LMFDB - Embedded newform 33.4.e.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$2.51217 + 1.82520i$ of defining polynomial
Character	$\chi$	$=$	33.31
Dual form			33.4.e.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45957 + 4.49208i) q^{2} +(-2.42705 + 1.76336i) q^{3} +(-11.5763 - 8.41069i) q^{4} +(1.86000 + 5.72450i) q^{5} +(-4.37870 - 13.4762i) q^{6} +(-8.05785 - 5.85437i) q^{7} +(24.1083 - 17.5157i) q^{8} +(2.78115 - 8.55951i) q^{9} +O(q^{10})$	\(q+(-1.45957 + 4.49208i) q^{2} +(-2.42705 + 1.76336i) q^{3} +(-11.5763 - 8.41069i) q^{4} +(1.86000 + 5.72450i) q^{5} +(-4.37870 - 13.4762i) q^{6} +(-8.05785 - 5.85437i) q^{7} +(24.1083 - 17.5157i) q^{8} +(2.78115 - 8.55951i) q^{9} -28.4297 q^{10} +(8.30870 + 35.5242i) q^{11} +42.9273 q^{12} +(-27.8826 + 85.8139i) q^{13} +(38.0593 - 27.6517i) q^{14} +(-14.6086 - 10.6138i) q^{15} +(8.12031 + 24.9917i) q^{16} +(13.8539 + 42.6379i) q^{17} +(34.3907 + 24.9863i) q^{18} +(110.890 - 80.5660i) q^{19} +(26.6150 - 81.9125i) q^{20} +29.8801 q^{21} +(-171.704 - 14.5265i) q^{22} -71.4719 q^{23} +(-27.6257 + 85.0232i) q^{24} +(71.8169 - 52.1780i) q^{25} +(-344.786 - 250.502i) q^{26} +(8.34346 + 25.6785i) q^{27} +(44.0409 + 135.544i) q^{28} +(119.601 + 86.8950i) q^{29} +(69.0003 - 50.1317i) q^{30} +(2.38514 - 7.34071i) q^{31} +114.279 q^{32} +(-82.8074 - 71.5677i) q^{33} -211.753 q^{34} +(18.5257 - 57.0163i) q^{35} +(-104.187 + 75.6962i) q^{36} +(-8.18776 - 5.94875i) q^{37} +(200.058 + 615.716i) q^{38} +(-83.6479 - 257.442i) q^{39} +(145.110 + 105.429i) q^{40} +(-305.780 + 222.162i) q^{41} +(-43.6120 + 134.224i) q^{42} +276.048 q^{43} +(202.598 - 481.121i) q^{44} +54.1718 q^{45} +(104.318 - 321.057i) q^{46} +(191.854 - 139.390i) q^{47} +(-63.7778 - 46.3373i) q^{48} +(-75.3376 - 231.865i) q^{49} +(129.566 + 398.764i) q^{50} +(-108.810 - 79.0549i) q^{51} +(1044.53 - 758.897i) q^{52} +(-68.6297 + 211.221i) q^{53} -127.528 q^{54} +(-187.904 + 113.638i) q^{55} -296.805 q^{56} +(-127.068 + 391.076i) q^{57} +(-564.905 + 410.427i) q^{58} +(-136.832 - 99.4144i) q^{59} +(79.8449 + 245.737i) q^{60} +(70.1651 + 215.946i) q^{61} +(29.4938 + 21.4285i) q^{62} +(-72.5206 + 52.6893i) q^{63} +(-231.761 + 713.286i) q^{64} -543.103 q^{65} +(442.351 - 267.520i) q^{66} -362.669 q^{67} +(198.237 - 610.110i) q^{68} +(173.466 - 126.030i) q^{69} +(229.082 + 166.438i) q^{70} +(-219.919 - 676.841i) q^{71} +(-82.8771 - 255.070i) q^{72} +(845.463 + 614.265i) q^{73} +(38.6729 - 28.0975i) q^{74} +(-82.2948 + 253.277i) q^{75} -1961.31 q^{76} +(141.021 - 334.890i) q^{77} +1278.54 q^{78} +(15.6957 - 48.3063i) q^{79} +(-127.961 + 92.9694i) q^{80} +(-65.5304 - 47.6106i) q^{81} +(-551.665 - 1697.85i) q^{82} +(-378.188 - 1163.94i) q^{83} +(-345.902 - 251.313i) q^{84} +(-218.312 + 158.613i) q^{85} +(-402.911 + 1240.03i) q^{86} -443.504 q^{87} +(822.541 + 710.895i) q^{88} +964.845 q^{89} +(-79.0673 + 243.344i) q^{90} +(727.060 - 528.240i) q^{91} +(827.381 + 601.128i) q^{92} +(7.15542 + 22.0221i) q^{93} +(346.128 + 1065.27i) q^{94} +(667.455 + 484.934i) q^{95} +(-277.362 + 201.515i) q^{96} +(78.8462 - 242.664i) q^{97} +1151.52 q^{98} +(327.177 + 27.6797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9}+O(q^{10}) $ 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9} + 8 q^{10} - 87 q^{11} - 18 q^{12} + 171 q^{13} + 12 q^{14} - 63 q^{15} + 44 q^{16} + 36 q^{17} + 81 q^{18} + 324 q^{19} - 87 q^{20} - 66 q^{21} - 521 q^{22} - 84 q^{23} + 18 q^{24} + 263 q^{25} - 774 q^{26} - 54 q^{27} + 387 q^{28} + 393 q^{29} + 204 q^{30} + 15 q^{31} + 102 q^{32} - 216 q^{33} - 712 q^{34} + 1002 q^{35} - 144 q^{36} - 747 q^{37} - 36 q^{38} + 513 q^{39} + 41 q^{40} + 159 q^{41} + 396 q^{42} - 644 q^{43} + 219 q^{44} + 216 q^{45} + 753 q^{46} - 351 q^{47} - 423 q^{48} - 1967 q^{49} + 330 q^{50} + 63 q^{51} + 2871 q^{52} - 531 q^{53} - 162 q^{54} - 716 q^{55} + 1470 q^{56} - 453 q^{57} - 1205 q^{58} - 1002 q^{59} - 261 q^{60} + 1449 q^{61} + 99 q^{62} + 27 q^{63} - 1118 q^{64} - 954 q^{65} + 897 q^{66} - 518 q^{67} + 873 q^{68} + 693 q^{69} + 26 q^{70} + 429 q^{71} + 54 q^{72} + 2547 q^{73} + 468 q^{74} - 231 q^{75} - 2276 q^{76} - 2697 q^{77} + 1638 q^{78} + 2805 q^{79} - 1620 q^{80} - 162 q^{81} - 1631 q^{82} - 2553 q^{83} - 1509 q^{84} - 197 q^{85} - 1713 q^{86} - 3906 q^{87} + 2866 q^{88} + 1788 q^{89} - 648 q^{90} + 2885 q^{91} + 423 q^{92} + 45 q^{93} + 1159 q^{94} + 3009 q^{95} - 504 q^{96} + 9 q^{97} + 5550 q^{98} + 27 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9 + 8 * q^10 - 87 * q^11 - 18 * q^12 + 171 * q^13 + 12 * q^14 - 63 * q^15 + 44 * q^16 + 36 * q^17 + 81 * q^18 + 324 * q^19 - 87 * q^20 - 66 * q^21 - 521 * q^22 - 84 * q^23 + 18 * q^24 + 263 * q^25 - 774 * q^26 - 54 * q^27 + 387 * q^28 + 393 * q^29 + 204 * q^30 + 15 * q^31 + 102 * q^32 - 216 * q^33 - 712 * q^34 + 1002 * q^35 - 144 * q^36 - 747 * q^37 - 36 * q^38 + 513 * q^39 + 41 * q^40 + 159 * q^41 + 396 * q^42 - 644 * q^43 + 219 * q^44 + 216 * q^45 + 753 * q^46 - 351 * q^47 - 423 * q^48 - 1967 * q^49 + 330 * q^50 + 63 * q^51 + 2871 * q^52 - 531 * q^53 - 162 * q^54 - 716 * q^55 + 1470 * q^56 - 453 * q^57 - 1205 * q^58 - 1002 * q^59 - 261 * q^60 + 1449 * q^61 + 99 * q^62 + 27 * q^63 - 1118 * q^64 - 954 * q^65 + 897 * q^66 - 518 * q^67 + 873 * q^68 + 693 * q^69 + 26 * q^70 + 429 * q^71 + 54 * q^72 + 2547 * q^73 + 468 * q^74 - 231 * q^75 - 2276 * q^76 - 2697 * q^77 + 1638 * q^78 + 2805 * q^79 - 1620 * q^80 - 162 * q^81 - 1631 * q^82 - 2553 * q^83 - 1509 * q^84 - 197 * q^85 - 1713 * q^86 - 3906 * q^87 + 2866 * q^88 + 1788 * q^89 - 648 * q^90 + 2885 * q^91 + 423 * q^92 + 45 * q^93 + 1159 * q^94 + 3009 * q^95 - 504 * q^96 + 9 * q^97 + 5550 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−1.45957	+	4.49208i	−0.516034	+	1.58819i	0.265358	+	0.964150i	$0.414510\pi$
