LMFDB - Embedded newform 45.4.e.c.16.2

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			16.2
Root			$-1.52087 - 2.63422i$ of defining polynomial
Character	$\chi$	$=$	45.16
Dual form			45.4.e.c.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52087 + 2.63422i) q^{2} +(4.01867 + 3.29398i) q^{3} +(-0.626094 - 1.08443i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-14.7890 + 5.57636i) q^{6} +(6.85611 - 11.8751i) q^{7} -20.5251 q^{8} +(5.29939 + 26.4748i) q^{9} +O(q^{10})$	\(q+(-1.52087 + 2.63422i) q^{2} +(4.01867 + 3.29398i) q^{3} +(-0.626094 - 1.08443i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-14.7890 + 5.57636i) q^{6} +(6.85611 - 11.8751i) q^{7} -20.5251 q^{8} +(5.29939 + 26.4748i) q^{9} -15.2087 q^{10} +(-15.9034 + 27.5455i) q^{11} +(1.05602 - 6.42029i) q^{12} +(-29.1216 - 50.4401i) q^{13} +(20.8545 + 36.1211i) q^{14} +(-4.21668 + 25.6363i) q^{15} +(36.2248 - 62.7431i) q^{16} +109.055 q^{17} +(-77.8003 - 26.3050i) q^{18} +129.695 q^{19} +(3.13047 - 5.42213i) q^{20} +(66.6689 - 25.1383i) q^{21} +(-48.3740 - 83.7863i) q^{22} +(-39.8342 - 68.9949i) q^{23} +(-82.4836 - 67.6093i) q^{24} +(-12.5000 + 21.6506i) q^{25} +177.161 q^{26} +(-65.9111 + 123.850i) q^{27} -17.1703 q^{28} +(-4.51769 + 7.82486i) q^{29} +(-61.1187 - 50.0972i) q^{30} +(16.6904 + 28.9087i) q^{31} +(28.0860 + 48.6463i) q^{32} +(-154.645 + 58.3108i) q^{33} +(-165.858 + 287.275i) q^{34} +68.5611 q^{35} +(25.3921 - 22.3225i) q^{36} -22.1645 q^{37} +(-197.250 + 341.647i) q^{38} +(49.1186 - 298.628i) q^{39} +(-51.3127 - 88.8763i) q^{40} +(-60.8698 - 105.430i) q^{41} +(-35.1747 + 213.853i) q^{42} +(-5.07086 + 8.78298i) q^{43} +39.8281 q^{44} +(-101.391 + 89.1341i) q^{45} +242.331 q^{46} +(220.746 - 382.343i) q^{47} +(352.250 - 132.820i) q^{48} +(77.4875 + 134.212i) q^{49} +(-38.0218 - 65.8556i) q^{50} +(438.255 + 359.225i) q^{51} +(-36.4657 + 63.1604i) q^{52} -593.610 q^{53} +(-226.006 - 361.984i) q^{54} -159.034 q^{55} +(-140.722 + 243.738i) q^{56} +(521.202 + 427.214i) q^{57} +(-13.7416 - 23.8012i) q^{58} +(-221.230 - 383.182i) q^{59} +(30.4407 - 11.4780i) q^{60} +(-72.2881 + 125.207i) q^{61} -101.536 q^{62} +(350.725 + 118.583i) q^{63} +408.736 q^{64} +(145.608 - 252.200i) q^{65} +(81.5912 - 496.052i) q^{66} +(-431.360 - 747.138i) q^{67} +(-68.2786 - 118.262i) q^{68} +(67.1873 - 408.481i) q^{69} +(-104.273 + 180.605i) q^{70} -818.541 q^{71} +(-108.771 - 543.398i) q^{72} +495.052 q^{73} +(33.7093 - 58.3863i) q^{74} +(-121.550 + 45.8320i) q^{75} +(-81.2014 - 140.645i) q^{76} +(218.071 + 377.710i) q^{77} +(711.950 + 583.563i) q^{78} +(-585.263 + 1013.71i) q^{79} +362.248 q^{80} +(-672.833 + 280.601i) q^{81} +370.300 q^{82} +(212.022 - 367.232i) q^{83} +(-69.0017 - 56.5586i) q^{84} +(272.637 + 472.221i) q^{85} +(-15.4242 - 26.7156i) q^{86} +(-43.9300 + 16.5644i) q^{87} +(326.419 - 565.374i) q^{88} +1031.37 q^{89} +(-80.5969 - 402.648i) q^{90} -798.643 q^{91} +(-49.8799 + 86.3945i) q^{92} +(-28.1513 + 171.152i) q^{93} +(671.452 + 1162.99i) q^{94} +(324.238 + 561.597i) q^{95} +(-47.3718 + 288.008i) q^{96} +(-799.356 + 1384.53i) q^{97} -471.394 q^{98} +(-813.541 - 275.066i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.52087	+	2.63422i	−0.537709	+	0.931339i	0.461318	+	0.887235i	$0.347377\pi$
$2$	−1.52087	+	2.63422i	−0.537709	+	0.931339i	−0.999027	+	0.0441043i	$0.985957\pi$
$3$	4.01867	+	3.29398i	0.773393	+	0.633927i
$3$	4.01867	+	3.29398i	0.773393	+	0.633927i
$4$	−0.626094	−	1.08443i	−0.0782617	−	0.135553i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	−14.7890	+	5.57636i	−1.00626	+	0.379423i
$7$	6.85611	−	11.8751i	0.370195	−	0.641197i	−0.619400	−	0.785075i	$-0.712624\pi$
$7$	6.85611	−	11.8751i	0.370195	−	0.641197i	0.989595	+	0.143879i	$0.0459575\pi$
$8$	−20.5251			−0.907090
$9$	5.29939	+	26.4748i	0.196274	+	0.980549i
$10$	−15.2087			−0.480941
$11$	−15.9034	+	27.5455i	−0.435914	+	0.755026i	−0.997370	−	0.0724812i	$-0.976908\pi$
$11$	−15.9034	+	27.5455i	−0.435914	+	0.755026i	0.561455	+	0.827507i	$0.310242\pi$
$12$	1.05602	−	6.42029i	0.0254038	−	0.154448i
$13$	−29.1216	−	50.4401i	−0.621298	−	1.07612i	−0.989244	−	0.146272i	$-0.953272\pi$
$13$	−29.1216	−	50.4401i	−0.621298	−	1.07612i	0.367946	−	0.929847i	$-0.380061\pi$
$14$	20.8545	+	36.1211i	0.398115	+	0.689555i
$15$	−4.21668	+	25.6363i	−0.0725828	+	0.441284i
$16$	36.2248	−	62.7431i	0.566012	−	0.980361i
$17$	109.055			1.55586			0.777932	−	0.628348i	$-0.216269\pi$
$17$	109.055			1.55586			0.777932	+	0.628348i	$0.216269\pi$
$18$	−77.8003	−	26.3050i	−1.01876	−	0.344453i
$19$	129.695			1.56601			0.783004	−	0.622017i	$-0.213687\pi$
$19$	129.695			1.56601			0.783004	+	0.622017i	$0.213687\pi$
$20$	3.13047	−	5.42213i	0.0349997	−	0.0606213i
$21$	66.6689	−	25.1383i	0.692778	−	0.261221i
$22$	−48.3740	−	83.7863i	−0.468790	−	0.811968i
$23$	−39.8342	−	68.9949i	−0.361131	−	0.625497i	0.627017	−	0.779006i	$-0.284276\pi$
$23$	−39.8342	−	68.9949i	−0.361131	−	0.625497i	−0.988147	+	0.153509i	$0.950943\pi$
$24$	−82.4836	−	67.6093i	−0.701537	−	0.575028i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	177.161			1.33631
$27$	−65.9111	+	123.850i	−0.469800	+	0.882773i
$28$	−17.1703			−0.115888
$29$	−4.51769	+	7.82486i	−0.0289280	+	0.0501048i	−0.880127	−	0.474738i	$-0.842543\pi$
$29$	−4.51769	+	7.82486i	−0.0289280	+	0.0501048i	0.851199	+	0.524843i	$0.175876\pi$
$30$	−61.1187	−	50.0972i	−0.371957	−	0.304882i
$31$	16.6904	+	28.9087i	0.0966998	+	0.167489i	0.910317	−	0.413912i	$-0.135838\pi$
$31$	16.6904	+	28.9087i	0.0966998	+	0.167489i	−0.813617	+	0.581401i	$0.802505\pi$
$32$	28.0860	+	48.6463i	0.155154	+	0.268735i
$33$	−154.645	+	58.3108i	−0.815764	+	0.307594i
$34$	−165.858	+	287.275i	−0.836602	+	1.44904i
$35$	68.5611			0.331113
$36$	25.3921	−	22.3225i	0.117556	−	0.103345i
$37$	−22.1645			−0.0984817			−0.0492408	−	0.998787i	$-0.515680\pi$
$37$	−22.1645			−0.0984817			−0.0492408	+	0.998787i	$0.515680\pi$
$38$	−197.250	+	341.647i	−0.842056	+	1.45848i
$39$	49.1186	−	298.628i	0.201673	−	1.22612i
$40$	−51.3127	−	88.8763i	−0.202831	−	0.351314i
$41$	−60.8698	−	105.430i	−0.231860	−	0.401593i	0.726495	−	0.687171i	$-0.241148\pi$
$41$	−60.8698	−	105.430i	−0.231860	−	0.401593i	−0.958356	+	0.285578i	$0.907814\pi$
$42$	−35.1747	+	213.853i	−0.129228	+	0.785672i
$43$	−5.07086	+	8.78298i	−0.0179837	+	0.0311487i	−0.874877	−	0.484345i	$-0.839058\pi$
$43$	−5.07086	+	8.78298i	−0.0179837	+	0.0311487i	0.856894	+	0.515493i	$0.172391\pi$
$44$	39.8281			0.136462
$45$	−101.391	+	89.1341i	−0.335877	+	0.295274i
$46$	242.331			0.776733
$47$	220.746	−	382.343i	0.685088	−	1.18661i	−0.288321	−	0.957534i	$-0.593097\pi$
$47$	220.746	−	382.343i	0.685088	−	1.18661i	0.973409	−	0.229073i	$-0.0735695\pi$
$48$	352.250	−	132.820i	1.05923	−	0.399395i
$49$	77.4875	+	134.212i	0.225911	+	0.391289i
$50$	−38.0218	−	65.8556i	−0.107542	−	0.186268i
$51$	438.255	+	359.225i	1.20329	+	0.986304i
$52$	−36.4657	+	63.1604i	−0.0972477	+	0.168438i
$53$	−593.610			−1.53846			−0.769232	−	0.638969i	$-0.779361\pi$
$53$	−593.610			−1.53846			−0.769232	+	0.638969i	$0.779361\pi$
$54$	−226.006	−	361.984i	−0.569546	−	0.912218i
$55$	−159.034			−0.389894
$56$	−140.722	+	243.738i	−0.335800	+	0.581623i
$57$	521.202	+	427.214i	1.21114	+	0.992734i
$58$	−13.7416	−	23.8012i	−0.0311097	−	0.0538836i
$59$	−221.230	−	383.182i	−0.488164	−	0.845525i	0.511743	−	0.859139i	$-0.329000\pi$
$59$	−221.230	−	383.182i	−0.488164	−	0.845525i	−0.999907	+	0.0136133i	$0.995667\pi$
$60$	30.4407	−	11.4780i	0.0654980	−	0.0246968i
$61$	−72.2881	+	125.207i	−0.151730	+	0.262804i	−0.931864	−	0.362809i	$-0.881818\pi$
$61$	−72.2881	+	125.207i	−0.151730	+	0.262804i	0.780133	+	0.625613i	$0.215151\pi$
$62$	−101.536			−0.207985
$63$	350.725	+	118.583i	0.701385	+	0.237145i
$64$	408.736			0.798312
$65$	145.608	−	252.200i	0.277853	−	0.481255i
$66$	81.5912	−	496.052i	0.152169	−	0.925149i
$67$	−431.360	−	747.138i	−0.786553	−	1.36235i	−0.928067	−	0.372414i	$-0.878530\pi$
$67$	−431.360	−	747.138i	−0.786553	−	1.36235i	0.141514	−	0.989936i	$-0.454803\pi$
$68$	−68.2786	−	118.262i	−0.121765	−	0.210902i
$69$	67.1873	−	408.481i	0.117223	−	0.712685i
$70$	−104.273	+	180.605i	−0.178042	+	0.308378i
$71$	−818.541			−1.36821			−0.684105	−	0.729384i	$-0.739807\pi$
$71$	−818.541			−1.36821			−0.684105	+	0.729384i	$0.739807\pi$
$72$	−108.771	−	543.398i	−0.178038	−	0.889446i
$73$	495.052			0.793719			0.396859	−	0.917879i	$-0.370100\pi$
$73$	495.052			0.793719			0.396859	+	0.917879i	$0.370100\pi$
$74$	33.7093	−	58.3863i	0.0529545	−	0.0917198i
$75$	−121.550	+	45.8320i	−0.187139	+	0.0705629i
$76$	−81.2014	−	140.645i	−0.122558	−	0.212277i
$77$	218.071	+	377.710i	0.322747	+	0.559014i
$78$	711.950	+	583.563i	1.03349	+	0.847122i
