397$	3969.33			0.501800			0.250900	+	0.968013i	$0.419273\pi$
$398$	−3039.86	−	5265.19i	−0.382850	−	0.663115i
$399$	1217.17	−	639.743i	0.152719	−	0.0802687i
$400$	354.802	−	614.535i	0.0443503	−	0.0768169i
$401$	−2187.35	+	3788.60i	−0.272396	+	0.471804i	−0.969475	−	0.245190i	$-0.921150\pi$
$401$	−2187.35	+	3788.60i	−0.272396	+	0.471804i	0.697079	+	0.716995i	$0.254483\pi$
$402$	186.133	−	4688.13i	0.0230932	−	0.581649i
$403$	−2854.67	−	4944.44i	−0.352857	−	0.611166i
$404$	−3113.66			−0.383442
$405$	2298.54	−	2828.91i	0.282013	−	0.347086i
$406$	1382.61			0.169010
$407$	7207.05	+	12483.0i	0.877740	+	1.52029i
$408$	18.5217	−	466.507i	0.00224746	−	0.0566067i
$409$	4436.16	−	7683.66i	0.536318	−	0.928930i	−0.462780	−	0.886473i	$-0.653148\pi$
$409$	4436.16	−	7683.66i	0.536318	−	0.928930i	0.999098	−	0.0424573i	$-0.0135186\pi$
$410$	−355.855	+	616.358i	−0.0428644	+	0.0742433i
$411$	13673.9	−	7186.99i	1.64108	−	0.862550i
$412$	2527.95	+	4378.55i	0.302290	+	0.523581i
$413$	2049.93			0.244238
$414$	−5306.33	−	422.020i	−0.629932	−	0.0500994i
$415$	−4526.11			−0.535368
$416$	1371.01	+	2374.65i	0.161584	+	0.279872i
$417$	−9202.53	−	5811.67i	−1.08069	−	0.682491i
$418$	5527.71	−	9574.27i	0.646816	−	1.12032i
$419$	507.087	−	878.300i	0.0591236	−	0.102405i	−0.834949	−	0.550328i	$-0.814503\pi$
$419$	507.087	−	878.300i	0.0591236	−	0.102405i	0.894072	+	0.447923i	$0.147836\pi$
$420$	193.490	+	122.195i	0.0224794	+	0.0141964i
$421$	7446.57	+	12897.8i	0.862051	+	1.49312i	0.869946	+	0.493147i	$0.164154\pi$
$421$	7446.57	+	12897.8i	0.862051	+	1.49312i	−0.00789511	+	0.999969i	$0.502513\pi$
$422$	−10056.1			−1.16000
$423$	1609.54	+	3381.63i	0.185008	+	0.388701i
$424$	−4836.63			−0.553980
$425$	−45.7605	−	79.2595i	−0.00522285	−	0.00904624i
$426$	−3132.42	+	1646.40i	−0.356259	+	0.187249i
$427$	−675.563	+	1170.11i	−0.0765639	+	0.132613i
$428$	1429.37	−	2475.75i	0.161429	−	0.279602i
$429$	−222.025	+	5592.15i	−0.0249871	+	0.629351i
$430$	−2297.37	−	3979.17i	−0.257649	−	0.446261i
$431$	−4363.90			−0.487707			−0.243853	−	0.969812i	$-0.578412\pi$
$431$	−4363.90			−0.487707			−0.243853	+	0.969812i	$0.578412\pi$
$432$	−3660.74	+	1567.42i	−0.407703	+	0.174566i
$433$	9301.59			1.03235			0.516173	−	0.856484i	$-0.327356\pi$
$433$	9301.59			1.03235			0.516173	+	0.856484i	$0.327356\pi$
$434$	847.177	+	1467.35i	0.0937000	+	0.162293i
$435$	234.774	−	5913.25i	0.0258771	−	0.651767i
$436$	1362.12	−	2359.26i	0.149619	−	0.259147i
$437$	−4297.57	+	7443.62i	−0.470437	+	0.814820i
$438$	−515.026	+	270.697i	−0.0561847	+	0.0295306i
$439$	−760.076	−	1316.49i	−0.0826343	−	0.143127i	0.821746	−	0.569853i	$-0.193000\pi$
$439$	−760.076	−	1316.49i	−0.0826343	−	0.143127i	−0.904381	+	0.426727i	$0.859667\pi$
$440$	6462.20			0.700166
$441$	−5134.63	+	7457.76i	−0.554436	+	0.805286i
$442$	−164.313			−0.0176823
$443$	−2231.24	−	3864.62i	−0.239299	−	0.414478i	0.721214	−	0.692712i	$-0.243584\pi$
$443$	−2231.24	−	3864.62i	−0.239299	−	0.414478i	−0.960513	+	0.278234i	$0.910251\pi$
$444$	−3829.52	−	2418.45i	−0.409326	−	0.258502i
$445$	1659.08	−	2873.62i	0.176737	−	0.306118i
$446$	4493.49	−	7782.96i	0.477070	−	0.826309i
$447$	1203.51	+	760.053i	0.127347	+	0.0804235i
$448$	−720.919	−	1248.67i	−0.0760273	−	0.131683i
$449$	−5371.66			−0.564598			−0.282299	−	0.959326i	$-0.591097\pi$
$449$	−5371.66			−0.564598			−0.282299	+	0.959326i	$0.591097\pi$
$450$	−839.995	+	1220.04i	−0.0879950	+	0.127808i
$451$	−3415.71			−0.356628
$452$	1449.29	+	2510.25i	0.150816	+	0.261222i
$453$	4309.04	−	2264.83i	0.446923	−	0.234903i
$454$	−4245.54	+	7353.49i	−0.438883	+	0.760168i
$455$	141.438	−	244.978i	0.0145730	−	0.0252412i
$456$	−484.038	+	12191.5i	−0.0497087	+	1.25201i
$457$	−7762.71	−	13445.4i	−0.794583	−	1.37626i	−0.923104	−	0.384551i	$-0.874356\pi$
$457$	−7762.71	−	13445.4i	−0.794583	−	1.37626i	0.128520	−	0.991707i	$-0.458977\pi$
$458$	−2712.36			−0.276725
$459$	−60.9982	+	509.966i	−0.00620294	+	0.0518588i
$460$	−1430.46			−0.144990
$461$	28.2090	+	48.8594i	0.00284994	+	0.00493624i	0.867447	−	0.497530i	$-0.165760\pi$
$461$	28.2090	+	48.8594i	0.00284994	+	0.00493624i	−0.864597	+	0.502466i	$0.832426\pi$
$462$	65.8901	−	1659.57i	0.00663525	−	0.167122i
$463$	−6686.89	+	11582.0i	−0.671201	+	1.16255i	0.306363	+	0.951915i	$0.400888\pi$
$463$	−6686.89	+	11582.0i	−0.671201	+	1.16255i	−0.977564	+	0.210640i	$0.932445\pi$
$464$	−3232.68	+	5599.17i	−0.323434	+	0.560204i
$465$	6419.53	−	3374.10i	0.640212	−	0.336495i
$466$	2421.62	+	4194.37i	0.240729	+	0.416954i
$467$	2677.46			0.265306			0.132653	−	0.991163i	$-0.457650\pi$
$467$	2677.46			0.265306			0.132653	+	0.991163i	$0.457650\pi$
$468$	−755.776	−	1587.88i	−0.0746490	−	0.156838i
$469$	−1138.14			−0.112056
$470$	−760.972	−	1318.04i	−0.0746830	−	0.129355i
$471$	1750.48	+	1105.48i	0.171248	+	0.108148i
$472$	−9094.66	+	15752.4i	−0.886898	+	1.53615i
$473$	11025.8	−	19097.2i	1.07181	−	1.85643i
$474$	−11646.4	−	7355.02i	−1.12856	−	0.712716i
$475$	1195.88	+	2071.33i	0.115517	+	0.200082i
$476$	−32.2456			−0.00310499
$477$	5303.96	+	421.831i	0.509123	+	0.0404912i
$478$	−1923.75			−0.184080
$479$	1734.96	+	3005.05i	0.165496	+	0.286647i	0.936831	−	0.349782i	$-0.113744\pi$
$479$	1734.96	+	3005.05i	0.165496	+	0.286647i	−0.771335	+	0.636429i	$0.780411\pi$