$2$	−1.45957	+	4.49208i	−0.516034	+	1.58819i	−0.781392	+	0.624040i	$0.785490\pi$
$3$	−2.42705	+	1.76336i	−0.467086	+	0.339358i
$3$	−2.42705	+	1.76336i	−0.467086	+	0.339358i
$4$	−11.5763	−	8.41069i	−1.44704	−	1.05134i
$5$	1.86000	+	5.72450i	0.166364	+	0.512014i	0.999134	−	0.0416038i	$-0.0132467\pi$
$5$	1.86000	+	5.72450i	0.166364	+	0.512014i	−0.832771	+	0.553618i	$0.813247\pi$
$6$	−4.37870	−	13.4762i	−0.297933	−	0.916942i
$7$	−8.05785	−	5.85437i	−0.435083	−	0.316106i	0.348595	−	0.937273i	$-0.386659\pi$
$7$	−8.05785	−	5.85437i	−0.435083	−	0.316106i	−0.783678	+	0.621167i	$0.786659\pi$
$8$	24.1083	−	17.5157i	1.06545	−	0.774094i
$9$	2.78115	−	8.55951i	0.103006	−	0.317019i
$10$	−28.4297			−0.899026
$11$	8.30870	+	35.5242i	0.227743	+	0.973721i
$11$	8.30870	+	35.5242i	0.227743	+	0.973721i
$12$	42.9273			1.03267
$13$	−27.8826	+	85.8139i	−0.594865	+	1.83081i	−0.0394690	+	0.999221i	$0.512567\pi$
$13$	−27.8826	+	85.8139i	−0.594865	+	1.83081i	−0.555396	+	0.831586i	$0.687433\pi$
$14$	38.0593	−	27.6517i	0.726555	−	0.527873i
$15$	−14.6086	−	10.6138i	−0.251462	−	0.182698i
$16$	8.12031	+	24.9917i	0.126880	+	0.390496i
$17$	13.8539	+	42.6379i	0.197651	+	0.608306i	0.999935	+	0.0113645i	$0.00361750\pi$
$17$	13.8539	+	42.6379i	0.197651	+	0.608306i	−0.802285	+	0.596941i	$0.796382\pi$
$18$	34.3907	+	24.9863i	0.450332	+	0.327185i
$19$	110.890	−	80.5660i	1.33894	−	0.972795i	0.339456	−	0.940622i	$-0.389757\pi$
$19$	110.890	−	80.5660i	1.33894	−	0.972795i	0.999482	−	0.0321734i	$-0.0102429\pi$
$20$	26.6150	−	81.9125i	0.297564	−	0.915809i
$21$	29.8801			0.310494
$22$	−171.704	−	14.5265i	−1.66398	−	0.140775i
$23$	−71.4719			−0.647953			−0.323977	−	0.946065i	$-0.605020\pi$
$23$	−71.4719			−0.647953			−0.323977	+	0.946065i	$0.605020\pi$
$24$	−27.6257	+	85.0232i	−0.234961	+	0.723137i
$25$	71.8169	−	52.1780i	0.574535	−	0.417424i
$26$	−344.786	−	250.502i	−2.60070	−	1.88952i
$27$	8.34346	+	25.6785i	0.0594703	+	0.183031i
$28$	44.0409	+	135.544i	0.297248	+	0.914837i
$29$	119.601	+	86.8950i	0.765838	+	0.556414i	0.900695	−	0.434451i	$-0.143058\pi$
$29$	119.601	+	86.8950i	0.765838	+	0.556414i	−0.134857	+	0.990865i	$0.543058\pi$
$30$	69.0003	−	50.1317i	0.419922	−	0.305092i
$31$	2.38514	−	7.34071i	0.0138188	−	0.0425300i	−0.943909	−	0.330205i	$-0.892882\pi$
$31$	2.38514	−	7.34071i	0.0138188	−	0.0425300i	0.957728	+	0.287675i	$0.0928822\pi$
$32$	114.279			0.631310
$33$	−82.8074	−	71.5677i	−0.436815	−	0.377526i
$34$	−211.753			−1.06810