$79$	−585.263	+	1013.71i	−0.833510	+	1.44368i	0.0617284	+	0.998093i	$0.480339\pi$
$79$	−585.263	+	1013.71i	−0.833510	+	1.44368i	−0.895238	+	0.445588i	$0.852995\pi$
$80$	362.248			0.506256
$81$	−672.833	+	280.601i	−0.922953	+	0.384912i
$82$	370.300			0.498693
$83$	212.022	−	367.232i	0.280390	−	0.485651i	−0.691090	−	0.722768i	$-0.742869\pi$
$83$	212.022	−	367.232i	0.280390	−	0.485651i	0.971481	+	0.237118i	$0.0762027\pi$
$84$	−69.0017	−	56.5586i	−0.0896273	−	0.0734648i
$85$	272.637	+	472.221i	0.347902	+	0.602584i
$86$	−15.4242	−	26.7156i	−0.0193400	−	0.0334978i
$87$	−43.9300	+	16.5644i	−0.0541355	+	0.0204125i
$88$	326.419	−	565.374i	0.395413	−	0.684876i
$89$	1031.37			1.22837			0.614183	−	0.789163i	$-0.289486\pi$
$89$	1031.37			1.22837			0.614183	+	0.789163i	$0.289486\pi$
$90$	−80.5969	−	402.648i	−0.0943962	−	0.471587i
$91$	−798.643			−0.920006
$92$	−49.8799	+	86.3945i	−0.0565254	+	0.0979049i
$93$	−28.1513	+	171.152i	−0.0313888	+	0.190835i
$94$	671.452	+	1162.99i	0.736756	+	1.27610i
$95$	324.238	+	561.597i	0.350170	+	0.606512i
$96$	−47.3718	+	288.008i	−0.0503632	+	0.306195i
$97$	−799.356	+	1384.53i	−0.836725	+	1.44925i	0.0558930	+	0.998437i	$0.482199\pi$
$97$	−799.356	+	1384.53i	−0.836725	+	1.44925i	−0.892618	+	0.450814i	$0.851134\pi$
$98$	−471.394			−0.485897
$99$	−813.541	−	275.066i	−0.825898	−	0.279244i
$100$	31.3047			0.0313047
$101$	107.000	−	185.330i	0.105415	−	0.182584i	−0.808493	−	0.588506i	$-0.799716\pi$
$101$	107.000	−	185.330i	0.105415	−	0.182584i	0.913908	+	0.405922i	$0.133050\pi$
$102$	−1612.81	+	608.129i	−1.56561	+	0.590331i
$103$	−836.160	−	1448.27i	−0.799897	−	1.38546i	−0.919683	−	0.392662i	$-0.871554\pi$
$103$	−836.160	−	1448.27i	−0.799897	−	1.38546i	0.119786	−	0.992800i	$-0.461779\pi$
$104$	597.723	+	1035.29i	0.563573	+	0.976137i
$105$	275.524	+	225.839i	0.256080	+	0.209901i
$106$	902.804	−	1563.70i	0.827246	−	1.43283i
$107$	−600.699			−0.542727			−0.271363	−	0.962477i	$-0.587475\pi$
$107$	−600.699			−0.542727			−0.271363	+	0.962477i	$0.587475\pi$
$108$	175.572	−	6.06581i	0.156430	−	0.00540447i
$109$	−771.570			−0.678009			−0.339005	−	0.940785i	$-0.610090\pi$
$109$	−771.570			−0.678009			−0.339005	+	0.940785i	$0.610090\pi$
$110$	241.870	−	418.931i	0.209649	−	0.363123i
$111$	−89.0718	−	73.0094i	−0.0761650	−	0.0624302i
$112$	−496.722	−	860.348i	−0.419070	−	0.725850i
$113$	583.338	+	1010.37i	0.485627	+	0.841131i	0.999864	−	0.0165177i	$-0.00525800\pi$
$113$	583.338	+	1010.37i	0.485627	+	0.841131i	−0.514237	+	0.857648i	$0.671925\pi$
$114$	−1918.06	+	723.228i	−1.57581	+	0.594180i
$115$	199.171	−	344.974i	0.161503	−	0.279731i
$116$	11.3140			0.00905583
$117$	1181.06	−	1038.29i	0.933244	−	0.820427i
$118$	1345.85			1.04996
$119$	747.692	−	1295.04i	0.575973	−	0.997615i
$120$	86.5478	−	526.187i	0.0658391	−	0.400284i
$121$	159.663	+	276.545i	0.119957	+	0.207772i
$122$	−219.882	−	380.846i	−0.163173	−	0.282624i
$123$	102.667	−	624.190i	0.0752618	−	0.457572i
$124$	20.8996	−	36.1991i	0.0151358	−	0.0262159i
$125$	−125.000			−0.0894427
$126$	−845.783	+	743.539i	−0.598003	+	0.525712i
$127$	1630.10			1.13896			0.569479	−	0.822006i	$-0.307145\pi$
$127$	1630.10			1.13896			0.569479	+	0.822006i	$0.307145\pi$
$128$	−846.322	+	1465.87i	−0.584414	+	1.01223i
$129$	−49.3091	+	18.5926i	−0.0336544	+	0.0126898i
$130$	442.901	+	767.128i	0.298808	+	0.517550i
$131$	−129.412	−	224.149i	−0.0863115	−	0.149496i	0.819638	−	0.572882i	$-0.194175\pi$
$131$	−129.412	−	224.149i	−0.0863115	−	0.149496i	−0.905949	+	0.423386i	$0.860841\pi$
$132$	160.056	+	131.193i	0.105538	+	0.0865067i
$133$	889.206	−	1540.15i	0.579729	−	1.00412i
$134$	2624.17			1.69175
$135$	−701.062	+	24.2208i	−0.446947	+	0.0154415i
$136$	−2238.36			−1.41131
$137$	−526.385	+	911.726i	−0.328264	+	0.568569i	−0.982167	−	0.188009i	$-0.939797\pi$
$137$	−526.385	+	911.726i	−0.328264	+	0.568569i	0.653904	+	0.756578i	$0.273130\pi$
$138$	973.847	+	798.232i	0.600720	+	0.492392i
$139$	−1192.25	−	2065.03i	−0.727519	−	1.26010i	−0.957929	−	0.287006i	$-0.907340\pi$
$139$	−1192.25	−	2065.03i	−0.727519	−	1.26010i	0.230410	−	0.973094i	$-0.425993\pi$
$140$	−42.9257	−	74.3495i	−0.0259135	−	0.0448834i
$141$	2146.54	−	809.378i	1.28206	−	0.483418i
$142$	1244.89	−	2156.22i	0.735699	−	1.27427i
$143$	1852.53			1.08333
$144$	1853.08	+	626.544i	1.07239	+	0.362583i
$145$	−45.1769			−0.0258740
$146$	−752.910	+	1304.08i	−0.426790	+	0.739221i
$147$	−130.696	+	794.597i	−0.0733308	+	0.445831i
$148$	13.8771	+	24.0358i	0.00770735	+	0.0133495i
$149$	−573.144	−	992.715i	−0.315126	−	0.545815i	0.664338	−	0.747432i	$-0.268714\pi$
$149$	−573.144	−	992.715i	−0.315126	−	0.545815i	−0.979464	+	0.201617i	$0.935380\pi$
$150$	64.1303	−	389.895i	0.0349081	−	0.212232i
$151$	583.058	−	1009.89i	0.314229	−	0.544261i	−0.665044	−	0.746804i	$-0.731587\pi$
$151$	583.058	−	1009.89i	0.314229	−	0.544261i	0.979273	+	0.202543i	$0.0649207\pi$
$152$	−2662.01			−1.42051
$153$	577.924	+	2887.21i	0.305375	+	1.52560i
$154$	−1326.63			−0.694175
$155$	−83.4522	+	144.544i	−0.0432454	+	0.0749033i
$156$	−354.593	+	133.704i	−0.181988	+	0.0686208i
$157$	1737.81	+	3009.97i	0.883390	+	1.53008i	0.847548	+	0.530719i	$0.178078\pi$
$157$	1737.81	+	3009.97i	0.883390	+	1.53008i	0.0358423	+	0.999357i	$0.488589\pi$
$158$	−1780.22	−	3083.43i	−0.896371	−	1.55256i
$159$	−2385.52	−	1955.34i	−1.18984	−	0.975274i
$160$	−140.430	+	243.232i	−0.0693872	+	0.120182i
$161$	−1092.43			−0.534755
$162$	284.126	−	2199.15i	0.137796	−	1.06655i
$163$	−2223.32			−1.06837			−0.534183	−	0.845369i	$-0.679381\pi$
$163$	−2223.32			−1.06837			−0.534183	+	0.845369i	$0.679381\pi$
$164$	−76.2204	+	132.018i	−0.0362915	+	0.0628588i
$165$	−639.105	−	523.855i	−0.301541	−	0.247164i
$166$	644.915	+	1117.03i	0.301537	+	0.522277i
$167$	793.991	+	1375.23i	0.367909	+	0.637238i	0.989239	−	0.146312i	$-0.0467403\pi$
$167$	793.991	+	1375.23i	0.367909	+	0.637238i	−0.621329	+	0.783550i	$0.713407\pi$
$168$	−1368.39	+	515.967i	−0.628412	+	0.236951i
$169$	−597.632	+	1035.13i	−0.272022	+	0.471156i
$170$	−1658.58			−0.748280
$171$	687.306	+	3433.66i	0.307366	+	1.53555i
$172$	12.6993			0.00562974
$173$	−753.898	+	1305.79i	−0.331317	+	0.573857i	−0.982770	−	0.184831i	$-0.940826\pi$
$173$	−753.898	+	1305.79i	−0.331317	+	0.573857i	0.651454	+	0.758689i	$0.274160\pi$
$174$	23.1776	−	140.914i	0.0100982	−	0.0613945i
$175$	171.403	+	296.878i	0.0740390	+	0.128239i
$176$	1152.19	+	1995.66i	0.493465	+	0.854707i
$177$	373.143	−	2268.61i	0.158458	−	0.963384i
$178$	−1568.58	+	2716.85i	−0.660504	+	1.14403i
$179$	1572.66			0.656683			0.328341	−	0.944559i	$-0.393510\pi$
$179$	1572.66			0.656683			0.328341	+	0.944559i	$0.393510\pi$
$180$	160.140	+	54.1446i	0.0663117	+	0.0224206i
$181$	1984.41			0.814918			0.407459	−	0.913223i	$-0.366415\pi$
$181$	1984.41			0.814918			0.407459	+	0.913223i	$0.366415\pi$
$182$	1214.63	−	2103.81i	0.494695	−	0.856838i
$183$	−702.930	+	265.048i	−0.283946	+	0.107065i
$184$	817.601	+	1416.13i	0.327578	+	0.567382i
$185$	−55.4113	−	95.9751i	−0.0220212	−	0.0381418i
$186$	−408.040	−	334.458i	−0.160854	−	0.131847i
$187$	−1734.34	+	3003.97i	−0.678223	+	1.17472i
$188$	−552.831			−0.214465
$189$	1018.84	+	1631.83i	0.392114	+	0.628032i
$190$	−1972.50			−0.753158
$191$	1174.18	−	2033.73i	0.444819	−	0.770450i	−0.553220	−	0.833035i	$-0.686601\pi$
$191$	1174.18	−	2033.73i	0.444819	−	0.770450i	0.998040	+	0.0625853i	$0.0199345\pi$
$192$	1642.57	+	1346.37i	0.617409	+	0.506071i
$193$	117.085	+	202.797i	0.0436681	+	0.0756354i	0.887033	−	0.461705i	$-0.152762\pi$
$193$	117.085	+	202.797i	0.0436681	+	0.0756354i	−0.843365	+	0.537341i	$0.819429\pi$
$194$	−2431.43	−	4211.37i	−0.899829	−	1.55855i
$195$	1415.89	−	533.880i	0.519970	−	0.196061i
$196$	97.0288	−	168.059i	0.0353604	−	0.0612460i
$197$	−717.846			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$197$	−717.846			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$198$	1961.87	−	1724.71i	0.704163	−	0.619040i
$199$	1701.45			0.606094			0.303047	−	0.952976i	$-0.401996\pi$
$199$	1701.45			0.606094			0.303047	+	0.952976i	$0.401996\pi$
$200$	256.564	−	444.381i	0.0907090	−	0.157113i
$201$	727.564	−	4423.39i	0.255315	−	1.55225i
$202$	325.467	+	563.725i	0.113365	+	0.196354i
$203$	61.9475	+	107.296i	0.0214180	+	0.0370971i
$204$	115.164	−	700.164i	0.0395248	−	0.240300i
$205$	304.349	−	527.148i	0.103691	−	0.179598i
$206$	5086.77			1.72045
$207$	1615.53	−	1420.23i	0.542450	−	0.476875i
$208$	−4219.69			−1.40665
$209$	−2062.60	+	3572.52i	−0.682645	+	1.18238i
$210$	−1013.95	+	382.321i	−0.333186	+	0.125632i
$211$	2469.33	+	4277.01i	0.805667	+	1.39546i	0.915840	+	0.401544i	$0.131526\pi$
$211$	2469.33	+	4277.01i	0.805667	+	1.39546i	−0.110172	+	0.993912i	$0.535140\pi$