$480$	−3083.09	+	1620.47i	−0.293173	+	0.154092i
$481$	−2799.31	+	4848.55i	−0.265359	+	0.459616i
$482$	−524.320	+	908.149i	−0.0495480	+	0.0858196i
$483$	−51.2270	+	1290.25i	−0.00482589	+	0.121550i
$484$	2295.91	+	3976.64i	0.215619	+	0.373463i
$485$	3626.68			0.339544
$486$	7876.89	−	2655.75i	0.735191	−	0.247875i
$487$	−14040.6			−1.30645			−0.653224	−	0.757165i	$-0.726584\pi$
$487$	−14040.6			−1.30645			−0.653224	+	0.757165i	$0.726584\pi$
$488$	−5994.38	−	10382.6i	−0.556051	−	0.963108i
$489$	98.5669	−	2482.60i	0.00911523	−	0.229585i
$490$	1839.76	−	3186.56i	0.169616	−	0.293784i
$491$	−4907.72	+	8500.42i	−0.451084	+	0.781301i	−0.998454	−	0.0555902i	$-0.982296\pi$
$491$	−4907.72	+	8500.42i	−0.451084	+	0.781301i	0.547369	+	0.836891i	$0.315629\pi$
$492$	950.060	−	499.351i	0.0870570	−	0.0457571i
$493$	416.934	+	722.151i	0.0380888	+	0.0659717i
$494$	4294.07			0.391092
$495$	−7086.58	−	563.606i	−0.643471	−	0.0511762i
$496$	−7923.12			−0.717255
$497$	429.212	+	743.418i	0.0387380	+	0.0670962i
$498$	−8727.28	−	5511.53i	−0.785299	−	0.495939i
$499$	6026.00	−	10437.3i	0.540603	−	0.936351i	−0.458267	−	0.888815i	$-0.651530\pi$
$499$	6026.00	−	10437.3i	0.540603	−	0.936351i	0.998869	−	0.0475367i	$-0.0151371\pi$
$500$	−199.026	+	344.723i	−0.0178014	+	0.0308330i
$501$	−1495.34	−	944.354i	−0.133347	−	0.0842128i
$502$	7562.36	+	13098.4i	0.672360	+	1.16456i
$503$	−4695.09			−0.416191			−0.208095	−	0.978109i	$-0.566726\pi$
$503$	−4695.09			−0.416191			−0.208095	+	0.978109i	$0.566726\pi$
$504$	787.760	+	1655.08i	0.0696223	+	0.146276i
$505$	−4888.91			−0.430799
$506$	5190.89	+	8990.89i	0.456054	+	0.789909i
$507$	8180.98	−	4299.92i	0.716627	−	0.376659i
$508$	−3245.31	+	5621.05i	−0.283440	+	0.490932i
$509$	409.907	−	709.979i	0.0356951	−	0.0618257i	−0.847626	−	0.530594i	$-0.821969\pi$
$509$	409.907	−	709.979i	0.0356951	−	0.0618257i	0.883321	+	0.468769i	$0.155302\pi$
$510$	8.28016	−	208.552i	0.000718925	−	0.0181076i
$511$	70.5702	+	122.231i	0.00610928	+	0.0105816i
$512$	9378.41			0.809514
$513$	1594.09	−	13327.2i	0.137195	−	1.14700i
$514$	15924.4			1.36653
$515$	3969.26	+	6874.96i	0.339624	+	0.588247i
$516$	−274.891	+	6923.67i	−0.0234523	+	0.590693i
$517$	3652.13	−	6325.68i	0.310678	−	0.538110i
$518$	830.748	−	1438.90i	0.0704652	−	0.122049i
$519$	−17368.1	+	9128.68i	−1.46893	+	0.772070i
$520$	1255.00	+	2173.73i	0.105837	+	0.183316i
$521$	3282.80			0.276050			0.138025	−	0.990429i	$-0.455925\pi$
$521$	3282.80			0.276050			0.138025	+	0.990429i	$0.455925\pi$
$522$	7653.38	−	11116.1i	0.641723	−	0.932066i
$523$	−10768.1			−0.900300			−0.450150	−	0.892953i	$-0.648629\pi$
$523$	−10768.1			−0.900300			−0.450150	+	0.892953i	$0.648629\pi$
$524$	375.196	+	649.859i	0.0312796	+	0.0541779i
$525$	303.808	+	191.864i	0.0252558	+	0.0159498i
$526$	−6931.76	+	12006.2i	−0.574599	+	0.995235i
$527$	−510.941	+	884.975i	−0.0422333	+	0.0731502i
$528$	6566.71	+	4147.07i	0.541249	+	0.341815i
$529$	2047.78	+	3546.87i	0.168306	+	0.291515i
$530$	−2162.22			−0.177209
$531$	11347.3	−	16481.2i	0.927362	−	1.34694i
$532$	842.690			0.0686752
$533$	−663.353	−	1148.96i	−0.0539081	−	0.0933716i
$534$	6698.32	−	3520.63i	0.542818	−	0.285305i
$535$	2244.33	−	3887.29i	0.181366	−	0.314135i
$536$	5049.44	−	8745.89i	0.406908	−	0.704785i
$537$	38.4765	−	969.106i	0.00309196	−	0.0778771i
$538$	6304.88	+	10920.4i	0.505247	+	0.875113i
$539$	17659.1			1.41119
$540$	2053.49	−	879.242i	0.163645	−	0.0700677i
$541$	−16037.9			−1.27453			−0.637266	−	0.770644i	$-0.719935\pi$
$541$	−16037.9			−1.27453			−0.637266	+	0.770644i	$0.719935\pi$
$542$	5404.04	+	9360.06i	0.428272	+	0.741788i
$543$	296.585	−	7470.08i	0.0234395	−	0.590372i
$544$	245.388	−	425.025i	0.0193399	−	0.0334978i
$545$	2138.73	−	3704.39i	0.168097	−	0.291153i
$546$	571.037	−	300.137i	0.0447585	−	0.0235250i
$547$	−1024.56	−	1774.59i	−0.0800862	−	0.138713i	0.823201	−	0.567751i	$-0.192186\pi$
$547$	−1024.56	−	1774.59i	−0.0800862	−	0.138713i	−0.903287	+	0.429037i	$0.858853\pi$
$548$	9466.92			0.737968
$549$	5668.04	+	11908.5i	0.440630	+	0.925764i
$550$	2888.93			0.223972
$551$	−10895.9	−	18872.3i	−0.842437	−	1.45914i
$552$	−9687.52	−	6117.95i	−0.746971	−	0.471734i
$553$	−1670.69	+	2893.72i	−0.128472	+	0.222520i
$554$	2552.01	−	4420.21i	0.195712	−	0.338983i
$555$	−6012.91	−	3797.33i	−0.459881	−	0.290428i
$556$	−3335.09	−	5776.54i	−0.254387	−	0.440611i
$557$	3644.07			0.277207			0.138603	−	0.990348i	$-0.455739\pi$
$557$	3644.07			0.277207			0.138603	+	0.990348i	$0.455739\pi$
$558$	16486.9	+	1311.23i	1.25080	+	0.0994778i
$559$	8565.12			0.648061
$560$	−196.280	−	339.967i	−0.0148113	−	0.0256540i
$561$	886.679	−	466.038i	0.0667301	−	0.0350733i
$562$	3602.64	−	6239.96i	0.270406	−	0.468357i
$563$	−175.368	+	303.746i	−0.0131277	+	0.0227378i	−0.872515	−	0.488588i	$-0.837512\pi$
$563$	−175.368	+	303.746i	−0.0131277	+	0.0227378i	0.859387	+	0.511326i	$0.170845\pi$
$564$	−91.0536	+	2293.37i	−0.00679796	+	0.171220i
$565$	2275.60	+	3941.46i	0.169443	+	0.293484i
$566$	−4420.07			−0.328250
$567$	−719.525	−	1883.71i	−0.0532932	−	0.139521i
$568$	−7616.93			−0.562675
$569$	9724.34	+	16843.1i	0.716460	+	1.24095i	0.962394	+	0.271658i	$0.0875721\pi$