$35$	18.5257	−	57.0163i	0.0894690	−	0.275357i
$36$	−104.187	+	75.6962i	−0.482347	+	0.350445i
$37$	−8.18776	−	5.94875i	−0.0363800	−	0.0264316i	0.569447	−	0.822028i	$-0.307158\pi$
$37$	−8.18776	−	5.94875i	−0.0363800	−	0.0264316i	−0.605827	+	0.795597i	$0.707158\pi$
$38$	200.058	+	615.716i	0.854046	+	2.62848i
$39$	−83.6479	−	257.442i	−0.343446	−	1.05702i
$40$	145.110	+	105.429i	0.573599	+	0.416744i
$41$	−305.780	+	222.162i	−1.16475	+	0.846242i	−0.990371	−	0.138436i	$-0.955793\pi$
$41$	−305.780	+	222.162i	−1.16475	+	0.846242i	−0.174381	+	0.984678i	$0.555793\pi$
$42$	−43.6120	+	134.224i	−0.160226	+	0.493124i
$43$	276.048			0.979000			0.489500	−	0.872003i	$-0.337179\pi$
$43$	276.048			0.979000			0.489500	+	0.872003i	$0.337179\pi$
$44$	202.598	−	481.121i	0.694156	−	1.64845i
$45$	54.1718			0.179455
$46$	104.318	−	321.057i	0.334366	−	1.02907i
$47$	191.854	−	139.390i	0.595421	−	0.432599i	−0.248830	−	0.968547i	$-0.580046\pi$
$47$	191.854	−	139.390i	0.595421	−	0.432599i	0.844251	+	0.535949i	$0.180046\pi$
$48$	−63.7778	−	46.3373i	−0.191782	−	0.139338i
$49$	−75.3376	−	231.865i	−0.219643	−	0.675992i
$50$	129.566	+	398.764i	0.366469	+	1.12788i
$51$	−108.810	−	79.0549i	−0.298753	−	0.217057i
$52$	1044.53	−	758.897i	2.78559	−	2.02385i
$53$	−68.6297	+	211.221i	−0.177868	+	0.547422i	−0.999753	−	0.0222318i	$-0.992923\pi$
$53$	−68.6297	+	211.221i	−0.177868	+	0.547422i	0.821885	+	0.569654i	$0.192923\pi$
$54$	−127.528			−0.321377
$55$	−187.904	+	113.638i	−0.460671	+	0.278599i
$56$	−296.805			−0.708254
$57$	−127.068	+	391.076i	−0.295274	+	0.908759i
$58$	−564.905	+	410.427i	−1.27889	+	0.929168i
$59$	−136.832	−	99.4144i	−0.301933	−	0.219367i	0.426494	−	0.904490i	$-0.359748\pi$
$59$	−136.832	−	99.4144i	−0.301933	−	0.219367i	−0.728427	+	0.685123i	$0.759748\pi$
$60$	79.8449	+	245.737i	0.171799	+	0.528743i
$61$	70.1651	+	215.946i	0.147274	+	0.453263i	0.997296	−	0.0734835i	$-0.0234116\pi$
$61$	70.1651	+	215.946i	0.147274	+	0.453263i	−0.850022	+	0.526747i	$0.823412\pi$
$62$	29.4938	+	21.4285i	0.0604147	+	0.0438939i
$63$	−72.5206	+	52.6893i	−0.145028	+	0.105369i
$64$	−231.761	+	713.286i	−0.452658	+	1.39314i
$65$	−543.103			−1.03636
$66$	442.351	−	267.520i	0.824994	−	0.498930i
$67$	−362.669			−0.661300			−0.330650	−	0.943753i	$-0.607268\pi$
$67$	−362.669			−0.661300			−0.330650	+	0.943753i	$0.607268\pi$
$68$	198.237	−	610.110i	0.353526	−	1.08804i
$69$	173.466	−	126.030i	0.302650	−	0.219888i
$70$	229.082	+	166.438i	0.391151	+	0.284188i
$71$	−219.919	−	676.841i	−0.367600	−	1.13136i	−0.948337	−	0.317265i	$-0.897236\pi$
$71$	−219.919	−	676.841i	−0.367600	−	1.13136i	0.580737	−	0.814091i	$-0.302764\pi$
$72$	−82.8771	−	255.070i	−0.135655	−	0.417503i
$73$	845.463	+	614.265i	1.35553	+	0.984853i	0.998715	+	0.0506801i	$0.0161389\pi$