$212$	371.656	+	643.727i	0.120403	+	0.208544i
$213$	−3289.44	−	2696.26i	−1.05816	−	0.867345i
$214$	913.585	−	1582.38i	0.291829	−	0.505463i
$215$	−50.7086			−0.0160851
$216$	1352.83	−	2542.03i	0.426150	−	0.800754i
$217$	457.726			0.143191
$218$	1173.46	−	2032.49i	0.364572	−	0.631456i
$219$	1989.45	+	1630.69i	0.613857	+	0.503160i
$220$	99.5703	+	172.461i	0.0305137	+	0.0528514i
$221$	−3175.85	−	5500.73i	−0.966655	−	1.67430i
$222$	327.790	−	123.597i	0.0990983	−	0.0373662i
$223$	1526.57	−	2644.10i	0.458416	−	0.794001i	−0.540461	−	0.841369i	$-0.681750\pi$
$223$	1526.57	−	2644.10i	0.458416	−	0.794001i	0.998877	+	0.0473684i	$0.0150835\pi$
$224$	770.242			0.229750
$225$	−639.439	−	216.200i	−0.189463	−	0.0640593i
$226$	−3548.73			−1.04450
$227$	419.976	−	727.420i	0.122797	−	0.212690i	−0.798073	−	0.602561i	$-0.794147\pi$
$227$	419.976	−	727.420i	0.122797	−	0.212690i	0.920869	+	0.389871i	$0.127480\pi$
$228$	136.960	−	832.682i	0.0397825	−	0.241867i
$229$	−700.753	−	1213.74i	−0.202214	−	0.350245i	0.747027	−	0.664793i	$-0.231480\pi$
$229$	−700.753	−	1213.74i	−0.202214	−	0.350245i	−0.949242	+	0.314548i	$0.898147\pi$
$230$	605.827	+	1049.32i	0.173683	+	0.300827i
$231$	−367.814	+	2236.21i	−0.104764	+	0.636935i
$232$	92.7259	−	160.606i	0.0262403	−	0.0454496i
$233$	−2856.99			−0.803295			−0.401647	−	0.915794i	$-0.631562\pi$
$233$	−2856.99			−0.803295			−0.401647	+	0.915794i	$0.631562\pi$
$234$	938.843	+	4690.30i	0.262282	+	1.31032i
$235$	2207.46			0.612761
$236$	−277.021	+	479.815i	−0.0764092	+	0.132345i
$237$	−5691.11	+	2145.90i	−1.55982	+	0.588149i
$238$	2274.29	+	3939.18i	0.619412	+	1.07285i
$239$	854.917	+	1480.76i	0.231381	+	0.400763i	0.958215	−	0.286050i	$-0.0923424\pi$
$239$	854.917	+	1480.76i	0.231381	+	0.400763i	−0.726834	+	0.686813i	$0.759009\pi$
$240$	1455.75	+	1193.24i	0.391535	+	0.320930i
$241$	2166.23	−	3752.02i	0.579000	−	1.00286i	−0.416594	−	0.909092i	$-0.636776\pi$
$241$	2166.23	−	3752.02i	0.579000	−	1.00286i	0.995594	−	0.0937648i	$-0.0298902\pi$
$242$	−971.309			−0.258009
$243$	−3628.19	−	1088.66i	−0.957812	−	0.287396i
$244$	181.036			0.0474987
$245$	−387.437	+	671.061i	−0.101030	+	0.174990i
$246$	1488.11	+	1219.76i	0.385686	+	0.316135i
$247$	−3776.93	−	6541.84i	−0.972957	−	1.68521i
$248$	−342.573	−	593.354i	−0.0877154	−	0.151927i
$249$	2061.70	−	777.390i	0.524719	−	0.197852i
$250$	190.109	−	329.278i	0.0480941	−	0.0833015i
$251$	−1724.73			−0.433722			−0.216861	−	0.976202i	$-0.569582\pi$
$251$	−1724.73			−0.433722			−0.216861	+	0.976202i	$0.569582\pi$
$252$	−90.9920	−	454.580i	−0.0227459	−	0.113634i
$253$	2534.00			0.629688
$254$	−2479.16	+	4294.04i	−0.612428	+	1.06076i
$255$	−459.850	+	2795.76i	−0.112929	+	0.686578i
$256$	−939.349	−	1627.00i	−0.229333	−	0.397217i
$257$	2926.63	+	5069.07i	0.710342	+	1.23035i	0.964729	+	0.263246i	$0.0847932\pi$
$257$	2926.63	+	5069.07i	0.710342	+	1.23035i	−0.254386	+	0.967103i	$0.581873\pi$
$258$	26.0156	−	158.168i	0.00627776	−	0.0381671i
$259$	−151.962	+	263.206i	−0.0364574	+	0.0631462i
$260$	−364.657			−0.0869810
$261$	−231.103	−	78.1380i	−0.0548081	−	0.0185311i
$262$	787.277			0.185642
$263$	−196.180	+	339.794i	−0.0459962	+	0.0796677i	−0.888107	−	0.459637i	$-0.847980\pi$
$263$	−196.180	+	339.794i	−0.0459962	+	0.0796677i	0.842111	+	0.539305i	$0.181313\pi$
$264$	3174.10	−	1196.83i	0.739971	−	0.279015i
$265$	−1484.03	−	2570.41i	−0.344011	−	0.595845i
$266$	2704.73	+	4684.73i	0.623450	+	1.07985i
$267$	4144.72	+	3397.30i	0.950010	+	0.778695i
$268$	−540.144	+	935.557i	−0.123114	+	0.213240i
$269$	−4610.33			−1.04497			−0.522485	−	0.852648i	$-0.674995\pi$
$269$	−4610.33			−1.04497			−0.522485	+	0.852648i	$0.674995\pi$
$270$	1002.42	−	1883.59i	0.225946	−	0.424562i
$271$	−1155.72			−0.259058			−0.129529	−	0.991576i	$-0.541347\pi$
$271$	−1155.72			−0.259058			−0.129529	+	0.991576i	$0.541347\pi$
$272$	3950.49	−	6842.44i	0.880638	−	1.52531i
$273$	−3209.48	−	2630.71i	−0.711526	−	0.583216i
$274$	−1601.13	−	2773.23i	−0.353020	−	0.611449i
$275$	−397.585	−	688.638i	−0.0871829	−	0.151005i
$276$	−485.033	+	182.888i	−0.105781	+	0.0398860i
$277$	304.205	−	526.898i	0.0659852	−	0.114290i	−0.831145	−	0.556055i	$-0.812314\pi$
$277$	304.205	−	526.898i	0.0659852	−	0.114290i	0.897131	+	0.441765i	$0.145648\pi$
$278$	7253.02			1.56477
$279$	−676.904	+	595.075i	−0.145251	+	0.127693i
$280$	−1407.22			−0.300349
$281$	−1374.62	+	2380.91i	−0.291825	+	0.505456i	−0.974241	−	0.225508i	$-0.927596\pi$
$281$	−1374.62	+	2380.91i	−0.291825	+	0.505456i	0.682416	+	0.730964i	$0.260929\pi$
$282$	−1132.52	+	6885.42i	−0.239151	+	1.45397i
$283$	−510.780	−	884.697i	−0.107289	−	0.185830i	0.807382	−	0.590029i	$-0.200884\pi$
$283$	−510.780	−	884.697i	−0.107289	−	0.185830i	−0.914671	+	0.404199i	$0.867550\pi$
$284$	512.483	+	887.647i	0.107078	+	0.185465i
$285$	−546.884	+	3324.91i	−0.113665	+	0.691054i
$286$	−2817.46	+	4879.98i	−0.582516	+	1.00895i
$287$	−1669.32			−0.343334
$288$	−1139.06	+	1001.37i	−0.233056	+	0.204882i
$289$	6979.96			1.42071
$290$	68.7082	−	119.006i	0.0139127	−	0.0240975i
$291$	−7772.95	+	2930.89i	−1.56584	+	0.590418i
$292$	−309.949	−	536.848i	−0.0621178	−	0.107591i
$293$	2616.25	+	4531.47i	0.521648	+	0.903521i	0.999683	+	0.0251800i	$0.00801588\pi$
$293$	2616.25	+	4531.47i	0.521648	+	0.903521i	−0.478035	+	0.878341i	$0.658651\pi$
$294$	−1894.37	−	1552.76i	−0.375790	−	0.308023i
$295$	1106.15	−	1915.91i	0.218314	−	0.378130i
$296$	454.929			0.0893317
$297$	−2363.29	−	3785.18i	−0.461724	−	0.739524i
$298$	3486.71			0.677785
$299$	−2320.07	+	4018.48i	−0.448739	+	0.777240i
$300$	125.803	+	103.117i	0.0242108	+	0.0198449i
$301$	69.5327	+	120.434i	0.0133149	+	0.0230622i
$302$	1773.51	+	3071.81i	0.337927	+	0.585307i
$303$	1040.47	−	392.322i	0.197272	−	0.0743839i
$304$	4698.18	−	8137.49i	0.886379	−	1.53525i
$305$	−722.881			−0.135712
$306$	−8484.50	−	2868.69i	−1.58506	−	0.535921i
$307$	−4912.68			−0.913296			−0.456648	−	0.889648i	$-0.650950\pi$
$307$	−4912.68			−0.913296			−0.456648	+	0.889648i	$0.650950\pi$
$308$	273.066	−	472.964i	0.0505174	−	0.0874988i
$309$	1410.33	−	8574.42i	0.259647	−	1.57858i
$310$	−253.840	−	439.664i	−0.0465069	−	0.0805524i
$311$	414.430	+	717.813i	0.0755632	+	0.130879i	0.901331	−	0.433131i	$-0.142591\pi$
$311$	414.430	+	717.813i	0.0755632	+	0.130879i	−0.825768	+	0.564010i	$0.809258\pi$
$312$	−1008.16	+	6129.36i	−0.182936	+	1.11220i
$313$	−4618.60	+	7999.66i	−0.834054	+	1.44462i	0.0607442	+	0.998153i	$0.480653\pi$
$313$	−4618.60	+	7999.66i	−0.834054	+	1.44462i	−0.894798	+	0.446471i	$0.852681\pi$
$314$	−10571.9			−1.90003
$315$	363.332	+	1815.14i	0.0649887	+	0.324672i
$316$	1465.72			0.260928
$317$	4549.20	−	7879.45i	0.806021	−	1.39607i	−0.109578	−	0.993978i	$-0.534950\pi$
$317$	4549.20	−	7879.45i	0.806021	−	1.39607i	0.915599	−	0.402091i	$-0.131717\pi$
$318$	8778.88	−	3310.18i	1.54810	−	0.583729i
$319$	−143.693	−	248.884i	−0.0252203	−	0.0436828i
$320$	1021.84	+	1769.88i	0.178508	+	0.309185i
$321$	−2414.01	−	1978.69i	−0.419741	−	0.344049i
$322$	1661.45	−	2877.71i	0.287543	−	0.498039i
$323$	14143.9			2.43649
$324$	725.548	+	553.955i	0.124408	+	0.0949855i
$325$	1456.08			0.248519
$326$	3381.38	−	5856.72i	0.574470	−	0.995011i
$327$	−3100.68	−	2541.54i	−0.524368	−	0.429808i
$328$	1249.36	+	2163.95i	0.210318	+	0.364281i
$329$	−3026.92	−	5242.78i	−0.507233	−	0.878553i
$330$	2351.95	−	886.831i	0.392335	−	0.147935i
$331$	−2981.73	+	5164.50i	−0.495137	+	0.857603i	−0.999984	−	0.00560570i	$-0.998216\pi$
$331$	−2981.73	+	5164.50i	−0.495137	+	0.857603i	0.504847	+	0.863209i	$0.331549\pi$
$332$	−530.982			−0.0877754
$333$	−117.458	−	586.801i	−0.0193294	−	0.0965661i
$334$	−4830.23			−0.791313
$335$	2156.80	−	3735.69i	0.351757	−	0.609261i
$336$	837.807	−	5093.65i	0.136030	−	0.827027i
$337$	−298.427	−	516.890i	−0.0482384	−	0.0835514i	0.840898	−	0.541194i	$-0.182027\pi$
$337$	−298.427	−	516.890i	−0.0482384	−	0.0835514i	−0.889136	+	0.457642i	$0.848694\pi$
$338$	−1817.84	−	3148.60i	−0.292537	−	0.506690i
$339$	−983.901	+	5981.85i	−0.157635	+	0.958377i
$340$	341.393	−	591.310i	0.0544548	−	0.0943185i
$341$	−1061.74			−0.168611
$342$	−10090.3	−	3411.63i	−1.59539	−	0.539415i
$343$	6828.34			1.07492
$344$	104.080	−	180.272i	0.0163128	−	0.0282546i
$345$	1936.74	−	730.272i	0.302234	−	0.113961i
$346$	−2293.16	−	3971.87i	−0.356304	−	0.617137i
$347$	2281.05	+	3950.90i	0.352891	+	0.611226i	0.986755	−	0.162219i	$-0.0518652\pi$
$347$	2281.05	+	3950.90i	0.352891	+	0.611226i	−0.633863	+	0.773445i	$0.718532\pi$
$348$	45.4671	+	37.2680i	0.00700372	+	0.00574074i
$349$	−337.633	+	584.798i	−0.0517854	+	0.0896949i	−0.890756	−	0.454482i	$-0.849825\pi$
$349$	−337.633	+	584.798i	−0.0517854	+	0.0896949i	0.838971	+	0.544177i	$0.183158\pi$