$569$	9724.34	+	16843.1i	0.716460	+	1.24095i	−0.245934	+	0.969287i	$0.579095\pi$
$570$	−216.389	+	5450.20i	−0.0159010	+	0.400498i
$571$	7572.97	−	13116.8i	0.555024	−	0.961330i	−0.442877	−	0.896582i	$-0.646042\pi$
$571$	7572.97	−	13116.8i	0.555024	−	0.961330i	0.997902	−	0.0647480i	$-0.0206244\pi$
$572$	−1714.90	+	2970.29i	−0.125356	+	0.217123i
$573$	1795.82	−	943.880i	0.130927	−	0.0688153i
$574$	196.862	+	340.975i	0.0143151	+	0.0247945i
$575$	−2246.03			−0.162897
$576$	−14029.8	−	1115.81i	−1.01489	−	0.0807154i
$577$	−6365.11			−0.459243			−0.229621	−	0.973280i	$-0.573749\pi$
$577$	−6365.11			−0.459243			−0.229621	+	0.973280i	$0.573749\pi$
$578$	−5375.95	−	9311.41i	−0.386868	−	0.670076i
$579$	−17200.3	−	10862.5i	−1.23458	−	0.779673i
$580$	1813.37	−	3140.85i	0.129821	−	0.224856i
$581$	−1251.94	+	2168.43i	−0.0893965	+	0.154839i
$582$	6992.99	+	4416.28i	0.498056	+	0.314537i
$583$	−5188.57	−	8986.87i	−0.368591	−	0.638419i
$584$	−1252.36			−0.0887381
$585$	−1186.68	−	2493.21i	−0.0838686	−	0.176208i
$586$	−1054.86			−0.0743617
$587$	−5142.18	−	8906.52i	−0.361568	−	0.626254i	0.626651	−	0.779300i	$-0.284425\pi$
$587$	−5142.18	−	8906.52i	−0.361568	−	0.626254i	−0.988219	+	0.153046i	$0.951092\pi$
$588$	−4911.79	+	2581.63i	−0.344488	+	0.181063i
$589$	13352.7	−	23127.5i	0.934103	−	1.61791i
$590$	−4065.77	+	7042.13i	−0.283704	+	0.491389i
$591$	−184.018	+	4634.85i	−0.0128079	+	0.322593i
$592$	3884.73	+	6728.56i	0.269699	+	0.467132i
$593$	666.566			0.0461595			0.0230798	−	0.999734i	$-0.492653\pi$
$593$	666.566			0.0461595			0.0230798	+	0.999734i	$0.492653\pi$
$594$	−12978.1	−	9716.23i	−0.896461	−	0.671148i
$595$	−50.6303			−0.00348847
$596$	436.165	+	755.460i	0.0299765	+	0.0519209i
$597$	−571.113	+	14384.6i	−0.0391526	+	0.986136i
$598$	−2016.21	+	3492.18i	−0.137875	+	0.238806i
$599$	−12606.6	+	21835.3i	−0.859922	+	1.48943i	0.0120807	+	0.999927i	$0.496155\pi$
$599$	−12606.6	+	21835.3i	−0.859922	+	1.48943i	−0.872003	+	0.489501i	$0.837179\pi$
$600$	−2822.22	+	1483.36i	−0.192028	+	0.100930i
$601$	10309.3	+	17856.3i	0.699712	+	1.21194i	0.968566	+	0.248755i	$0.0800215\pi$
$601$	10309.3	+	17856.3i	0.699712	+	1.21194i	−0.268855	+	0.963181i	$0.586645\pi$
$602$	−2541.86			−0.172090
$603$	−6300.11	+	9150.54i	−0.425473	+	0.617975i
$604$	2983.30			0.200975
$605$	3604.92	+	6243.90i	0.242249	+	0.419588i
$606$	−9426.83	−	5953.32i	−0.631912	−	0.399071i
$607$	2541.76	−	4402.45i	0.169962	−	0.294382i	−0.768444	−	0.639916i	$-0.778969\pi$
$607$	2541.76	−	4402.45i	0.169962	−	0.294382i	0.938406	+	0.345534i	$0.112302\pi$
$608$	−6412.85	+	11107.4i	−0.427755	+	0.740894i
$609$	−2768.06	−	1748.11i	−0.184183	−	0.116317i
$610$	−2679.79	−	4641.53i	−0.177871	−	0.308082i
$611$	2837.07			0.187849
$612$	−178.494	+	259.252i	−0.0117895	+	0.0171236i
$613$	2625.18			0.172969			0.0864845	−	0.996253i	$-0.472437\pi$
$613$	2625.18			0.172969			0.0864845	+	0.996253i	$0.472437\pi$
$614$	3535.47	+	6123.62i	0.232378	+	0.402491i
$615$	1491.73	−	784.054i	0.0978090	−	0.0514083i
$616$	1787.48	−	3096.00i	0.116915	−	0.202502i
$617$	815.659	−	1412.76i	0.0532208	−	0.0921811i	−0.838188	−	0.545382i	$-0.816385\pi$
$617$	815.659	−	1412.76i	0.0532208	−	0.0921811i	0.891408	+	0.453201i	$0.149718\pi$
$618$	−718.220	+	18089.8i	−0.0467493	+	1.17747i
$619$	−1592.33	−	2758.00i	−0.103395	−	0.179085i	0.809687	−	0.586863i	$-0.199637\pi$
$619$	−1592.33	−	2758.00i	−0.103395	−	0.179085i	−0.913081	+	0.407778i	$0.866304\pi$
$620$	4444.47			0.287894
$621$	10090.0	+	7553.99i	0.652007	+	0.488134i
$622$	−5297.40			−0.341489
$623$	−917.821	−	1589.71i	−0.0590236	−	0.102232i
$624$	−119.676	+	3014.27i	−0.00767767	+	0.193377i
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−2750.67	+	4764.29i	−0.175621	+	0.304184i
$627$	−23172.0	+	12179.2i	−1.47592	+	0.775742i
$628$	634.392	+	1098.80i	0.0403105	+	0.0698199i
$629$	1002.06			0.0635214
$630$	352.169	+	739.907i	0.0222710	+	0.0467914i
$631$	10436.7			0.658447			0.329223	−	0.944252i	$-0.393213\pi$
$631$	10436.7			0.658447			0.329223	+	0.944252i	$0.393213\pi$
$632$	−14824.3	−	25676.4i	−0.933037	−	1.61607i
$633$	20132.7	+	12714.4i	1.26415	+	0.798346i
$634$	4067.54	−	7045.18i	0.254799	−	0.441325i
$635$	−5095.62	+	8825.87i	−0.318446	+	0.551565i
$636$	2756.99	+	1741.12i	0.171889	+	0.108553i
$637$	3429.52	+	5940.11i	0.213316	+	0.369475i
$638$	−26321.7			−1.63336
$639$	8352.89	+	664.317i	0.517113	+	0.0411267i
$640$	356.968			0.0220475
$641$	−4541.73	−	7866.50i	−0.279856	−	0.484724i	0.691493	−	0.722383i	$-0.256953\pi$
$641$	−4541.73	−	7866.50i	−0.279856	−	0.484724i	−0.971349	+	0.237659i	$0.923620\pi$
$642$	9061.16	−	4762.54i	0.557034	−	0.292776i
$643$	−8593.81	+	14884.9i	−0.527071	+	0.912914i	0.472431	+	0.881368i	$0.343377\pi$
$643$	−8593.81	+	14884.9i	−0.527071	+	0.912914i	−0.999502	+	0.0315465i	$0.989957\pi$
$644$	−395.672	+	685.323i	−0.0242106	+	0.0419340i
$645$	−431.619	+	10871.2i	−0.0263488	+	0.663647i
$646$	−384.285	−	665.601i	−0.0234048	−	0.0405383i
$647$	2359.17			0.143352			0.0716758	−	0.997428i	$-0.477165\pi$
$647$	2359.17			0.143352			0.0716758	+	0.997428i	$0.477165\pi$
$648$	17667.3	+	2828.11i	1.07105	+	0.171448i
$649$	−39025.7			−2.36039
$650$	561.049	+	971.766i	0.0338556	+	0.0586397i
$651$	159.163	−	4008.85i	0.00958234	−	0.241350i