$73$	845.463	+	614.265i	1.35553	+	0.984853i	0.356820	+	0.934173i	$0.383861\pi$
$74$	38.6729	−	28.0975i	0.0607517	−	0.0441387i
$75$	−82.2948	+	253.277i	−0.126701	+	0.389946i
$76$	−1961.31			−2.96023
$77$	141.021	−	334.890i	0.208713	−	0.495640i
$78$	1278.54			1.85597
$79$	15.6957	−	48.3063i	0.0223532	−	0.0687959i	−0.939258	−	0.343213i	$-0.888485\pi$
$79$	15.6957	−	48.3063i	0.0223532	−	0.0687959i	0.961611	+	0.274417i	$0.0884848\pi$
$80$	−127.961	+	92.9694i	−0.178831	+	0.129929i
$81$	−65.5304	−	47.6106i	−0.0898908	−	0.0653095i
$82$	−551.665	−	1697.85i	−0.742942	−	2.28654i
$83$	−378.188	−	1163.94i	−0.500139	−	1.53927i	−0.808792	−	0.588095i	$-0.799878\pi$
$83$	−378.188	−	1163.94i	−0.500139	−	1.53927i	0.308653	−	0.951175i	$-0.400122\pi$
$84$	−345.902	−	251.313i	−0.449298	−	0.326434i
$85$	−218.312	+	158.613i	−0.278580	+	0.202400i
$86$	−402.911	+	1240.03i	−0.505197	+	1.55484i
$87$	−443.504			−0.546536
$88$	822.541	+	710.895i	0.996399	+	0.861156i
$89$	964.845			1.14914			0.574569	−	0.818456i	$-0.305170\pi$
$89$	964.845			1.14914			0.574569	+	0.818456i	$0.305170\pi$
$90$	−79.0673	+	243.344i	−0.0926047	+	0.285008i
$91$	727.060	−	528.240i	0.837545	−	0.608512i
$92$	827.381	+	601.128i	0.937614	+	0.681216i
$93$	7.15542	+	22.0221i	0.00797831	+	0.0245547i
$94$	346.128	+	1065.27i	0.379791	+	1.16888i
$95$	667.455	+	484.934i	0.720836	+	0.523718i
$96$	−277.362	+	201.515i	−0.294876	+	0.214240i
$97$	78.8462	−	242.664i	0.0825321	−	0.254008i	−0.901272	−	0.433253i	$-0.857366\pi$
$97$	78.8462	−	242.664i	0.0825321	−	0.254008i	0.983804	+	0.179245i	$0.0573656\pi$
$98$	1151.52			1.18695
$99$	327.177	+	27.6797i	0.332147	+	0.0281002i
$100$	−1270.23			−1.27023
$101$	41.9267	−	129.037i	0.0413055	−	0.127125i	−0.928277	−	0.371889i	$-0.878710\pi$
$101$	41.9267	−	129.037i	0.0413055	−	0.127125i	0.969583	+	0.244763i	$0.0787103\pi$
$102$	513.936	−	373.396i	0.498895	−	0.362468i
$103$	557.554	+	405.087i	0.533373	+	0.387518i	0.821618	−	0.570039i	$-0.193072\pi$
$103$	557.554	+	405.087i	0.533373	+	0.387518i	−0.288245	+	0.957557i	$0.593072\pi$
$104$	830.890	+	2557.21i	0.783418	+	2.41111i
$105$	55.5771	+	171.049i	0.0516550	+	0.158978i
$106$	−848.650	−	616.581i	−0.777625	−	0.564977i
$107$	−784.130	+	569.704i	−0.708455	+	0.514723i	−0.882675	−	0.469984i	$-0.844260\pi$
$107$	−784.130	+	569.704i	−0.708455	+	0.514723i	0.174220	+	0.984707i	$0.444260\pi$
$108$	119.388	−	367.437i	0.106371	−	0.327376i
$109$	−235.888			−0.207284			−0.103642	−	0.994615i	$-0.533050\pi$
$109$	−235.888			−0.207284			−0.103642	+	0.994615i	$0.533050\pi$
$110$	−236.214	−	1009.94i	−0.204746	−	0.875400i
$111$	30.3619			0.0259624
$112$	80.8787	−	248.919i	0.0682350	−	0.210006i
$113$	−416.768	+	302.800i	−0.346958	+	0.252080i	−0.747592	−	0.664159i	$-0.768790\pi$