$350$	−1042.73			−0.159246
$351$	8166.42	−	282.140i	1.24185	−	0.0429046i
$352$	−1786.65			−0.270536
$353$	1680.91	−	2911.43i	0.253445	−	0.438979i	−0.711027	−	0.703165i	$-0.751770\pi$
$353$	1680.91	−	2911.43i	0.253445	−	0.438979i	0.964472	+	0.264185i	$0.0851030\pi$
$354$	5408.52	+	4433.20i	0.812033	+	0.665598i
$355$	−2046.35	−	3544.38i	−0.305941	−	0.529905i
$356$	−645.732	−	1118.44i	−0.0961341	−	0.166509i
$357$	7270.57	−	2741.46i	1.07787	−	0.406424i
$358$	−2391.81	+	4142.74i	−0.353104	+	0.611594i
$359$	7701.61			1.13224			0.566122	−	0.824322i	$-0.308443\pi$
$359$	7701.61			1.13224			0.566122	+	0.824322i	$0.308443\pi$
$360$	2081.06	−	1829.49i	0.304670	−	0.267840i
$361$	9961.87			1.45238
$362$	−3018.03	+	5227.39i	−0.438189	+	0.758965i
$363$	−269.300	+	1637.27i	−0.0389382	+	0.236734i
$364$	500.026	+	866.070i	0.0720013	+	0.124710i
$365$	1237.63	+	2143.64i	0.177481	+	0.307406i
$366$	370.868	−	2254.78i	0.0529661	−	0.322020i
$367$	−2954.75	+	5117.77i	−0.420263	+	0.727917i	−0.995965	−	0.0897425i	$-0.971396\pi$
$367$	−2954.75	+	5117.77i	−0.420263	+	0.727917i	0.575702	+	0.817660i	$0.304729\pi$
$368$	−5771.94			−0.817617
$369$	2468.66	−	2170.23i	0.348274	−	0.306172i
$370$	337.093			0.0473639
$371$	−4069.86	+	7049.20i	−0.569532	+	0.986459i
$372$	203.228	−	76.6295i	0.0283249	−	0.0106803i
$373$	4212.19	+	7295.73i	0.584716	+	1.01276i	0.994911	+	0.100760i	$0.0321273\pi$
$373$	4212.19	+	7295.73i	0.584716	+	1.01276i	−0.410195	+	0.911998i	$0.634539\pi$
$374$	−5275.42	−	9137.30i	−0.729374	−	1.26331i
$375$	−502.334	−	411.748i	−0.0691744	−	0.0567001i
$376$	−4530.84	+	7847.64i	−0.621436	+	1.07636i
$377$	526.249			0.0718917
$378$	−5848.13	+	202.046i	−0.795754	+	0.0274923i
$379$	−3510.24			−0.475749			−0.237875	−	0.971296i	$-0.576451\pi$
$379$	−3510.24			−0.475749			−0.237875	+	0.971296i	$0.576451\pi$
$380$	406.007	−	703.225i	0.0548098	−	0.0949334i
$381$	6550.81	+	5369.50i	0.880862	+	0.722016i
$382$	3571.54	+	6186.09i	0.478367	+	0.828555i
$383$	−2866.01	−	4964.08i	−0.382367	−	0.662279i	0.609033	−	0.793145i	$-0.291558\pi$
$383$	−2866.01	−	4964.08i	−0.382367	−	0.662279i	−0.991400	+	0.130866i	$0.958224\pi$
$384$	−8229.64	+	3103.09i	−1.09366	+	0.412380i
$385$	−1090.36	+	1888.55i	−0.144337	+	0.249999i
$386$	−712.283			−0.0939229
$387$	−259.400	−	87.7056i	−0.0340725	−	0.0115202i
$388$	2001.89			0.261934
$389$	−7183.60	+	12442.4i	−0.936306	+	1.62173i	−0.164019	+	0.986457i	$0.552446\pi$
$389$	−7183.60	+	12442.4i	−0.936306	+	1.62173i	−0.772288	+	0.635273i	$0.780888\pi$
$390$	−747.030	+	4541.74i	−0.0969931	+	0.589692i
$391$	−4344.11	−	7524.23i	−0.561870	−	0.973188i
$392$	−1590.44	−	2754.72i	−0.204922	−	0.354934i
$393$	218.276	−	1327.06i	0.0280167	−	0.170334i
$394$	1091.75	−	1890.97i	0.139598	−	0.241791i
$395$	−5852.63			−0.745514
$396$	211.065	+	1054.44i	0.0267838	+	0.133807i
$397$	−9014.42			−1.13960			−0.569800	−	0.821784i	$-0.692979\pi$
$397$	−9014.42			−1.13960			−0.569800	+	0.821784i	$0.692979\pi$
$398$	−2587.69	+	4482.01i	−0.325902	+	0.564479i
$399$	8646.64	−	3260.32i	1.08490	−	0.409073i
$400$	905.619	+	1568.58i	0.113202	+	0.196072i
$401$	−5255.55	−	9102.87i	−0.654487	−	1.13361i	−0.982022	−	0.188766i	$-0.939551\pi$
$401$	−5255.55	−	9102.87i	−0.654487	−	1.13361i	0.327535	−	0.944839i	$-0.393782\pi$
$402$	10545.7	+	8643.97i	1.30839	+	1.07244i
$403$	972.104	−	1683.73i	0.120159	−	0.208121i
$404$	−267.969			−0.0329998
$405$	−2897.12	−	2211.95i	−0.355454	−	0.271389i
$406$	−376.857			−0.0460667
$407$	352.491	−	610.533i	0.0429296	−	0.0743562i
$408$	−8995.23	−	7373.12i	−1.09150	−	0.894666i
$409$	−1659.10	−	2873.65i	−0.200580	−	0.347415i	0.748135	−	0.663546i	$-0.230949\pi$
$409$	−1659.10	−	2873.65i	−0.200580	−	0.347415i	−0.948715	+	0.316131i	$0.897616\pi$
$410$	925.751	+	1603.45i	0.111511	+	0.193143i
$411$	−5118.57	+	1930.02i	−0.614308	+	0.231632i
$412$	−1047.03	+	1813.51i	−0.125203	+	0.216857i
$413$	−6067.11			−0.722864
$414$	1284.20	+	6415.66i	0.152452	+	0.761625i
$415$	2120.22			0.250789
$416$	1635.81	−	2833.31i	0.192794	−	0.333929i
$417$	2010.93	−	12225.9i	0.236153	−	1.43575i
$418$	−6273.89	−	10866.7i	−0.734129	−	1.27155i
$419$	243.069	+	421.008i	0.0283406	+	0.0490873i	0.879848	−	0.475255i	$-0.157644\pi$
$419$	243.069	+	421.008i	0.0283406	+	0.0490873i	−0.851507	+	0.524343i	$0.824311\pi$
$420$	72.4016	−	440.182i	0.00841151	−	0.0511398i
$421$	−2525.96	+	4375.10i	−0.292418	+	0.506482i	−0.974381	−	0.224904i	$-0.927793\pi$
$421$	−2525.96	+	4375.10i	−0.292418	+	0.506482i	0.681963	+	0.731387i	$0.261126\pi$
$422$	−15022.1			−1.73286
$423$	11292.3	+	3818.03i	1.29799	+	0.438863i
$424$	12183.9			1.39553
$425$	−1363.19	+	2361.11i	−0.155586	+	0.269484i
$426$	12105.4	−	4564.48i	1.37678	−	0.519130i
$427$	991.230	+	1716.86i	0.112340	+	0.194578i
$428$	376.094	+	651.414i	0.0424747	+	0.0735684i
$429$	7444.70	+	6102.19i	0.837840	+	0.686752i
$430$	77.1212	−	133.578i	0.00864910	−	0.0149807i
$431$	6944.24			0.776084			0.388042	−	0.921642i	$-0.373152\pi$
$431$	6944.24			0.776084			0.388042	+	0.921642i	$0.373152\pi$
$432$	5383.10	+	8621.89i	0.599525	+	0.960234i
$433$	−13738.3			−1.52476			−0.762378	−	0.647131i	$-0.775968\pi$
$433$	−13738.3			−1.52476			−0.762378	+	0.647131i	$0.775968\pi$
$434$	−696.142	+	1205.75i	−0.0769952	+	0.133360i
$435$	−181.551	−	148.812i	−0.0200108	−	0.0164022i
$436$	483.075	+	836.711i	0.0530622	+	0.0919064i
$437$	−5166.31	−	8948.31i	−0.565533	−	0.979533i
$438$	−7321.31	+	2760.59i	−0.798688	+	0.301155i
$439$	−4240.92	+	7345.48i	−0.461066	+	0.798589i	−0.999014	−	0.0443883i	$-0.985866\pi$
$439$	−4240.92	+	7345.48i	−0.461066	+	0.798589i	0.537949	+	0.842978i	$0.319199\pi$
$440$	3264.19			0.353668
$441$	−3142.61	+	2762.71i	−0.339338	+	0.298317i
$442$	19320.2			2.07912
$443$	279.098	−	483.411i	0.0299330	−	0.0518455i	−0.850671	−	0.525699i	$-0.823804\pi$
$443$	279.098	−	483.411i	0.0299330	−	0.0518455i	0.880604	+	0.473853i	$0.157137\pi$
$444$	−23.4061	+	142.303i	−0.00250181	+	0.0152103i
$445$	2578.42	+	4465.95i	0.274671	+	0.475744i
$446$	4643.44	+	8042.67i	0.492989	+	0.853882i
$447$	966.707	−	5877.32i	0.102290	−	0.621896i
$448$	2802.34	−	4853.79i	0.295531	−	0.511875i
$449$	14775.0			1.55295			0.776476	−	0.630147i	$-0.217005\pi$
$449$	14775.0			1.55295			0.776476	+	0.630147i	$0.217005\pi$
$450$	1542.02	−	1355.61i	0.161537	−	0.142009i
$451$	3872.15			0.404285
$452$	730.449	−	1265.17i	0.0760120	−	0.131657i
$453$	5669.66	−	2137.82i	0.588044	−	0.221729i
$454$	1277.46	+	2212.62i	0.132058	+	0.228730i
$455$	−1996.61	−	3458.23i	−0.205720	−	0.356317i
$456$	−10697.7	−	8768.60i	−1.09861	−	0.900499i
$457$	7103.97	−	12304.4i	0.727154	−	1.25947i	−0.230927	−	0.972971i	$-0.574176\pi$
$457$	7103.97	−	12304.4i	0.727154	−	1.25947i	0.958081	−	0.286497i	$-0.0924909\pi$
$458$	4263.02			0.434930
$459$	−7187.92	+	13506.4i	−0.730944	+	1.37347i
$460$	−498.799			−0.0505579
$461$	3851.26	−	6670.57i	0.389091	−	0.673925i	−0.603237	−	0.797562i	$-0.706123\pi$
$461$	3851.26	−	6670.57i	0.389091	−	0.673925i	0.992328	+	0.123637i	$0.0394558\pi$
$462$	−5331.29	−	4369.90i	−0.536870	−	0.440056i
$463$	−3954.53	−	6849.45i	−0.396939	−	0.687518i	0.596408	−	0.802682i	$-0.296594\pi$
$463$	−3954.53	−	6849.45i	−0.396939	−	0.687518i	−0.993347	+	0.115163i	$0.963261\pi$
$464$	327.304	+	566.908i	0.0327472	+	0.0567199i
$465$	−811.490	+	305.982i	−0.0809289	+	0.0305153i
$466$	4345.11	−	7525.96i	0.431939	−	0.748140i
$467$	11639.8			1.15337			0.576685	−	0.816967i	$-0.304346\pi$
$467$	11639.8			1.15337			0.576685	+	0.816967i	$0.304346\pi$
$468$	−1865.41	−	630.711i	−0.184249	−	0.0622962i
$469$	−11829.8			−1.16471
$470$	−3357.26	+	5814.95i	−0.329487	+	0.570688i
$471$	−2931.11	+	17820.4i	−0.286749	+	1.74336i
$472$	4540.77	+	7864.84i	0.442809	+	0.766967i
$473$	−161.288	−	279.359i	−0.0156787	−	0.0271563i
$474$	3002.65	−	18255.3i	0.290962	−	1.76897i
$475$	−1621.19	+	2807.99i	−0.156601	+	0.271240i
$476$	−1872.50			−0.180307
$477$	−3145.77	−	15715.7i	−0.301960	−	1.50854i
$478$	−5200.87			−0.497662
$479$	9347.93	−	16191.1i	0.891687	−	1.54445i	0.0538341	−	0.998550i	$-0.482856\pi$
$479$	9347.93	−	16191.1i	0.891687	−	1.54445i	0.837853	−	0.545897i	$-0.183811\pi$
$480$	−1365.54	+	514.894i	−0.129850	+	0.0489616i
$481$	645.465	+	1117.98i	0.0611865	+	0.105978i
$482$	6589.10	+	11412.7i	0.622667	+	1.07849i
$483$	−4390.12	−	3598.45i	−0.413576	−	0.338996i
$484$	199.928	−	346.286i	0.0187761	−	0.0325212i
$485$	−7993.56			−0.748390
$486$	8385.77	−	7901.75i	0.782687	−	0.737512i
$487$	−2249.54			−0.209315			−0.104658	−	0.994508i	$-0.533375\pi$
$487$	−2249.54			−0.209315			−0.104658	+	0.994508i	$0.533375\pi$
$488$	1483.72	−	2569.88i	0.137633	−	0.238387i
$489$	−8934.78	−	7323.57i	−0.826267	−	0.677266i