$652$	761.320	−	1318.64i	0.0457294	−	0.0792057i
$653$	−2718.06	+	4707.81i	−0.162888	+	0.282130i	−0.935903	−	0.352257i	$-0.885414\pi$
$653$	−2718.06	+	4707.81i	−0.162888	+	0.282130i	0.773015	+	0.634387i	$0.218748\pi$
$654$	8634.82	−	4538.46i	0.516282	−	0.271357i
$655$	589.113	+	1020.37i	0.0351428	+	0.0608691i
$656$	−1841.13			−0.109579
$657$	1373.36	+	109.226i	0.0815526	+	0.00648599i
$658$	−841.954			−0.0498826
$659$	−1544.45	−	2675.07i	−0.0912950	−	0.158128i	0.816761	−	0.576976i	$-0.195767\pi$
$659$	−1544.45	−	2675.07i	−0.0912950	−	0.158128i	−0.908056	+	0.418848i	$0.862434\pi$
$660$	−3683.59	−	2326.30i	−0.217248	−	0.137199i
$661$	9526.94	−	16501.2i	0.560598	−	0.970984i	−0.436846	−	0.899536i	$-0.643905\pi$
$661$	9526.94	−	16501.2i	0.560598	−	0.970984i	0.997444	−	0.0714479i	$-0.0227620\pi$
$662$	2801.70	−	4852.68i	0.164488	−	0.284902i
$663$	328.963	+	207.750i	0.0192698	+	0.0121694i
$664$	−11108.7	−	19240.8i	−0.649248	−	1.12453i
$665$	1323.15			0.0771570
$666$	−6970.05	−	14644.1i	−0.405532	−	0.852022i
$667$	20464.1			1.18796
$668$	−541.928	−	938.646i	−0.0313889	−	0.0543672i
$669$	−18836.6	+	9900.51i	−1.08859	+	0.572161i
$670$	2257.36	−	3909.86i	0.130163	−	0.225449i
$671$	12861.1	−	22276.1i	0.739937	−	1.28161i
$672$	−76.4409	+	1925.32i	−0.00438806	+	0.110522i
$673$	14618.7	+	25320.4i	0.837312	+	1.45027i	0.892134	+	0.451771i	$0.149208\pi$
$673$	14618.7	+	25320.4i	0.837312	+	1.45027i	−0.0548215	+	0.998496i	$0.517459\pi$
$674$	−7796.61			−0.445570
$675$	3224.28	−	1380.54i	0.183856	−	0.0787214i
$676$	5663.98			0.322257
$677$	−7235.62	−	12532.5i	−0.410764	−	0.711465i	0.584209	−	0.811603i	$-0.301405\pi$
$677$	−7235.62	−	12532.5i	−0.410764	−	0.711465i	−0.994974	+	0.100138i	$0.968071\pi$
$678$	−411.760	+	10371.0i	−0.0233238	+	0.587457i
$679$	1003.16	−	1737.52i	0.0566975	−	0.0982030i
$680$	224.625	−	389.062i	0.0126676	−	0.0219410i
$681$	17797.2	−	9354.19i	1.00145	−	0.526363i
$682$	−16128.2	−	27934.9i	−0.905545	−	1.56845i
$683$	5782.94			0.323980			0.161990	−	0.986792i	$-0.448209\pi$
$683$	5782.94			0.323980			0.161990	+	0.986792i	$0.448209\pi$
$684$	4664.66	−	6775.15i	0.260757	−	0.378734i
$685$	14864.5			0.829112
$686$	−2058.77	−	3565.89i	−0.114583	−	0.198464i
$687$	5430.28	+	3429.38i	0.301569	+	0.190450i
$688$	5943.10	−	10293.8i	0.329329	−	0.570415i
$689$	2015.31	−	3490.62i	0.111433	−	0.193007i
$690$	−4330.81	−	2735.04i	−0.238944	−	0.150900i
$691$	−5527.56	−	9574.01i	−0.304310	−	0.527080i	0.672797	−	0.739827i	$-0.265093\pi$
$691$	−5527.56	−	9574.01i	−0.304310	−	0.527080i	−0.977107	+	0.212746i	$0.931759\pi$
$692$	−12024.6			−0.660557
$693$	−2230.20	+	3239.24i	−0.122249	+	0.177559i
$694$	17046.5			0.932386
$695$	−5236.58	−	9070.02i	−0.285805	−	0.495029i
$696$	25713.9	−	13515.2i	1.40041	−	0.736052i
$697$	−118.730	+	205.646i	−0.00645223	+	0.0111756i
$698$	763.674	−	1322.72i	0.0414119	−	0.0717275i
$699$	454.962	−	11459.1i	0.0246184	−	0.620064i
$700$	110.103	+	190.704i	0.00594501	+	0.0102971i
$701$	−13554.2			−0.730294			−0.365147	−	0.930950i	$-0.618981\pi$
$701$	−13554.2			−0.730294			−0.365147	+	0.930950i	$0.618981\pi$
$702$	747.872	−	6252.48i	0.0402088	−	0.336160i
$703$	−26187.4			−1.40495
$704$	13724.6	+	23771.7i	0.734751	+	1.27263i
$705$	−142.967	+	3600.92i	−0.00763754	+	0.192367i
$706$	−5981.91	+	10361.0i	−0.318884	+	0.552324i
$707$	−1352.30	+	2342.25i	−0.0719354	+	0.124596i
$708$	10854.8	−	5705.27i	0.576198	−	0.302849i
$709$	4694.58	+	8131.26i	0.248672	+	0.430713i	0.963158	−	0.268937i	$-0.0866724\pi$
$709$	4694.58	+	8131.26i	0.248672	+	0.430713i	−0.714485	+	0.699650i	$0.753339\pi$
$710$	−3405.15			−0.179990
$711$	14017.3	+	29450.3i	0.739365	+	1.55340i
$712$	16287.9			0.857326
$713$	12539.1	+	21718.3i	0.658614	+	1.14075i
$714$	−97.6258	−	61.6536i	−0.00511702	−	0.00323155i
$715$	−2692.64	+	4663.80i	−0.140838	+	0.243939i
$716$	297.188	−	514.745i	0.0155118	−	0.0268672i
$717$	3851.45	+	2432.31i	0.200607	+	0.126689i
$718$	4428.84	+	7670.97i	0.230199	+	0.398716i
$719$	−26301.8			−1.36424			−0.682122	−	0.731238i	$-0.738943\pi$
$719$	−26301.8			−1.36424			−0.682122	+	0.731238i	$0.738943\pi$
$720$	−3819.80	−	303.794i	−0.197716	−	0.0157246i
$721$	4391.67			0.226844
$722$	2516.86	+	4359.33i	0.129734	+	0.224705i
$723$	2197.94	−	1155.23i	0.113060	−	0.0594241i
$724$	2290.79	−	3967.76i	0.117592	−	0.203675i
$725$	2847.26	−	4931.59i	0.145854	−	0.252627i
$726$	−652.294	+	16429.3i	−0.0333456	+	0.839876i
$727$	12769.3	+	22117.1i	0.651427	+	1.12830i	0.982777	+	0.184797i	$0.0591626\pi$
$727$	12769.3	+	22117.1i	0.651427	+	1.12830i	−0.331350	+	0.943508i	$0.607504\pi$
$728$	1388.56			0.0706915
$729$	−19127.7	−	4642.23i	−0.971789	−	0.235850i
$730$	−559.868			−0.0283858
$731$	−766.510	−	1327.63i	−0.0387830	−	0.0671742i
$732$	−320.649	+	8076.18i	−0.0161906	+	0.407792i
$733$	−3491.06	+	6046.70i	−0.175914	+	0.304693i	−0.940477	−	0.339856i	$-0.889622\pi$
$733$	−3491.06	+	6046.70i	−0.175914	+	0.304693i	0.764563	+	0.644549i	$0.222955\pi$
$734$	12332.7	−	21360.8i	0.620174	−	1.07417i
$735$	−7712.23	+	4053.54i	−0.387034	+	0.203425i
$736$	−6022.10	−	10430.6i	−0.301600	−	0.522387i
$737$	21667.5			1.08295
$738$	3831.13	+	304.695i	0.191092	+	0.0151978i
$739$	8863.91			0.441224			0.220612	−	0.975362i	$-0.429195\pi$