$490$	−1178.48	−	2041.19i	−0.108650	−	0.188187i
$491$	−994.175	−	1721.96i	−0.0913778	−	0.158271i	0.816713	−	0.577044i	$-0.195794\pi$
$491$	−994.175	−	1721.96i	−0.0913778	−	0.158271i	−0.908091	+	0.418773i	$0.862460\pi$
$492$	−741.168	+	279.466i	−0.0679155	+	0.0256084i
$493$	−492.676	+	853.339i	−0.0450081	+	0.0779563i
$494$	22976.9			2.09267
$495$	−842.784	−	4210.40i	−0.0765259	−	0.382310i
$496$	2418.43			0.218933
$497$	−5612.01	+	9720.28i	−0.506505	+	0.877292i
$498$	−1087.76	+	6613.29i	−0.0978790	+	0.595078i
$499$	−1206.95	−	2090.50i	−0.108278	−	0.187543i	0.806795	−	0.590832i	$-0.201200\pi$
$499$	−1206.95	−	2090.50i	−0.108278	−	0.187543i	−0.915073	+	0.403289i	$0.867867\pi$
$500$	78.2617	+	135.553i	0.00699994	+	0.0121243i
$501$	−1339.20	+	8142.00i	−0.119423	+	0.726063i
$502$	2623.10	−	4543.34i	0.233216	−	0.403942i
$503$	−8758.56			−0.776391			−0.388196	−	0.921577i	$-0.626902\pi$
$503$	−8758.56			−0.776391			−0.388196	+	0.921577i	$0.626902\pi$
$504$	−7198.67	−	2433.94i	−0.636219	−	0.215111i
$505$	1070.00			0.0942860
$506$	−3853.88	+	6675.12i	−0.338589	+	0.586453i
$507$	−5811.38	+	2191.25i	−0.509058	+	0.191947i
$508$	−1020.59	−	1767.72i	−0.0891368	−	0.154389i
$509$	5924.01	+	10260.7i	0.515869	+	0.893511i	0.999830	+	0.0184220i	$0.00586422\pi$
$509$	5924.01	+	10260.7i	0.515869	+	0.893511i	−0.483961	+	0.875089i	$0.660802\pi$
$510$	−6665.30	−	5463.34i	−0.578714	−	0.474354i
$511$	3394.13	−	5878.81i	0.293831	−	0.508930i
$512$	−7826.64			−0.675570
$513$	−8548.36	+	16062.7i	−0.735710	+	1.38243i
$514$	−17804.1			−1.52783
$515$	4180.80	−	7241.36i	0.357725	−	0.619597i
$516$	51.0344	+	41.8313i	0.00435400	+	0.00356884i
$517$	7021.23	+	12161.1i	0.597279	+	1.03452i
$518$	−462.230	−	800.606i	−0.0392070	−	0.0679085i
$519$	−7330.91	+	2764.21i	−0.620022	+	0.233787i
$520$	−2988.62	+	5176.43i	−0.252037	+	0.436542i
$521$	3816.55			0.320933			0.160466	−	0.987041i	$-0.448700\pi$
$521$	3816.55			0.320933			0.160466	+	0.987041i	$0.448700\pi$
$522$	557.310	−	489.939i	0.0467295	−	0.0410806i
$523$	−12158.9			−1.01658			−0.508288	−	0.861187i	$-0.669722\pi$
$523$	−12158.9			−1.01658			−0.508288	+	0.861187i	$0.669722\pi$
$524$	−162.049	+	280.676i	−0.0135098	+	0.0233996i
$525$	−289.100	+	1757.65i	−0.0240331	+	0.146115i
$526$	−596.729	−	1033.57i	−0.0494651	−	0.0856761i
$527$	1820.17	+	3152.63i	0.150452	+	0.260590i
$528$	−1943.37	+	11815.2i	−0.160179	+	0.973846i
$529$	2909.97	−	5040.22i	0.239169	−	0.414253i
$530$	9028.04			0.739911
$531$	8972.28	−	7887.65i	0.733265	−	0.644623i
$532$	−2226.90			−0.181482
$533$	−3545.25	+	6140.55i	−0.288108	+	0.499018i
$534$	−15252.8	+	5751.27i	−1.23606	+	0.466071i
$535$	−1501.75	−	2601.10i	−0.121357	−	0.210197i
$536$	8853.71	+	15335.1i	0.713474	+	1.23577i
$537$	6320.00	+	5180.31i	0.507874	+	0.416289i
$538$	7011.72	−	12144.7i	0.561890	−	0.973222i
$539$	−4929.26			−0.393911
$540$	465.197	+	745.086i	0.0370720	+	0.0593767i
$541$	14919.8			1.18568			0.592840	−	0.805321i	$-0.298007\pi$
$541$	14919.8			1.18568			0.592840	+	0.805321i	$0.298007\pi$
$542$	1757.69	−	3044.42i	0.139298	−	0.241271i
$543$	7974.69	+	6536.61i	0.630252	+	0.516598i
$544$	3062.91	+	5305.12i	0.241399	+	0.418116i
$545$	−1928.92	−	3341.00i	−0.151607	−	0.262592i
$546$	11811.1	−	4453.52i	0.925766	−	0.349072i
$547$	513.578	−	889.543i	0.0401444	−	0.0695322i	−0.845255	−	0.534363i	$-0.820552\pi$
$547$	513.578	−	889.543i	0.0401444	−	0.0695322i	0.885400	+	0.464831i	$0.153885\pi$
$548$	1318.27			0.102762
$549$	−3697.91	−	1250.30i	−0.287473	−	0.0971973i
$550$	2418.70			0.187516
$551$	−585.923	+	1014.85i	−0.0453015	+	0.0784646i
$552$	−1379.02	+	8384.10i	−0.106332	+	0.646469i
$553$	8025.26	+	13900.2i	0.617123	+	1.06889i
$554$	925.313	+	1602.69i	0.0709617	+	0.122909i
$555$	93.4606	−	568.216i	0.00714808	−	0.0434584i
$556$	−1492.92	+	2585.81i	−0.113874	+	0.197235i
$557$	−10590.8			−0.805648			−0.402824	−	0.915277i	$-0.631971\pi$
$557$	−10590.8			−0.805648			−0.402824	+	0.915277i	$0.631971\pi$
$558$	−538.079	−	2688.15i	−0.0408220	−	0.203940i
$559$	590.685			0.0446929
$560$	2483.61	−	4301.74i	0.187414	−	0.324610i
$561$	−16864.8	+	6359.07i	−1.26922	+	0.478574i
$562$	−4181.23	−	7242.11i	−0.313834	−	0.543576i
$563$	1096.03	+	1898.38i	0.0820467	+	0.142109i	0.904129	−	0.427260i	$-0.140521\pi$
$563$	1096.03	+	1898.38i	0.0820467	+	0.142109i	−0.822082	+	0.569369i	$0.807188\pi$
$564$	−2221.64	−	1821.01i	−0.165865	−	0.135955i
$565$	−2916.69	+	5051.86i	−0.217179	+	0.376165i
$566$	3107.32			0.230761
$567$	−1280.84	+	9913.81i	−0.0948684	+	0.734287i
$568$	16800.6			1.24109
$569$	8284.89	−	14349.8i	0.610405	−	1.05725i	−0.380767	−	0.924671i	$-0.624340\pi$
$569$	8284.89	−	14349.8i	0.610405	−	1.05725i	0.991172	−	0.132582i	$-0.0423267\pi$
$570$	−7926.81	−	6497.37i	−0.582487	−	0.477447i
$571$	−3639.66	−	6304.08i	−0.266752	−	0.462027i	0.701269	−	0.712896i	$-0.252617\pi$
$571$	−3639.66	−	6304.08i	−0.266752	−	0.462027i	−0.968021	+	0.250869i	$0.919284\pi$
$572$	−1159.86	−	2008.93i	−0.0847833	−	0.146849i
$573$	11417.7	−	4305.19i	0.832429	−	0.313878i
$574$	2538.82	−	4397.36i	0.184614	−	0.319760i
$575$	1991.71			0.144452
$576$	2166.05	+	10821.2i	0.156688	+	0.782784i
$577$	−17938.0			−1.29422			−0.647112	−	0.762395i	$-0.724024\pi$
$577$	−17938.0			−1.29422			−0.647112	+	0.762395i	$0.724024\pi$
$578$	−10615.6	+	18386.8i	−0.763930	+	1.32317i
$579$	−197.484	+	1200.65i	−0.0141747	+	0.0861782i
$580$	28.2850	+	48.9910i	0.00202495	+	0.00350731i
$581$	−2907.29	−	5035.57i	−0.207598	−	0.359571i
$582$	4101.03	−	24933.2i	0.292085	−	1.77580i
$583$	9440.42	−	16351.3i	0.670639	−	1.16158i
$584$	−10161.0			−0.719974
$585$	7448.59	+	2518.44i	0.526430	+	0.177991i
$586$	−15915.9			−1.12198
$587$	−5754.83	+	9967.67i	−0.404646	+	0.700868i	−0.994280	−	0.106803i	$-0.965939\pi$
$587$	−5754.83	+	9967.67i	−0.404646	+	0.700868i	0.589634	+	0.807671i	$0.299272\pi$
$588$	943.509	−	355.762i	0.0661729	−	0.0249513i
$589$	2164.67	+	3749.32i	0.151433	+	0.262289i
$590$	3364.62	+	5827.70i	0.234778	+	0.406648i
$591$	−2884.79	−	2364.57i	−0.200785	−	0.164578i
$592$	−802.904	+	1390.67i	−0.0557418	+	0.0965476i
$593$	−9612.80			−0.665684			−0.332842	−	0.942983i	$-0.608008\pi$
$593$	−9612.80			−0.665684			−0.332842	+	0.942983i	$0.608008\pi$
$594$	13565.3	−	468.664i	0.937021	−	0.0323729i
$595$	7476.92			0.515166
$596$	−717.684	+	1243.07i	−0.0493247	+	0.0854328i
$597$	6837.57	+	5604.55i	0.468749	+	0.384219i
$598$	−7057.05	−	12223.2i	−0.482582	−	0.835857i
$599$	−3686.00	−	6384.33i	−0.251429	−	0.435487i	0.712491	−	0.701681i	$-0.247567\pi$
$599$	−3686.00	−	6384.33i	−0.251429	−	0.435487i	−0.963919	+	0.266194i	$0.914234\pi$
$600$	2494.83	−	940.706i	0.169752	−	0.0640069i
$601$	12095.3	−	20949.7i	0.820927	−	1.42189i	−0.0840654	−	0.996460i	$-0.526790\pi$
$601$	12095.3	−	20949.7i	0.820927	−	1.42189i	0.904993	−	0.425427i	$-0.139876\pi$
$602$	−423.001			−0.0286383
$603$	17494.4	−	15379.6i	1.18147	−	1.03865i
$604$	−1460.20			−0.0983684
$605$	−798.317	+	1382.72i	−0.0536466	+	0.0929186i
$606$	−548.956	+	3337.50i	−0.0367984	+	0.223724i
$607$	658.866	+	1141.19i	0.0440569	+	0.0763088i	0.887213	−	0.461360i	$-0.152638\pi$
$607$	658.866	+	1141.19i	0.0440569	+	0.0763088i	−0.843156	+	0.537669i	$0.819305\pi$
$608$	3642.62	+	6309.20i	0.242973	+	0.420842i
$609$	−104.485	+	635.242i	−0.00695230	+	0.0422681i
$610$	1099.41	−	1904.23i	0.0729733	−	0.126393i
$611$	−25713.9			−1.70257
$612$	2769.13	−	2434.38i	0.182901	−	0.160791i
$613$	−4137.52			−0.272615			−0.136307	−	0.990667i	$-0.543523\pi$
$613$	−4137.52			−0.272615			−0.136307	+	0.990667i	$0.543523\pi$
$614$	7471.56	−	12941.1i	0.491087	−	0.850588i
$615$	2959.49	−	1115.91i	0.194046	−	0.0731674i
$616$	−4475.93	−	7752.54i	−0.292760	−	0.507076i
$617$	3895.81	+	6747.74i	0.254197	+	0.440281i	0.964677	−	0.263436i	$-0.0848557\pi$
$617$	3895.81	+	6747.74i	0.254197	+	0.440281i	−0.710480	+	0.703717i	$0.751522\pi$
$618$	20442.0	+	16755.7i	1.33058	+	1.09064i
$619$	−10978.2	+	19014.8i	−0.712844	+	1.23468i	0.250941	+	0.968002i	$0.419260\pi$
$619$	−10978.2	+	19014.8i	−0.712844	+	1.23468i	−0.963785	+	0.266680i	$0.914073\pi$
$620$	208.996			0.0135379
$621$	11170.5	−	385.927i	0.721831	−	0.0249384i
$622$	−2521.18			−0.162524
$623$	7071.17	−	12247.6i	0.454736	−	0.787625i
$624$	−16957.5	−	13899.6i	−1.08789	−	0.891712i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−14048.6	−	24332.9i	−0.896957	−	1.55357i
$627$	−20056.7	+	7562.63i	−1.27749	+	0.481694i
$628$	2176.06	−	3769.05i	0.138271	−	0.239493i
$629$	−2417.15			−0.153224
$630$	−5334.08	−	1803.50i	−0.337325	−	0.114053i
$631$	−11152.7			−0.703618			−0.351809	−	0.936072i	$-0.614433\pi$
$631$	−11152.7			−0.703618			−0.351809	+	0.936072i	$0.614433\pi$
$632$	12012.6	−	20806.4i	0.756068	−	1.30955i
$633$	−4164.95	+	25321.8i	−0.261520	+	1.58997i
$634$	13837.5	+	23967.2i	0.866810	+	1.50136i
$635$	4075.24	+	7058.52i	0.254679	+	0.441116i
$636$	−626.861	+	3811.15i	−0.0390828	+	0.237613i
$637$	4513.11	−	7816.94i	0.280716	−	0.486214i
$638$	874.155			0.0542447
$639$	−4337.77	−	21670.7i	−0.268544	−	1.34160i
$640$	−8463.22			−0.522716
$641$	−2404.72	+	4165.10i	−0.148176	+	0.256648i	−0.930553	−	0.366156i	$-0.880674\pi$
$641$	−2404.72	+	4165.10i	−0.148176	+	0.256648i	0.782377	+	0.622805i	$0.214007\pi$
$642$	8883.71	−	3349.71i	0.546125	−	0.205923i
$643$	1276.51	+	2210.98i	0.0782904	+	0.135603i	0.902512	−	0.430664i	$-0.141721\pi$
$643$	1276.51	+	2210.98i	0.0782904	+	0.135603i	−0.824222	+	0.566267i	$0.808387\pi$
$644$	683.964	+	1184.66i	0.0418509	+	0.0724879i
$645$	−203.781	−	167.033i	−0.0124401	−	0.0101968i
$646$	−21511.0	+	37258.2i	−1.31013	+	2.26920i
$647$	8446.00			0.513210			0.256605	−	0.966516i	$-0.417396\pi$
$647$	8446.00			0.513210			0.256605	+	0.966516i	$0.417396\pi$
$648$	13810.0	−	5759.36i	0.837201	−	0.349150i
$649$	14073.2			0.851191
$650$	−2214.51	+	3835.64i	−0.133631	+	0.231456i
$651$	1839.45	+	1507.74i	0.110743	+	0.0907727i
$652$	1392.01	+	2411.02i	0.0836122	+	0.144821i
$653$	−4047.44	−	7010.37i	−0.242555	−	0.420118i	0.718886	−	0.695128i	$-0.244652\pi$
$653$	−4047.44	−	7010.37i	−0.242555	−	0.420118i	−0.961441	+	0.275010i	$0.911319\pi$
$654$	11410.7	−	4302.55i	0.682254	−	0.257252i
$655$	647.062	−	1120.74i	0.0385997	−	0.0668566i
$656$	−8819.97			−0.524942
$657$	2623.47	+	13106.4i	0.155786	+	0.778280i
$658$	18414.2			1.09097
$659$	−1087.67	+	1883.89i	−0.0642936	+	0.111360i	−0.896380	−	0.443286i	$-0.853813\pi$
$659$	−1087.67	+	1883.89i	−0.0642936	+	0.111360i	0.832087	+	0.554645i	$0.187146\pi$
$660$	−167.942	+	1021.04i	−0.00990477	+	0.0602184i
$661$	4438.47	+	7687.66i	0.261175	+	0.452368i	0.966554	−	0.256462i	$-0.0825567\pi$
$661$	4438.47	+	7687.66i	0.261175	+	0.452368i	−0.705379	+	0.708830i	$0.749223\pi$
$662$	−9069.64	−	15709.1i	−0.532480	−	0.922282i
$663$	5356.62	−	32566.8i	0.313776	−	1.90768i
$664$	−4351.77	+	7537.48i	−0.254339	+	0.440529i
$665$	8892.06			0.518525
$666$	1724.41	+	583.037i	0.100329	+	0.0339223i
$667$	719.834			0.0417872
$668$	994.226	−	1722.05i	0.0575865	−	0.0997427i
$669$	14844.4	−	5597.27i	0.857874	−	0.323472i
$670$	6560.43	+	11363.0i	0.378286	+	0.655211i
$671$	−2299.25	−	3982.42i	−0.132283	−	0.229120i
$672$	3095.35	+	2537.16i	0.177687	+	0.145645i
$673$	4583.96	−	7939.65i	0.262554	−	0.454757i	−0.704366	−	0.709837i	$-0.748769\pi$
$673$	4583.96	−	7939.65i	0.262554	−	0.454757i	0.966920	+	0.255080i	$0.0821019\pi$
$674$	1815.47			0.103753
$675$	−1857.54	−	2975.14i	−0.105921	−	0.169649i
$676$	1496.70			0.0851557
$677$	9438.93	−	16348.7i	0.535846	−	0.928112i	−0.463276	−	0.886214i	$-0.653326\pi$
$677$	9438.93	−	16348.7i	0.535846	−	0.928112i	0.999122	−	0.0418983i	$-0.0133405\pi$
$678$	−14261.2	−	11689.4i	−0.807812	−	0.662139i
$679$	10961.0	+	18984.9i	0.619503	+	1.07301i
$680$	−5595.90	−	9692.39i	−0.315578	−	0.546597i
$681$	4083.85	−	1539.87i	0.229800	−	0.0866488i
$682$	1614.77	−	2796.86i	0.0906638	−	0.157034i
$683$	−27207.5			−1.52426			−0.762128	−	0.647426i	$-0.775845\pi$
$683$	−27207.5			−1.52426			−0.762128	+	0.647426i	$0.775845\pi$
$684$	3293.23	−	2895.13i	0.184094	−	0.161839i
$685$	−5263.85			−0.293608
$686$	−10385.0	+	17987.4i	−0.577991	+	1.00111i
$687$	1181.94	−	7185.89i	0.0656388	−	0.399067i
$688$	367.381	+	636.323i	0.0203580	+	0.0352610i
$689$	17286.9	+	29941.7i	0.955845	+	1.65557i
$690$	−1021.83	+	6212.46i	−0.0563775	+	0.342760i
$691$	8703.62	−	15075.1i	0.479162	−	0.829934i	−0.520552	−	0.853830i	$-0.674274\pi$
$691$	8703.62	−	15075.1i	0.479162	−	0.829934i	0.999714	+	0.0238963i	$0.00760715\pi$
$692$	1888.04			0.103718
$693$	−8844.17	+	7775.03i	−0.484794	+	0.426189i
$694$	−13876.7			−0.759011
$695$	5961.24	−	10325.2i	0.325356	−	0.563534i
$696$	901.668	−	339.985i	0.0491058	−	0.0185159i
$697$	−6638.15	−	11497.6i	−0.360743	−	0.624825i
$698$	−1026.99	−	1778.80i	−0.0556909	−	0.0964595i
$699$	−11481.3	−	9410.87i	−0.621263	−	0.509230i
$700$	214.628	−	371.747i	0.0115888	−	0.0200725i
$701$	18543.0			0.999086			0.499543	−	0.866289i	$-0.333501\pi$
$701$	18543.0			0.999086			0.499543	+	0.866289i	$0.333501\pi$
$702$	−11676.8	+	21941.3i	−0.627798	+	1.17966i
$703$	−2874.63			−0.154223
$704$	−6500.29	+	11258.8i	−0.347996	+	0.602746i
$705$	8871.05	+	7271.33i	0.473905	+	0.388446i
$706$	5112.91	+	8855.81i	0.272559	+	0.472086i
$707$	−1467.21	−	2541.28i	−0.0780482	−	0.135184i
$708$	−2693.76	+	1015.72i	−0.142991	+	0.0539165i
$709$	−13116.9	+	22719.1i	−0.694803	+	1.20343i	0.275444	+	0.961317i	$0.411175\pi$
$709$	−13116.9	+	22719.1i	−0.694803	+	1.20343i	−0.970247	+	0.242117i	$0.922158\pi$
$710$	12448.9			0.658029
$711$	−29939.2	−	10122.7i	−1.57920	−	0.533941i
$712$	−21168.9			−1.11424
$713$	1329.70	−	2303.11i	0.0698425	−	0.120971i
$714$	−3835.98	+	23321.7i	−0.201061	+	1.22240i
$715$	4631.32	+	8021.69i	0.242240	+	0.419572i
$716$	−984.633	−	1705.43i	−0.0513931	−	0.0890155i
$717$	−1441.96	+	8766.76i	−0.0751062	+	0.456626i
$718$	−11713.2	+	20287.8i	−0.608817	+	1.05450i
$719$	−3043.06			−0.157840			−0.0789199	−	0.996881i	$-0.525147\pi$
$719$	−3043.06			−0.157840			−0.0789199	+	0.996881i	$0.525147\pi$
$720$	1919.69	+	9590.44i	0.0993648	+	0.496409i
$721$	−22931.2			−1.18447
$722$	−15150.7	+	26241.8i	−0.780958	+	1.35266i
$723$	21064.4	−	7942.60i	1.08353	−	0.408559i
$724$	−1242.43	−	2151.95i	−0.0637769	−	0.110465i
$725$	−112.942	−	195.622i	−0.00578561	−	0.0100210i
$726$	−3903.37	−	3199.47i	−0.199542	−	0.163559i
$727$	−10971.2	+	19002.7i	−0.559698	+	0.969426i	0.437823	+	0.899061i	$0.355750\pi$
$727$	−10971.2	+	19002.7i	−0.559698	+	0.969426i	−0.997521	+	0.0703647i	$0.977584\pi$
$728$	16392.2			0.834528
$729$	−10994.5	−	16326.1i	−0.558577	−	0.829453i
$730$	−7529.10			−0.381732
$731$	−553.002	+	957.827i	−0.0279802	+	0.0484631i
$732$	727.525	+	596.330i	0.0367351	+	0.0301107i
$733$	13288.4	+	23016.2i	0.669604	+	1.15979i	0.978015	+	0.208535i	$0.0668694\pi$
$733$	13288.4	+	23016.2i	0.669604	+	1.15979i	−0.308411	+	0.951253i	$0.599797\pi$
$734$	−8987.58	−	15566.9i	−0.451959	−	0.782815i
$735$	−3767.44	+	1420.56i	−0.189067	+	0.0712901i
$736$	2237.56	−	3875.57i	0.112062	−	0.194097i
$737$	27440.4			1.37148
$738$	1962.37	+	9803.63i	0.0978803	+	0.488993i
$739$	28787.7			1.43298			0.716489	−	0.697598i	$-0.245748\pi$
$739$	28787.7			1.43298			0.716489	+	0.697598i	$0.245748\pi$
$740$	−69.3853	+	120.179i	−0.00344683	+	0.00597008i
$741$	6370.45	−	38730.6i	0.315822	−	1.92011i
$742$	−12379.5	−	21441.8i	−0.612485	−	1.06086i
$743$	2251.51	+	3899.73i	0.111171	+	0.192553i	0.916243	−	0.400624i	$-0.131207\pi$
$743$	2251.51	+	3899.73i	0.111171	+	0.192553i	−0.805072	+	0.593177i	$0.797873\pi$
$744$	577.808	−	3512.92i	0.0284724	−	0.173105i
$745$	2865.72	−	4963.58i	0.140929	−	0.244096i
$746$	−25624.8			−1.25763
$747$	10846.0	+	3667.13i	0.531238	+	0.179616i
$748$	4343.45			0.212316
$749$	−4118.46	+	7133.38i	−0.200915	+	0.347995i
$750$	1848.62	−	697.045i	0.0900027	−	0.0339366i
$751$	−2852.83	−	4941.24i	−0.138617	−	0.240091i	0.788357	−	0.615219i	$-0.210932\pi$
$751$	−2852.83	−	4941.24i	−0.138617	−	0.240091i	−0.926973	+	0.375128i	$0.877599\pi$
$752$	−15993.0	−	27700.6i	−0.775536	−	1.34327i
$753$	−6931.13	−	5681.24i	−0.335438	−	0.274948i
$754$	−800.356	+	1386.26i	−0.0386568	+	0.0669556i
$755$	5830.58			0.281055
$756$	1131.71	−	2126.53i	0.0544444	−	0.102303i
$757$	17397.6			0.835305			0.417652	−	0.908607i	$-0.362853\pi$
$757$	17397.6			0.835305			0.417652	+	0.908607i	$0.362853\pi$
$758$	5338.62	−	9246.77i	0.255815	−	0.443084i
$759$	10183.3	+	8346.94i	0.486996	+	0.399176i
$760$	−6655.02	−	11526.8i	−0.317636	−	0.550161i
$761$	17757.2	+	30756.3i	0.845857	+	1.46507i	0.884875	+	0.465829i	$0.154244\pi$
$761$	17757.2	+	30756.3i	0.845857	+	1.46507i	−0.0390179	+	0.999239i	$0.512423\pi$
$762$	−24107.4	+	9090.00i	−1.14609	+	0.432147i
$763$	−5289.97	+	9162.50i	−0.250996	+	0.434737i
$764$	−2940.58			−0.139249
$765$	−11057.2	+	9720.51i	−0.522579	+	0.459406i
$766$	17435.3			0.822408
$767$	−12885.1	+	22317.7i	−0.606591	+	1.05065i
$768$	1584.37	−	9632.57i	0.0744416	−	0.452585i
$769$	−15631.8	−	27075.1i	−0.733027	−	1.26964i	−0.955583	−	0.294721i	$-0.904773\pi$
$769$	−15631.8	−	27075.1i	−0.733027	−	1.26964i	0.222556	−	0.974920i	$-0.428560\pi$
$770$	−3316.58	−	5744.48i	−0.155222	−	0.268853i
$771$	−4936.26	+	30011.2i	−0.230577	+	1.40185i
$772$	146.612	−	253.940i	0.00683508	−	0.0118387i
$773$	−6676.47			−0.310654			−0.155327	−	0.987863i	$-0.549643\pi$
$773$	−6676.47			−0.310654			−0.155327	+	0.987863i	$0.549643\pi$