$739$	8863.91			0.441224			0.220612	+	0.975362i	$0.429195\pi$
$740$	−2179.14	−	3774.38i	−0.108252	−	0.187499i
$741$	−8596.94	−	5429.22i	−0.426203	−	0.269160i
$742$	−598.081	+	1035.91i	−0.0295906	+	0.0512524i
$743$	19472.4	−	33727.3i	0.961473	−	1.66532i	0.242668	−	0.970110i	$-0.421978\pi$
$743$	19472.4	−	33727.3i	0.961473	−	1.66532i	0.718806	−	0.695211i	$-0.244689\pi$
$744$	30099.3	+	19008.6i	1.48319	+	0.936680i
$745$	684.843	+	1186.18i	0.0336788	+	0.0583334i
$746$	13870.5			0.680742
$747$	10503.9	+	22068.7i	0.514482	+	1.08093i
$748$	613.879			0.0300075
$749$	−1241.58	−	2150.49i	−0.0605694	−	0.104909i
$750$	−1261.68	+	663.136i	−0.0614265	+	0.0322857i
$751$	−8795.16	+	15233.7i	−0.427350	+	0.740192i	−0.996637	−	0.0819470i	$-0.973886\pi$
$751$	−8795.16	+	15233.7i	−0.427350	+	0.740192i	0.569287	+	0.822139i	$0.307220\pi$
$752$	1968.57	−	3409.66i	0.0954604	−	0.165342i
$753$	1420.78	−	35785.2i	0.0687597	−	1.73185i
$754$	−5111.84	−	8853.97i	−0.246900	−	0.427643i
$755$	4684.22			0.225796
$756$	146.766	−	1227.02i	0.00706062	−	0.0590293i
$757$	−4075.85			−0.195693			−0.0978463	−	0.995202i	$-0.531195\pi$
$757$	−4075.85			−0.195693			−0.0978463	+	0.995202i	$0.531195\pi$
$758$	10232.1	+	17722.6i	0.490300	+	0.849225i
$759$	975.239	−	24563.3i	0.0466389	−	1.17469i
$760$	−5870.24	+	10167.6i	−0.280179	+	0.485284i
$761$	−20268.5	+	35106.1i	−0.965483	+	1.67227i	−0.257171	+	0.966366i	$0.582790\pi$
$761$	−20268.5	+	35106.1i	−0.965483	+	1.67227i	−0.708312	+	0.705899i	$0.750543\pi$
$762$	−20572.9	+	10813.1i	−0.978052	+	0.514064i
$763$	−1183.17	−	2049.30i	−0.0561382	−	0.0972343i
$764$	1243.31			0.0588761
$765$	−280.261	+	407.063i	−0.0132456	+	0.0192384i
$766$	−24463.7			−1.15393
$767$	−7579.06	−	13127.3i	−0.356798	−	0.617992i
$768$	−17632.6	−	11135.5i	−0.828464	−	0.523200i
$769$	−12016.3	+	20812.9i	−0.563485	+	0.975985i	0.433704	+	0.901056i	$0.357206\pi$
$769$	−12016.3	+	20812.9i	−0.563485	+	0.975985i	−0.997189	+	0.0749293i	$0.976127\pi$
$770$	799.092	−	1384.07i	0.0373991	−	0.0647771i
$771$	−31881.5	−	20134.1i	−1.48922	−	0.940484i
$772$	−6233.57	−	10796.9i	−0.290610	−	0.503351i
$773$	−20881.5			−0.971611			−0.485805	−	0.874067i	$-0.661474\pi$
$773$	−20881.5			−0.971611			−0.485805	+	0.874067i	$0.661474\pi$
$774$	−14070.3	+	20436.3i	−0.653420	+	0.949055i
$775$	6978.46			0.323450
$776$	8901.16	+	15417.3i	0.411770	+	0.713206i
$777$	−3482.48	+	1830.39i	−0.160789	+	0.0845106i
$778$	7209.64	−	12487.5i	0.332234	−	0.575446i
$779$	3102.82	−	5374.24i	0.142709	−	0.247179i
$780$	67.1320	−	1690.85i	0.00308168	−	0.0776183i
$781$	−8171.18	−	14152.9i	−0.374376	−	0.648439i
$782$	721.740			0.0330043
$783$	−29377.1	+	12578.4i	−1.34081	+	0.574093i
$784$	9518.60			0.433610
$785$	996.089	+	1725.28i	0.0452891	+	0.0784430i
$786$	−106.597	+	2684.87i	−0.00483741	+	0.121840i
$787$	2568.20	−	4448.25i	0.116323	−	0.201478i	−0.801985	−	0.597345i	$-0.796223\pi$
$787$	2568.20	−	4448.25i	0.116323	−	0.201478i	0.918308	+	0.395867i	$0.129556\pi$
$788$	−1421.33	+	2461.82i	−0.0642549	+	0.111293i
$789$	29057.8	−	15272.7i	1.31113	−	0.689130i
$790$	−6627.21	−	11478.7i	−0.298463	−	0.516953i
$791$	2517.77			0.113175
$792$	−14997.1	−	31508.9i	−0.672851	−	1.41366i
$793$	9990.86			0.447397
$794$	4355.23	+	7543.48i	0.194662	+	0.337164i
$795$	4328.87	+	2733.81i	0.193119	+	0.121960i
$796$	−4411.22	+	7640.45i	−0.196421	+	0.340212i
$797$	−10998.0	+	19049.1i	−0.488794	+	0.846615i	−0.999917	−	0.0128922i	$-0.995896\pi$
$797$	−10998.0	+	19049.1i	−0.488794	+	0.846615i	0.511123	+	0.859507i	$0.329230\pi$
$798$	2551.30	+	1611.22i	0.113177	+	0.0714745i
$799$	−253.895	−	439.760i	−0.0112418	−	0.0194713i
$800$	−3351.53			−0.148118
$801$	−17861.7	−	1420.57i	−0.787905	−	0.0626632i
$802$	−9600.03			−0.422679
$803$	−1343.49	−	2326.99i	−0.0590419	−	0.102264i
$804$	−6026.69	+	3167.62i	−0.264359	+	0.138947i
$805$	−621.262	+	1076.06i	−0.0272008	+	0.0471131i
$806$	6264.42	−	10850.3i	0.273765	−	0.474175i
$807$	1184.53	−	29834.7i	0.0516696	−	1.30140i
$808$	−11999.1	−	20783.1i	−0.522435	−	0.904885i
$809$	31094.2			1.35132			0.675658	−	0.737215i	$-0.263860\pi$
$809$	31094.2			1.35132			0.675658	+	0.737215i	$0.263860\pi$
$810$	7898.20	+	1264.31i	0.342610	+	0.0548435i
$811$	19130.6			0.828320			0.414160	−	0.910204i	$-0.364075\pi$
$811$	19130.6			0.828320			0.414160	+	0.910204i	$0.364075\pi$
$812$	−1003.17	−	1737.55i	−0.0433553	−	0.0750936i
$813$	1015.28	−	25571.9i	0.0437977	−	1.10313i
$814$	−15815.5	+	27393.2i	−0.680997	+	1.17952i
$815$	1195.38	−	2070.47i	0.0513773	−	0.0889881i
$816$	477.937	−	251.203i	0.0205038	−	0.0107768i
$817$	20031.6	+	34695.7i	0.857792	+	1.48574i
$818$	19469.8			0.832208
$819$	−1522.72	−	121.104i	−0.0649674	−	0.00516694i
$820$	1032.78			0.0439832
$821$	1778.81	+	3080.99i	0.0756162	+	0.130971i	0.901354	−	0.433083i	$-0.142574\pi$
$821$	1778.81	+	3080.99i	0.0756162	+	0.130971i	−0.825738	+	0.564054i	$0.809241\pi$
$822$	28661.8	+	18100.7i	1.21617	+	0.768049i
$823$	−3074.69	+	5325.52i	−0.130227	+	0.225560i	−0.923764	−	0.382962i	$-0.874904\pi$
$823$	−3074.69	+	5325.52i	−0.130227	+	0.225560i	0.793537	+	0.608522i	$0.208237\pi$
$824$	−19484.0	+	33747.2i	−0.823733	+	1.42675i
$825$	−5783.78	−	3652.63i	−0.244079	−	0.154143i
$826$	2249.23	+	3895.77i	0.0947464	+	0.164106i