$774$	625.551	−	549.930i	0.0290503	−	0.0255385i
$775$	−834.522			−0.0386799
$776$	16406.9	−	28417.5i	0.758985	−	1.31460i
$777$	−1477.68	+	557.179i	−0.0682260	+	0.0257254i
$778$	−21850.7	−	37846.5i	−1.00692	−	1.74404i
$779$	−7894.53	−	13673.7i	−0.363095	−	0.628898i
$780$	−1465.43	−	1201.17i	−0.0672705	−	0.0551396i
$781$	13017.6	−	22547.1i	0.596422	−	1.03303i
$782$	26427.3			1.20849
$783$	−671.341	−	1075.26i	−0.0306408	−	0.0490761i
$784$	11227.9			0.511473
$785$	−8689.04	+	15049.9i	−0.395064	+	0.684271i
$786$	3163.81	+	2593.28i	0.143574	+	0.117683i
$787$	−4716.91	−	8169.93i	−0.213646	−	0.370047i	0.739207	−	0.673479i	$-0.235201\pi$
$787$	−4716.91	−	8169.93i	−0.213646	−	0.370047i	−0.952853	+	0.303432i	$0.901867\pi$
$788$	449.439	+	778.451i	0.0203180	+	0.0351919i
$789$	−1907.66	+	719.306i	−0.0860766	+	0.0324562i
$790$	8901.10	−	15417.2i	0.400869	−	0.694326i
$791$	15997.7			0.719107
$792$	16698.0	+	5645.75i	0.749164	+	0.253299i
$793$	8420.57			0.377078
$794$	13709.8	−	23746.0i	0.612773	−	1.06135i
$795$	2503.06	−	15218.0i	0.111666	−	0.678900i
$796$	−1065.27	−	1845.10i	−0.0474340	−	0.0821580i
$797$	11738.1	+	20331.1i	0.521689	+	0.903592i	0.999682	+	0.0252283i	$0.00803128\pi$
$797$	11738.1	+	20331.1i	0.521689	+	0.903592i	−0.477992	+	0.878364i	$0.658635\pi$
$798$	−4562.00	+	27735.7i	−0.202372	+	1.23037i
$799$	24073.4	−	41696.4i	1.06590	−	1.84620i
$800$	−1404.30			−0.0620618
$801$	5465.61	+	27305.3i	0.241096	+	1.20447i
$802$	31972.0			1.40769
$803$	−7873.02	+	13636.5i	−0.345993	+	0.599278i
$804$	−5252.37	+	1980.47i	−0.230394	+	0.0868729i
$805$	−2731.08	−	4730.37i	−0.119575	−	0.207110i
$806$	2956.89	+	5121.48i	0.129221	+	0.223817i
$807$	−18527.4	−	15186.3i	−0.808173	−	0.662435i
$808$	−2196.19	+	3803.91i	−0.0956208	+	0.165620i
$809$	−33269.8			−1.44586			−0.722932	−	0.690919i	$-0.757206\pi$
$809$	−33269.8			−1.44586			−0.722932	+	0.690919i	$0.757206\pi$
$810$	10232.9	−	4267.58i	0.443886	−	0.185120i
$811$	27892.8			1.20771			0.603853	−	0.797096i	$-0.293631\pi$
$811$	27892.8			1.20771			0.603853	+	0.797096i	$0.293631\pi$
$812$	77.5699	−	134.355i	0.00335243	−	0.00580657i
$813$	−4644.44	−	3806.91i	−0.200354	−	0.164224i
$814$	1072.19	+	1857.08i	0.0461672	+	0.0799640i
$815$	−5558.30	−	9627.25i	−0.238894	−	0.413777i
$816$	38414.6	−	14484.7i	1.64801	−	0.621404i
$817$	−657.666	+	1139.11i	−0.0281626	+	0.0487790i
$818$	10093.1			0.431415
$819$	−4232.32	−	21143.9i	−0.180573	−	0.902111i
$820$	−762.204			−0.0324601
$821$	1848.66	−	3201.98i	0.0785856	−	0.136114i	−0.824054	−	0.566511i	$-0.808293\pi$
$821$	1848.66	−	3201.98i	0.0785856	−	0.136114i	0.902640	+	0.430397i	$0.141626\pi$
$822$	2700.58	−	16418.8i	0.114591	−	0.696680i
$823$	−3572.25	−	6187.32i	−0.151301	−	0.262061i	0.780405	−	0.625275i	$-0.215013\pi$
$823$	−3572.25	−	6187.32i	−0.151301	−	0.262061i	−0.931706	+	0.363213i	$0.881680\pi$
$824$	17162.3	+	29725.9i	0.725578	+	1.25674i
$825$	670.596	−	4077.04i	0.0282996	−	0.172054i
$826$	9227.29	−	15982.1i	0.388691	−	0.673232i
$827$	19866.9			0.835357			0.417679	−	0.908595i	$-0.362844\pi$
$827$	19866.9			0.835357			0.417679	+	0.908595i	$0.362844\pi$
$828$	−2551.61	−	862.723i	−0.107095	−	0.0362098i
$829$	−36736.5			−1.53910			−0.769548	−	0.638589i	$-0.779518\pi$
$829$	−36736.5			−1.53910			−0.769548	+	0.638589i	$0.779518\pi$
$830$	−3224.58	+	5585.13i	−0.134851	+	0.233569i
$831$	2958.09	−	1115.39i	0.123484	−	0.0465611i
$832$	−11903.0	−	20616.7i	−0.495990	−	0.859079i
$833$	8450.38	+	14636.5i	0.351487	+	0.608793i
$834$	29147.5	+	23891.3i	1.21018	+	0.991952i
$835$	−3969.96	+	6876.16i	−0.164534	+	0.284981i
$836$	5165.52			0.213700
$837$	−4680.42	+	161.703i	−0.193284	+	0.00667773i
$838$	−1478.71			−0.0609560
$839$	−15006.1	+	25991.4i	−0.617485	+	1.06951i	0.372458	+	0.928049i	$0.378515\pi$
$839$	−15006.1	+	25991.4i	−0.617485	+	1.06951i	−0.989943	+	0.141466i	$0.954818\pi$
$840$	−5655.16	−	4635.37i	−0.232288	−	0.190399i
$841$	12153.7	+	21050.8i	0.498326	+	0.863127i
$842$	−7683.32	−	13307.9i	−0.314471	−	0.544680i
$843$	−13366.8	+	5040.12i	−0.546117	+	0.205920i
$844$	3092.07	−	5355.62i	0.126106	−	0.218422i
$845$	−5976.32			−0.243304
$846$	−27231.7	+	23939.7i	−1.10667	+	0.972890i
$847$	4378.68			0.177631
$848$	−21503.4	+	37245.0i	−0.870789	+	1.50825i
$849$	861.519	−	5237.80i	0.0348260	−	0.211733i
$850$	−4146.46	−	7181.88i	−0.167320	−	0.289807i
$851$	882.905	+	1529.24i	0.0355648	+	0.0616000i
$852$	−864.391	+	5255.27i	−0.0347577	+	0.211318i
$853$	2690.51	−	4660.10i	0.107997	−	0.187056i	−0.806962	−	0.590604i	$-0.798890\pi$
$853$	2690.51	−	4660.10i	0.107997	−	0.187056i	0.914959	+	0.403548i	$0.132223\pi$
$854$	−6030.13			−0.241624
$855$	−13149.9	+	11560.3i	−0.525986	+	0.462401i
$856$	12329.4			0.492302
$857$	−7319.88	+	12678.4i	−0.291765	+	0.505352i	−0.974227	−	0.225569i	$-0.927576\pi$
$857$	−7319.88	+	12678.4i	−0.291765	+	0.505352i	0.682462	+	0.730921i	$0.260909\pi$
$858$	−27397.0	+	10330.4i	−1.09011	+	0.411041i
$859$	−14770.0	−	25582.4i	−0.586667	−	1.01614i	−0.994665	−	0.103154i	$-0.967107\pi$
$859$	−14770.0	−	25582.4i	−0.586667	−	1.01614i	0.407999	−	0.912983i	$-0.366227\pi$
$860$	31.7483	+	54.9897i	0.00125885	+	0.00218039i
$861$	−6708.44	−	5498.71i	−0.265532	−	0.217649i
$862$	−10561.3	+	18292.7i	−0.417307	+	0.722797i
$863$	3387.63			0.133622			0.0668112	−	0.997766i	$-0.478717\pi$
$863$	3387.63			0.133622			0.0668112	+	0.997766i	$0.478717\pi$
$864$	−7876.00	+	272.106i	−0.310124	+	0.0107144i
$865$	−7538.98			−0.296339
$866$	20894.1	−	36189.7i	0.819875	−	1.42007i
$867$	28050.2	+	22991.9i	1.09877	+	0.900628i
$868$	−286.580	−	496.370i	−0.0112064	−	0.0194100i
$869$	−18615.4	−	32242.8i	−0.726678	−	1.25864i
$870$	668.119	−	251.922i	0.0260360	−	0.00981721i
$871$	−25123.8	+	43515.7i	−0.977368	+	1.69285i
$872$	15836.5			0.615015
$873$	−40891.2	−	13825.7i	−1.58529	−	0.536000i
$874$	31429.2			1.21637
$875$	−857.014	+	1484.39i	−0.0331113	+	0.0573504i
$876$	522.783	−	3178.38i	0.0201635	−	0.122588i
$877$	122.052	+	211.400i	0.00469944	+	0.00813967i	0.868366	−	0.495925i	$-0.165171\pi$
$877$	122.052	+	211.400i	0.00469944	+	0.00813967i	−0.863666	+	0.504064i	$0.831837\pi$
$878$	−12899.8	−	22343.1i	−0.495838	−	0.858817i
$879$	−4412.75	+	26828.4i	−0.169327	+	1.02946i
$880$	−5760.97	+	9978.30i	−0.220684	+	0.382237i
$881$	13910.2			0.531948			0.265974	−	0.963980i	$-0.414307\pi$
$881$	13910.2			0.531948			0.265974	+	0.963980i	$0.414307\pi$
$882$	−2498.10	−	12480.1i	−0.0953689	−	0.476446i
$883$	−8805.87			−0.335607			−0.167803	−	0.985820i	$-0.553667\pi$
$883$	−8805.87			−0.335607			−0.167803	+	0.985820i	$0.553667\pi$
$884$	−3976.76	+	6887.95i	−0.151304	+	0.262067i
$885$	10756.2	−	4055.76i	0.408549	−	0.154049i
$886$	848.943	+	1470.41i	0.0321905	+	0.0557556i
$887$	−6640.41	−	11501.5i	−0.251368	−	0.435381i	0.712535	−	0.701637i	$-0.247547\pi$
$887$	−6640.41	−	11501.5i	−0.251368	−	0.435381i	−0.963903	+	0.266255i	$0.914214\pi$
$888$	1828.21	+	1498.53i	0.0690885	+	0.0566298i
$889$	11176.1	−	19357.6i	0.421637	−	0.730296i
$890$	−15685.8			−0.590773
$891$	2971.04	−	22996.0i	0.111710	−	0.864642i
$892$	−3823.11			−0.143506
$893$	28629.7	−	49588.2i	1.07285	−	1.85824i
$894$	14011.9	+	11485.2i	0.524194	+	0.429666i
$895$	3931.65	+	6809.82i	0.146839	+	0.254332i
$896$	11605.0	+	20100.4i	0.432695	+	0.749449i
$897$	−22560.4	+	8506.67i	−0.839765	+	0.316644i
$898$	−22470.9	+	38920.7i	−0.835036	+	1.44633i
$899$	−301.609			−0.0111893
$900$	165.896	+	828.786i	0.00614429	+	0.0306958i
$901$	−64736.1			−2.39364
$902$	−5889.04	+	10200.1i	−0.217387	+	0.376526i
$903$	−117.279	+	713.025i	−0.00432204	+	0.0262768i
$904$	−11973.1	−	20738.0i	−0.440507	−	0.762981i
$905$	4961.03	+	8592.76i	0.182221	+	0.315616i
$906$	−2991.33	+	18186.5i	−0.109691	+	0.666894i
$907$	542.122	−	938.982i	0.0198466	−	0.0343753i	−0.855932	−	0.517089i	$-0.827016\pi$
$907$	542.122	−	938.982i	0.0198466	−	0.0343753i	0.875778	+	0.482714i	$0.160349\pi$
$908$	−1051.78			−0.0384411
$909$	5473.61	+	1850.68i	0.199723	+	0.0675281i
$910$	12146.3			0.442469
$911$	−25094.4	+	43464.7i	−0.912638	+	1.58073i	−0.102314	+	0.994752i	$0.532625\pi$
$911$	−25094.4	+	43464.7i	−0.912638	+	1.58073i	−0.810324	+	0.585983i	$0.800709\pi$
$912$	45685.2	−	17226.2i	1.65876	−	0.625455i
$913$	6743.74	+	11680.5i	0.244452	+	0.423404i
$914$	21608.4	+	37426.9i	0.781995	+	1.35445i
$915$	−2905.02	−	2381.15i	−0.104958	−	0.0860312i
$916$	−877.475	+	1519.83i	−0.0316513	+	0.0548216i
$917$	−3549.06			−0.127808
$918$	−24647.0	−	39476.1i	−0.886136	−	1.41929i
$919$	30376.1			1.09033			0.545166	−	0.838328i	$-0.316467\pi$
$919$	30376.1			1.09033			0.545166	+	0.838328i	$0.316467\pi$
$920$	−4088.00	+	7080.63i	−0.146497	+	0.253741i
$921$	−19742.5	−	16182.3i	−0.706336	−	0.578962i
$922$	11714.5	+	20290.2i	0.418435	+	0.724751i
$923$	23837.2	+	41287.2i	0.850066	+	1.47236i
$924$	2655.30	−	1001.21i	0.0945377	−	0.0356466i
$925$	277.056	−	479.876i	0.00984817	−	0.0170575i
$926$	24057.3			0.853750
$927$	33911.6	−	29812.2i	1.20151	−	1.05627i
$928$	−507.534			−0.0179533
$929$	23098.8	−	40008.3i	0.815766	−	1.41295i	−0.0930102	−	0.995665i	$-0.529649\pi$
$929$	23098.8	−	40008.3i	0.815766	−	1.41295i	0.908776	−	0.417283i	$-0.137018\pi$
$930$	428.145	−	2603.01i	0.0150962	−	0.0917806i
$931$	10049.8	+	17406.7i	0.353778	+	0.612762i
$932$	1788.74	+	3098.20i	0.0628672	+	0.108889i
$933$	−699.007	+	4249.78i	−0.0245278	+	0.149123i
$934$	−17702.6	+	30661.7i	−0.620177	+	1.07418i
$935$	−17343.4			−0.606621
$936$	−24241.5	+	21311.0i	−0.846536	+	0.744201i
$937$	37004.7			1.29017			0.645085	−	0.764111i	$-0.276822\pi$
$937$	37004.7			1.29017			0.645085	+	0.764111i	$0.276822\pi$
$938$	17991.6	−	31162.4i	0.626277	−	1.08474i
$939$	−44911.3	+	16934.4i	−1.56084	+	0.588533i
$940$	−1382.08	−	2393.83i	−0.0479558	−	0.0830618i
$941$	−21907.2	−	37944.4i	−0.758932	−	1.31451i	−0.943396	−	0.331669i	$-0.892388\pi$
$941$	−21907.2	−	37944.4i	−0.758932	−	1.31451i	0.184464	−	0.982839i	$-0.440945\pi$
$942$	−42485.1	−	34823.7i	−1.46947	−	1.20448i
$943$	−4849.40	+	8399.41i	−0.167464	+	0.290055i
$944$	−32056.0			−1.10523
$945$	−4518.94	+	8491.27i	−0.155557	+	0.292297i
$946$	981.191			0.0337223
$947$	−2304.86	+	3992.14i	−0.0790898	+	0.136988i	−0.902857	−	0.429940i	$-0.858535\pi$
$947$	−2304.86	+	3992.14i	−0.0790898	+	0.136988i	0.823768	+	0.566928i	$0.191868\pi$
$948$	5890.24	+	4828.05i	0.201800	+	0.165409i
$949$	−14416.7	−	24970.5i	−0.493136	−	0.854136i
$950$	−4931.24	−	8541.17i	−0.168411	−	0.291697i
$951$	44236.5	−	16679.9i	1.50838	−	0.568752i
$952$	−15346.5	+	26580.8i	−0.522460	+	0.904927i
$953$	4281.80			0.145542			0.0727708	−	0.997349i	$-0.476816\pi$
$953$	4281.80			0.145542			0.0727708	+	0.997349i	$0.476816\pi$
$954$	46183.1	+	15614.9i	1.56733	+	0.529928i
$955$	11741.8			0.397859
$956$	1070.52	−	1854.19i	0.0362165	−	0.0627288i
$957$	242.363	−	1473.50i	0.00818651	−	0.0497718i
$958$	28434.0	+	49249.1i	0.958936	+	1.66093i
$959$	7217.91	+	12501.8i	0.243043	+	0.420963i
$960$	−1723.51	+	10478.5i	−0.0579437	+	0.352283i
$961$	14338.4	−	24834.8i	0.481298	−	0.833633i
$962$	−3926.68			−0.131602
$963$	−3183.34	−	15903.4i	−0.106523	−	0.532170i
$964$	−5425.05			−0.181254
$965$	−585.424	+	1013.98i	−0.0195290	+	0.0338252i
$966$	16155.9	−	6091.79i	0.538104	−	0.202899i
$967$	18114.9	+	31375.9i	0.602416	+	1.04341i	0.992454	+	0.122616i	$0.0391284\pi$
$967$	18114.9	+	31375.9i	0.602416	+	1.04341i	−0.390038	+	0.920799i	$0.627538\pi$
$968$	−3277.10	−	5676.11i	−0.108812	−	0.188468i
$969$	56839.7	+	46589.7i	1.88437	+	1.54456i
$970$	12157.2	−	21056.8i	0.402416	−	0.697005i
$971$	844.928			0.0279249			0.0139624	−	0.999903i	$-0.495555\pi$
$971$	844.928			0.0279249			0.0139624	+	0.999903i	$0.495555\pi$
$972$	1091.02	+	4616.10i	0.0360025	+	0.152327i
$973$	−32696.7			−1.07730
$974$	3421.26	−	5925.80i	0.112551	−	0.194943i
$975$	5851.50	+	4796.29i	0.192203	+	0.157543i
$976$	5237.24	+	9071.16i	0.171762	+	0.297501i
$977$	−22922.5	−	39702.9i	−0.750619	−	1.30011i	−0.947523	−	0.319687i	$-0.896422\pi$
$977$	−22922.5	−	39702.9i	−0.750619	−	1.30011i	0.196904	−	0.980423i	$-0.436911\pi$
$978$	32880.6	−	12398.0i	1.07506	−	0.405363i
$979$	−16402.2	+	28409.5i	−0.535463	+	0.927449i
$980$	970.288			0.0316273
$981$	−4088.85	−	20427.2i	−0.133075	−	0.664821i
$982$	6048.05			0.196539
$983$	20101.0	−	34815.9i	0.652210	−	1.12966i	−0.330376	−	0.943849i	$-0.607176\pi$
$983$	20101.0	−	34815.9i	0.652210	−	1.12966i	0.982586	−	0.185811i	$-0.0594911\pi$
$984$	−2107.26	+	12811.6i	−0.0682692	+	0.415059i
$985$	−1794.62	−	3108.37i	−0.0580520	−	0.100549i
$986$	−1498.59	−	2595.64i	−0.0484025	−	0.0838356i
$987$	5105.42	−	31039.6i	0.164648	−	1.00101i
$988$	−4729.43	+	8191.61i	−0.152291	+	0.263775i
$989$	807.974			0.0259778
$990$	12372.9	+	4183.39i	0.397209	+	0.134300i
$991$	1797.91			0.0576313			0.0288157	−	0.999585i	$-0.490826\pi$
$991$	1797.91			0.0576313			0.0288157	+	0.999585i	$0.490826\pi$
$992$	−937.534	+	1623.86i	−0.0300068	+	0.0519733i
$993$	−28994.3	+	10932.7i	−0.926594	+	0.349384i
$994$	−17070.3	−	29566.6i	−0.544704	−	0.943455i
$995$	4253.63	+	7367.50i	0.135527	+	0.234739i
$996$	−2133.84	−	1749.04i	−0.0678849	−	0.0556432i
$997$	−4566.04	+	7908.61i	−0.145043	+	0.251222i	−0.929389	−	0.369102i	$-0.879665\pi$
$997$	−4566.04	+	7908.61i	−0.145043	+	0.251222i	0.784346	+	0.620324i	$0.212999\pi$
$998$	7342.47			0.232888
$999$	1460.89	−	2745.07i	0.0462667	−	0.0869370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.e.c.16.2	✓	14
3.2	odd	2		135.4.e.c.46.6		14
5.2	odd	4		225.4.k.d.124.4		28
5.3	odd	4		225.4.k.d.124.11		28
5.4	even	2		225.4.e.d.151.6		14
9.2	odd	6		405.4.a.n.1.2		7
9.4	even	3	inner	45.4.e.c.31.2	yes	14
9.5	odd	6		135.4.e.c.91.6		14
9.7	even	3		405.4.a.m.1.6		7
45.4	even	6		225.4.e.d.76.6		14
45.13	odd	12		225.4.k.d.49.4		28
45.22	odd	12		225.4.k.d.49.11		28
45.29	odd	6		2025.4.a.ba.1.6		7
45.34	even	6		2025.4.a.bb.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.2	✓	14	1.1	even	1	trivial
45.4.e.c.31.2	yes	14	9.4	even	3	inner
135.4.e.c.46.6		14	3.2	odd	2
135.4.e.c.91.6		14	9.5	odd	6
225.4.e.d.76.6		14	45.4	even	6
225.4.e.d.151.6		14	5.4	even	2
225.4.k.d.49.4		28	45.13	odd	12
225.4.k.d.49.11		28	45.22	odd	12
225.4.k.d.124.4		28	5.2	odd	4
225.4.k.d.124.11		28	5.3	odd	4
405.4.a.m.1.6		7	9.7	even	3
405.4.a.n.1.2		7	9.2	odd	6
2025.4.a.ba.1.6		7	45.29	odd	6
2025.4.a.bb.1.2		7	45.34	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)

\(f(q)\)	\(=\)	\(q+(-1.52087 + 2.63422i) q^{2} +(4.01867 + 3.29398i) q^{3} +(-0.626094 - 1.08443i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-14.7890 + 5.57636i) q^{6} +(6.85611 - 11.8751i) q^{7} -20.5251 q^{8} +(5.29939 + 26.4748i) q^{9} +O(q^{10})\)	\(q+(-1.52087 + 2.63422i) q^{2} +(4.01867 + 3.29398i) q^{3} +(-0.626094 - 1.08443i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-14.7890 + 5.57636i) q^{6} +(6.85611 - 11.8751i) q^{7} -20.5251 q^{8} +(5.29939 + 26.4748i) q^{9} -15.2087 q^{10} +(-15.9034 + 27.5455i) q^{11} +(1.05602 - 6.42029i) q^{12} +(-29.1216 - 50.4401i) q^{13} +(20.8545 + 36.1211i) q^{14} +(-4.21668 + 25.6363i) q^{15} +(36.2248 - 62.7431i) q^{16} +109.055 q^{17} +(-77.8003 - 26.3050i) q^{18} +129.695 q^{19} +(3.13047 - 5.42213i) q^{20} +(66.6689 - 25.1383i) q^{21} +(-48.3740 - 83.7863i) q^{22} +(-39.8342 - 68.9949i) q^{23} +(-82.4836 - 67.6093i) q^{24} +(-12.5000 + 21.6506i) q^{25} +177.161 q^{26} +(-65.9111 + 123.850i) q^{27} -17.1703 q^{28} +(-4.51769 + 7.82486i) q^{29} +(-61.1187 - 50.0972i) q^{30} +(16.6904 + 28.9087i) q^{31} +(28.0860 + 48.6463i) q^{32} +(-154.645 + 58.3108i) q^{33} +(-165.858 + 287.275i) q^{34} +68.5611 q^{35} +(25.3921 - 22.3225i) q^{36} -22.1645 q^{37} +(-197.250 + 341.647i) q^{38} +(49.1186 - 298.628i) q^{39} +(-51.3127 - 88.8763i) q^{40} +(-60.8698 - 105.430i) q^{41} +(-35.1747 + 213.853i) q^{42} +(-5.07086 + 8.78298i) q^{43} +39.8281 q^{44} +(-101.391 + 89.1341i) q^{45} +242.331 q^{46} +(220.746 - 382.343i) q^{47} +(352.250 - 132.820i) q^{48} +(77.4875 + 134.212i) q^{49} +(-38.0218 - 65.8556i) q^{50} +(438.255 + 359.225i) q^{51} +(-36.4657 + 63.1604i) q^{52} -593.610 q^{53} +(-226.006 - 361.984i) q^{54} -159.034 q^{55} +(-140.722 + 243.738i) q^{56} +(521.202 + 427.214i) q^{57} +(-13.7416 - 23.8012i) q^{58} +(-221.230 - 383.182i) q^{59} +(30.4407 - 11.4780i) q^{60} +(-72.2881 + 125.207i) q^{61} -101.536 q^{62} +(350.725 + 118.583i) q^{63} +408.736 q^{64} +(145.608 - 252.200i) q^{65} +(81.5912 - 496.052i) q^{66} +(-431.360 - 747.138i) q^{67} +(-68.2786 - 118.262i) q^{68} +(67.1873 - 408.481i) q^{69} +(-104.273 + 180.605i) q^{70} -818.541 q^{71} +(-108.771 - 543.398i) q^{72} +495.052 q^{73} +(33.7093 - 58.3863i) q^{74} +(-121.550 + 45.8320i) q^{75} +(-81.2014 - 140.645i) q^{76} +(218.071 + 377.710i) q^{77} +(711.950 + 583.563i) q^{78} +(-585.263 + 1013.71i) q^{79} +362.248 q^{80} +(-672.833 + 280.601i) q^{81} +370.300 q^{82} +(212.022 - 367.232i) q^{83} +(-69.0017 - 56.5586i) q^{84} +(272.637 + 472.221i) q^{85} +(-15.4242 - 26.7156i) q^{86} +(-43.9300 + 16.5644i) q^{87} +(326.419 - 565.374i) q^{88} +1031.37 q^{89} +(-80.5969 - 402.648i) q^{90} -798.643 q^{91} +(-49.8799 + 86.3945i) q^{92} +(-28.1513 + 171.152i) q^{93} +(671.452 + 1162.99i) q^{94} +(324.238 + 561.597i) q^{95} +(-47.3718 + 288.008i) q^{96} +(-799.356 + 1384.53i) q^{97} -471.394 q^{98} +(-813.541 - 275.066i) 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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