$827$	21152.8			0.889425			0.444713	−	0.895673i	$-0.353306\pi$
$827$	21152.8			0.889425			0.444713	+	0.895673i	$0.353306\pi$
$828$	3319.72	+	6974.73i	0.139334	+	0.292740i
$829$	−17402.4			−0.729083			−0.364541	−	0.931187i	$-0.618774\pi$
$829$	−17402.4			−0.729083			−0.364541	+	0.931187i	$0.618774\pi$
$830$	−4966.14	−	8601.61i	−0.207684	−	0.359719i
$831$	−10698.0	+	5622.84i	−0.446580	+	0.234722i
$832$	−5330.81	+	9233.24i	−0.222131	+	0.384742i
$833$	613.829	−	1063.18i	0.0255317	−	0.0442222i
$834$	947.536	−	23865.6i	0.0393411	−	0.990884i
$835$	−850.906	−	1473.81i	−0.0352657	−	0.0610819i
$836$	−16042.8			−0.663698
$837$	−31349.7	−	23470.4i	−1.29463	−	0.969243i
$838$	2225.55			0.0917425
$839$	9037.12	+	15652.8i	0.371867	+	0.644092i	0.989853	−	0.142097i	$-0.0453845\pi$
$839$	9037.12	+	15652.8i	0.371867	+	0.644092i	−0.617986	+	0.786189i	$0.712051\pi$
$840$	−69.9731	+	1762.41i	−0.00287417	+	0.0723917i
$841$	−13747.5	+	23811.3i	−0.563675	+	0.976314i
$842$	−16341.1	+	28303.6i	−0.668825	+	1.15844i
$843$	−15102.2	+	7937.69i	−0.617019	+	0.324304i
$844$	7296.31	+	12637.6i	0.297570	+	0.515407i
$845$	8893.28			0.362057
$846$	−4660.59	+	6769.23i	−0.189402	+	0.275096i
$847$	3988.55			0.161804
$848$	−2796.74	−	4844.09i	−0.113255	−	0.196164i
$849$	8849.21	+	5588.54i	0.357720	+	0.225911i
$850$	100.419	−	173.931i	0.00405216	−	0.00701855i
$851$	12295.9	−	21297.1i	0.495297	−	0.857880i
$852$	4341.82	+	2741.99i	0.174587	+	0.110257i
$853$	−20396.1	−	35327.2i	−0.818699	−	1.41803i	−0.906641	−	0.421903i	$-0.861362\pi$
$853$	−20396.1	−	35327.2i	−0.818699	−	1.41803i	0.0879416	−	0.996126i	$-0.471971\pi$
$854$	−2964.97			−0.118805
$855$	7324.20	−	10638.0i	0.292962	−	0.425510i
$856$	22033.5			0.879778
$857$	5528.93	+	9576.39i	0.220379	+	0.381707i	0.954923	−	0.296854i	$-0.0959373\pi$
$857$	5528.93	+	9576.39i	0.220379	+	0.381707i	−0.734544	+	0.678561i	$0.762604\pi$
$858$	−10871.2	+	5713.88i	−0.432559	+	0.227353i
$859$	876.815	−	1518.69i	0.0348272	−	0.0603224i	−0.848086	−	0.529858i	$-0.822245\pi$
$859$	876.815	−	1518.69i	0.0348272	−	0.0603224i	0.882914	+	0.469535i	$0.155579\pi$
$860$	−3333.78	+	5774.27i	−0.132187	+	0.228955i
$861$	36.9855	−	931.554i	0.00146395	−	0.0368725i
$862$	−4788.17	−	8293.35i	−0.189194	−	0.327694i
$863$	−19186.5			−0.756796			−0.378398	−	0.925643i	$-0.623525\pi$
$863$	−19186.5			−0.756796			−0.378398	+	0.925643i	$0.623525\pi$
$864$	15056.3	+	11272.1i	0.592852	+	0.443847i
$865$	−18880.3			−0.742140
$866$	10205.9	+	17677.2i	0.400475	+	0.693642i
$867$	−1010.01	+	25439.0i	−0.0395635	+	0.996487i
$868$	1229.36	−	2129.32i	0.0480728	−	0.0832646i
$869$	31806.0	−	55089.6i	1.24159	−	2.15050i
$870$	11495.4	−	6041.98i	0.447966	−	0.235451i
$871$	4207.97	+	7288.41i	0.163699	+	0.283534i
$872$	20996.8			0.815415
$873$	−8416.58	−	17683.2i	−0.326298	−	0.685552i
$874$	−18861.6			−0.729980
$875$	172.878	+	299.434i	0.00667925	+	0.0115688i
$876$	713.872	+	450.831i	0.0275337	+	0.0173883i
$877$	4257.30	−	7373.86i	0.163921	−	0.283920i	−0.772350	−	0.635197i	$-0.780919\pi$
$877$	4257.30	−	7373.86i	0.163921	−	0.283920i	0.936272	+	0.351277i	$0.114252\pi$
$878$	1667.94	−	2888.96i	0.0641121	−	0.111045i
$879$	2111.89	+	1333.72i	0.0810377	+	0.0511777i
$880$	3736.70	+	6472.16i	0.143141	+	0.247928i
$881$	41177.0			1.57467			0.787337	−	0.616522i	$-0.211459\pi$
$881$	41177.0			1.57467			0.787337	+	0.616522i	$0.211459\pi$
$882$	−19806.9	−	1575.27i	−0.756159	−	0.0601384i
$883$	32540.4			1.24017			0.620086	−	0.784533i	$-0.287098\pi$
$883$	32540.4			1.24017			0.620086	+	0.784533i	$0.287098\pi$
$884$	119.219	+	206.494i	0.00453595	+	0.00785650i
$885$	17043.6	−	8958.11i	0.647362	−	0.340253i
$886$	4896.34	−	8480.70i	0.185661	−	0.321574i
$887$	−1083.05	+	1875.90i	−0.0409980	+	0.0710106i	−0.885796	−	0.464074i	$-0.846387\pi$
$887$	−1083.05	+	1875.90i	−0.0409980	+	0.0710106i	0.844798	+	0.535085i	$0.179720\pi$
$888$	1384.89	−	34881.3i	0.0523356	−	1.31818i
$889$	2818.95	+	4882.56i	0.106349	+	0.184202i
$890$	7281.53			0.274244
$891$	13698.1	+	35861.3i	0.515041	+	1.34837i
$892$	−13041.2			−0.489522
$893$	6635.17	+	11492.4i	0.248642	+	0.430661i
$894$	−123.919	+	3121.15i	−0.00463588	+	0.116764i
$895$	466.629	−	808.225i	0.0174276	−	0.0301855i
$896$	98.7391	−	171.021i	0.00368152	−	0.00637658i
$897$	8451.92	−	4442.32i	0.314606	−	0.165356i
$898$	−5893.91	−	10208.5i	−0.219023	−	0.379358i
$899$	−63582.3			−2.35883
$900$	2142.71	+	170.413i	0.0793598	+	0.00631160i
$901$	−721.416			−0.0266747
$902$	−3747.79	−	6491.36i	−0.138346	−	0.239622i
$903$	5088.93	+	3213.81i	0.187540	+	0.118437i
$904$	−11170.3	+	19347.5i	−0.410971	+	0.711823i
$905$	3596.88	−	6229.97i	0.132115	−	0.228830i
$906$	9032.15	+	5704.07i	0.331207	+	0.209167i
$907$	353.031	+	611.468i	0.0129241	+	0.0223853i	0.872415	−	0.488766i	$-0.162553\pi$
$907$	353.031	+	611.468i	0.0129241	+	0.0223853i	−0.859491	+	0.511151i	$0.829219\pi$
$908$	12321.6			0.450339
$909$	11345.9	+	23837.7i	0.413993	+	0.869799i
$910$	620.756			0.0226130
$911$	247.743	+	429.103i	0.00900997	+	0.0156057i	0.870495	−	0.492177i	$-0.163799\pi$
$911$	247.743	+	429.103i	0.00900997	+	0.0156057i	−0.861485	+	0.507783i	$0.830465\pi$
$912$	−12490.1	+	6564.81i	−0.453498	+	0.238358i
$913$	23834.0	−	41281.7i	0.863955	−	1.49641i
$914$	17034.8	−	29505.2i	0.616480	−	1.06777i
$915$	−503.465	+	12680.8i	−0.0181902	+	0.458157i
$916$	1967.99	+	3408.66i	0.0709871	+	0.122953i
$917$	651.806			0.0234728
$918$	−1036.09	+	443.623i	−0.0372507	+	0.0159496i
$919$	20473.6			0.734889			0.367445	−	0.930045i	$-0.380233\pi$
$919$	20473.6			0.734889			0.367445	+	0.930045i	$0.380233\pi$
$920$	−5512.56	−	9548.03i	−0.197547	−	0.342162i
$921$	664.227	−	16729.9i	0.0237644	−	0.598554i
$922$	−61.9030	+	107.219i	−0.00221114	+	0.00382980i
$923$	3173.80	−	5497.17i	0.113182	−	0.196037i
$924$	−2133.41	+	1121.32i	−0.0759569	+	0.0399229i
$925$	−3421.57	−	5926.33i	−0.121622	−	0.210656i
$926$	−29348.0			−1.04151
$927$	24309.8	−	35308.6i	0.861316	−	1.25101i
$928$	30536.5			1.08018
$929$	−24857.7	−	43054.7i	−0.877883	−	1.52054i	−0.853660	−	0.520831i	$-0.825622\pi$
$929$	−24857.7	−	43054.7i	−0.877883	−	1.52054i	−0.0242231	−	0.999707i	$-0.507711\pi$
$930$	13455.9	+	8497.82i	0.474449	+	0.299628i
$931$	−16041.5	+	27784.7i	−0.564704	+	0.978095i
$932$	3514.08	−	6086.57i	0.123506	−	0.213919i
$933$	10605.7	+	6697.79i	0.372148	+	0.235022i
$934$	2937.77	+	5088.36i	0.102919	+	0.178261i
$935$	963.880			0.0337136
$936$	7686.29	−	11163.9i	0.268413	−	0.389854i
$937$	−31524.9			−1.09912			−0.549560	−	0.835454i	$-0.685204\pi$
$937$	−31524.9			−1.09912			−0.549560	+	0.835454i	$0.685204\pi$
$938$	−1248.79	−	2162.97i	−0.0434696	−	0.0752916i
$939$	11530.7	−	6060.54i	0.400736	−	0.210626i
$940$	−1104.27	+	1912.64i	−0.0383161	+	0.0663655i
$941$	−18764.2	+	32500.6i	−0.650050	+	1.12592i	0.333060	+	0.942905i	$0.391919\pi$
$941$	−18764.2	+	32500.6i	−0.650050	+	1.12592i	−0.983110	+	0.183014i	$0.941415\pi$
$942$	−180.238	+	4539.65i	−0.00623404	+	0.157017i
$943$	2913.76	+	5046.78i	0.100620	+	0.174280i
$944$	−21035.6			−0.725265
$945$	230.444	−	1926.60i	0.00793265	−	0.0663198i
$946$	48390.9			1.66313
$947$	−12931.7	−	22398.3i	−0.443741	−	0.768582i	0.554222	−	0.832369i	$-0.313016\pi$
$947$	−12931.7	−	22398.3i	−0.443741	−	0.768582i	−0.997964	+	0.0637862i	$0.979682\pi$
$948$	−792.975	+	19972.7i	−0.0271673	+	0.684264i
$949$	521.829	−	903.834i	0.0178496	−	0.0309164i
$950$	−2624.29	+	4545.41i	−0.0896246	+	0.155234i
$951$	−17051.0	+	8962.00i	−0.581406	+	0.305586i
$952$	−124.265	−	215.233i	−0.00423051	−	0.00732746i
$953$	1060.03			0.0360312			0.0180156	−	0.999838i	$-0.494265\pi$
$953$	1060.03			0.0360312			0.0180156	+	0.999838i	$0.494265\pi$
$954$	5017.95	+	10542.7i	0.170296	+	0.357791i
$955$	1952.18			0.0661476
$956$	1395.81	+	2417.61i	0.0472213	+	0.0817897i
$957$	52697.3	+	33279.9i	1.78000	+	1.12412i
$958$	−3807.28	+	6594.40i	−0.128400	+	0.222396i
$959$	4111.58	−	7121.46i	0.138446	−	0.239796i
$960$	−11450.6	−	7231.36i	−0.384963	−	0.243116i
$961$	−24063.7	−	41679.5i	−0.807750	−	1.39906i
$962$	−12285.9			−0.411759
$963$	−24162.4	−	1921.67i	−0.808540	−	0.0643043i
$964$	1521.71			0.0508412
$965$	−9787.62	−	16952.6i	−0.326502	−	0.565518i
$966$	−2508.26	+	1318.34i	−0.0835424	+	0.0439098i
$967$	2592.51	−	4490.35i	0.0862145	−	0.149328i	−0.819694	−	0.572802i	$-0.805856\pi$
$967$	2592.51	−	4490.35i	0.0862145	−	0.149328i	0.905908	+	0.423474i	$0.139190\pi$
$968$	−17695.5	+	30649.5i	−0.587557	+	1.01768i
$969$	−72.1975	+	1818.44i	−0.00239352	+	0.0602855i
$970$	3979.27	+	6892.30i	0.131718	+	0.228143i
$971$	28314.9			0.935805			0.467903	−	0.883780i	$-0.345010\pi$
$971$	28314.9			0.935805			0.467903	+	0.883780i	$0.345010\pi$
$972$	−9052.69	−	7972.07i	−0.298730	−	0.263070i
$973$	−5793.85			−0.190897
$974$	−15405.6	−	26683.4i	−0.506806	−	0.877813i
$975$	105.407	−	2654.89i	0.00346229	−	0.0872046i
$976$	6932.38	−	12007.2i	0.227357	−	0.393793i
$977$	−22448.3	+	38881.6i	−0.735093	+	1.27322i	0.219590	+	0.975592i	$0.429528\pi$
$977$	−22448.3	+	38881.6i	−0.735093	+	1.27322i	−0.954683	+	0.297626i	$0.903805\pi$
$978$	4826.20	−	2536.65i	0.157796	−	0.0829376i
$979$	17473.1	+	30264.3i	0.570422	+	0.988001i
$980$	−5339.45			−0.174043
$981$	−23025.6	−	1831.26i	−0.749388	−	0.0595999i
$982$	−21539.4			−0.699950
$983$	7286.40	+	12620.4i	0.236419	+	0.409490i	0.959684	−	0.281081i	$-0.0906928\pi$
$983$	7286.40	+	12620.4i	0.236419	+	0.409490i	−0.723265	+	0.690571i	$0.757360\pi$
$984$	6994.32	+	4417.12i	0.226596	+	0.143102i
$985$	−2231.70	+	3865.42i	−0.0721908	+	0.125038i
$986$	−914.938	+	1584.72i	−0.0295513	+	0.0511843i
$987$	1685.63	+	1064.53i	0.0543610	+	0.0343306i
$988$	−3115.62	−	5396.41i	−0.100325	−	0.173768i
$989$	−37622.0			−1.20962
$990$	−6704.45	−	14086.1i	−0.215234	−	0.452206i
$991$	10602.1			0.339844			0.169922	−	0.985457i	$-0.445648\pi$
$991$	10602.1			0.339844			0.169922	+	0.985457i	$0.445648\pi$
$992$	18710.8	+	32408.1i	0.598860	+	1.03726i
$993$	−11744.6	+	6172.98i	−0.375332	+	0.197274i
$994$	−941.882	+	1631.39i	−0.0300550	+	0.0520568i
$995$	−6926.26	+	11996.6i	−0.220681	+	0.382230i
$996$	−594.221	+	14966.6i	−0.0189042	+	0.476141i
$997$	−13948.5	−	24159.5i	−0.443082	−	0.767441i	0.554834	−	0.831961i	$-0.312782\pi$
$997$	−13948.5	−	24159.5i	−0.443082	−	0.767441i	−0.997916	+	0.0645202i	$0.979448\pi$
$998$	26447.4			0.838857
$999$	−4560.91	+	38130.8i	−0.144445	+	1.20761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.e.c.31.5	yes	14
3.2	odd	2		135.4.e.c.91.3		14
5.2	odd	4		225.4.k.d.49.5		28
5.3	odd	4		225.4.k.d.49.10		28
5.4	even	2		225.4.e.d.76.3		14
9.2	odd	6		135.4.e.c.46.3		14
9.4	even	3		405.4.a.m.1.3		7
9.5	odd	6		405.4.a.n.1.5		7
9.7	even	3	inner	45.4.e.c.16.5	✓	14
45.4	even	6		2025.4.a.bb.1.5		7
45.7	odd	12		225.4.k.d.124.10		28
45.14	odd	6		2025.4.a.ba.1.3		7
45.34	even	6		225.4.e.d.151.3		14
45.43	odd	12		225.4.k.d.124.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.5	✓	14	9.7	even	3	inner
45.4.e.c.31.5	yes	14	1.1	even	1	trivial
135.4.e.c.46.3		14	9.2	odd	6
135.4.e.c.91.3		14	3.2	odd	2
225.4.e.d.76.3		14	5.4	even	2
225.4.e.d.151.3		14	45.34	even	6
225.4.k.d.49.5		28	5.2	odd	4
225.4.k.d.49.10		28	5.3	odd	4
225.4.k.d.124.5		28	45.43	odd	12
225.4.k.d.124.10		28	45.7	odd	12
405.4.a.m.1.3		7	9.4	even	3
405.4.a.n.1.5		7	9.5	odd	6
2025.4.a.ba.1.3		7	45.14	odd	6
2025.4.a.bb.1.5		7	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09722 + 1.90044i) q^{2} +(0.206141 - 5.19206i) q^{3} +(1.59221 - 2.75778i) q^{4} +(2.50000 - 4.33013i) q^{5} +(10.0934 - 5.30509i) q^{6} +(-1.38302 - 2.39547i) q^{7} +24.5436 q^{8} +(-26.9150 - 2.14059i) q^{9} +O(q^{10})\)	\(q+(1.09722 + 1.90044i) q^{2} +(0.206141 - 5.19206i) q^{3} +(1.59221 - 2.75778i) q^{4} +(2.50000 - 4.33013i) q^{5} +(10.0934 - 5.30509i) q^{6} +(-1.38302 - 2.39547i) q^{7} +24.5436 q^{8} +(-26.9150 - 2.14059i) q^{9} +10.9722 q^{10} +(26.3295 + 45.6040i) q^{11} +(-13.9904 - 8.83533i) q^{12} +(-10.2267 + 17.7132i) q^{13} +(3.03497 - 5.25672i) q^{14} +(-21.9669 - 13.8728i) q^{15} +(14.1921 + 24.5814i) q^{16} +3.66084 q^{17} +(-25.4637 - 53.4992i) q^{18} -95.6705 q^{19} +(-7.96104 - 13.7889i) q^{20} +(-12.7225 + 6.68694i) q^{21} +(-57.7786 + 100.075i) q^{22} +(44.9206 - 77.8047i) q^{23} +(5.05943 - 127.432i) q^{24} +(-12.5000 - 21.6506i) q^{25} -44.8840 q^{26} +(-16.6623 + 139.303i) q^{27} -8.80825 q^{28} +(113.890 + 197.264i) q^{29} +(2.26182 - 56.9684i) q^{30} +(-139.569 + 241.741i) q^{31} +(67.0306 - 116.100i) q^{32} +(242.206 - 127.303i) q^{33} +(4.01675 + 6.95722i) q^{34} -13.8302 q^{35} +(-48.7576 + 70.8175i) q^{36} +273.725 q^{37} +(-104.972 - 181.816i) q^{38} +(89.8599 + 56.7492i) q^{39} +(61.3589 - 106.277i) q^{40} +(-32.4323 + 56.1744i) q^{41} +(-26.6676 - 16.8414i) q^{42} +(-209.381 - 362.658i) q^{43} +167.688 q^{44} +(-76.5566 + 111.194i) q^{45} +197.151 q^{46} +(-69.3544 - 120.125i) q^{47} +(130.554 - 68.6190i) q^{48} +(167.674 - 290.421i) q^{49} +(27.4306 - 47.5111i) q^{50} +(0.754647 - 19.0073i) q^{51} +(32.5661 + 56.4062i) q^{52} -197.063 q^{53} +(-283.020 + 121.181i) q^{54} +263.295 q^{55} +(-33.9444 - 58.7934i) q^{56} +(-19.7216 + 496.727i) q^{57} +(-249.926 + 432.884i) q^{58} +(-370.552 + 641.814i) q^{59} +(-73.2340 + 38.4917i) q^{60} +(-244.234 - 423.026i) q^{61} -612.554 q^{62} +(32.0964 + 67.4346i) q^{63} +521.263 q^{64} +(51.1336 + 88.5660i) q^{65} +(507.687 + 320.620i) q^{66} +(205.734 - 356.341i) q^{67} +(5.82882 - 10.0958i) q^{68} +(-394.707 - 249.269i) q^{69} +(-15.1748 - 26.2836i) q^{70} -310.343 q^{71} +(-660.591 - 52.5377i) q^{72} -51.0260 q^{73} +(300.338 + 520.200i) q^{74} +(-114.988 + 60.4377i) q^{75} +(-152.327 + 263.839i) q^{76} +(72.8286 - 126.143i) q^{77} +(-9.25240 + 233.040i) q^{78} +(-603.999 - 1046.16i) q^{79} +141.921 q^{80} +(719.836 + 115.228i) q^{81} -142.342 q^{82} +(-452.611 - 783.945i) q^{83} +(-1.81574 + 45.7330i) q^{84} +(9.15210 - 15.8519i) q^{85} +(459.475 - 795.833i) q^{86} +(1047.68 - 550.661i) q^{87} +(646.220 + 1119.29i) q^{88} +663.633 q^{89} +(-295.317 - 23.4870i) q^{90} +56.5752 q^{91} +(-143.046 - 247.763i) q^{92} +(1226.36 + 774.485i) q^{93} +(152.194 - 263.608i) q^{94} +(-239.176 + 414.265i) q^{95} +(-588.982 - 371.960i) q^{96} +(362.668 + 628.159i) q^{97} +735.905 q^{98} +(-611.039 - 1283.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9	\( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 5 * q^3 - 36 * q^4 + 35 * q^5 - 31 * q^6 - 22 * q^7 - 36 * q^8 + 17 * q^9 + 20 * q^10 + 23 * q^11 + 287 * q^12 - 96 * q^13 - 21 * q^14 - 20 * q^15 - 324 * q^16 - 322 * q^17 - 89 * q^18 + 558 * q^19 + 180 * q^20 + 180 * q^21 - 311 * q^22 + 96 * q^23 + 48 * q^24 - 175 * q^25 + 716 * q^26 - 470 * q^27 + 674 * q^28 - 296 * q^29 + 80 * q^30 - 244 * q^31 - 314 * q^32 - 211 * q^33 - 125 * q^34 - 220 * q^35 - 2399 * q^36 + 808 * q^37 + 305 * q^38 + 634 * q^39 - 90 * q^40 - 47 * q^41 + 1941 * q^42 - 525 * q^43 - 110 * q^44 + 185 * q^45 + 1434 * q^46 + 164 * q^47 + 2051 * q^48 - 1225 * q^49 + 50 * q^50 + 1517 * q^51 - 1682 * q^52 - 1012 * q^53 - 4066 * q^54 + 230 * q^55 - 981 * q^56 + 337 * q^57 - 1183 * q^58 - 85 * q^59 + 65 * q^60 - 828 * q^61 + 1572 * q^62 - 828 * q^63 + 4472 * q^64 + 480 * q^65 + 4930 * q^66 - 1093 * q^67 + 2473 * q^68 - 822 * q^69 + 105 * q^70 - 656 * q^71 - 4626 * q^72 + 4170 * q^73 - 1316 * q^74 + 25 * q^75 - 2789 * q^76 + 24 * q^77 - 5314 * q^78 - 2110 * q^79 - 3240 * q^80 - 2167 * q^81 - 124 * q^82 + 1290 * q^83 + 5775 * q^84 - 805 * q^85 - 2569 * q^86 + 3604 * q^87 - 2271 * q^88 + 6096 * q^89 + 730 * q^90 + 6676 * q^91 + 2763 * q^92 - 696 * q^93 + 517 * q^94 + 1395 * q^95 - 593 * q^96 - 1787 * q^97 - 2558 * q^98 + 2320 * q^99

Introduction

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