$113$	−416.768	+	302.800i	−0.346958	+	0.252080i	0.400634	+	0.916238i	$0.368790\pi$
$114$	−1571.28	−	1141.60i	−1.29091	−	0.937901i
$115$	−132.938	−	409.141i	−0.107796	−	0.331761i
$116$	−653.689	−	2011.85i	−0.523220	−	1.61031i
$117$	656.979	+	477.323i	0.519126	+	0.377167i
$118$	646.293	−	469.559i	0.504204	−	0.366326i
$119$	137.985	−	424.675i	0.106295	−	0.327142i
$120$	−538.099			−0.409345
$121$	−1192.93	+	590.319i	−0.896267	+	0.443515i
$122$	−1072.46			−0.795867
$123$	350.393	−	1078.40i	0.256861	−	0.790536i
$124$	−89.3515	+	64.9177i	−0.0647097	+	0.0470144i
$125$	1040.97	+	756.306i	0.744854	+	0.541168i
$126$	−130.836	−	402.672i	−0.0925064	−	0.284705i
$127$	319.132	+	982.188i	0.222980	+	0.686261i	0.998490	+	0.0549264i	$0.0174924\pi$
$127$	319.132	+	982.188i	0.222980	+	0.686261i	−0.775511	+	0.631334i	$0.782508\pi$
$128$	−2126.24	−	1544.80i	−1.46824	−	1.06674i
$129$	−669.983	+	486.771i	−0.457277	+	0.332231i
$130$	792.694	−	2439.66i	0.534799	−	1.64594i
$131$	1366.16			0.911157			0.455578	−	0.890196i	$-0.349432\pi$
$131$	1366.16			0.911157			0.455578	+	0.890196i	$0.349432\pi$
$132$	356.670	+	1524.96i	0.235183	+	1.00553i
$133$	−1365.19			−0.890056
$134$	529.339	−	1629.14i	0.341253	−	1.05027i
$135$	−131.478	+	95.5242i	−0.0838208	+	0.0608994i
$136$	1080.83	+	785.267i	0.681472	+	0.495118i
$137$	467.210	+	1437.92i	0.291361	+	0.896716i	0.984420	+	0.175835i	$0.0562625\pi$
$137$	467.210	+	1437.92i	0.291361	+	0.896716i	−0.693059	+	0.720881i	$0.743737\pi$
$138$	312.954	+	963.172i	0.193046	+	0.594135i
$139$	848.109	+	616.187i	0.517523	+	0.376002i	0.815670	−	0.578518i	$-0.196369\pi$
$139$	848.109	+	616.187i	0.517523	+	0.376002i	−0.298147	+	0.954520i	$0.596369\pi$
$140$	−694.005	+	504.224i	−0.418958	+	0.304391i
$141$	−219.845	+	676.614i	−0.131307	+	0.404122i
$142$	3361.41			1.98650
$143$	−3280.13	−	277.505i	−1.91817	−	0.162280i
$144$	236.501			0.136864
$145$	−274.973	+	846.279i	−0.157484	+	0.484687i
$146$	−3993.34	+	2901.33i	−2.26364	+	1.64463i
$147$	591.709	+	429.902i	0.331995	+	0.241209i
$148$	44.7510	+	137.729i	0.0248548	+	0.0764952i
$149$	−119.658	−	368.270i	−0.0657905	−	0.202482i	0.912757	−	0.408502i	$-0.133949\pi$
$149$	−119.658	−	368.270i	−0.0657905	−	0.202482i	−0.978548	+	0.206020i	$0.933949\pi$
$150$	−1017.63	−	739.350i	−0.553926	−	0.402451i
$151$	−549.139	+	398.973i	−0.295949	+	0.215019i	−0.725844	−	0.687859i	$-0.758551\pi$
$151$	−549.139	+	398.973i	−0.295949	+	0.215019i	0.429895	+	0.902879i	$0.358551\pi$
$152$	1262.19	−	3884.63i	0.673535	−	2.07293i
$153$	403.489			0.213204
$154$	1298.53	+	1122.27i	0.679468	+	0.587243i
$155$	46.4582			0.0240749
$156$	−1196.93	+	3683.76i	−0.614300	+	1.89062i
$157$	2919.99	−	2121.50i	1.48434	−	1.07843i	0.508210	−	0.861233i	$-0.330308\pi$
$157$	2919.99	−	2121.50i	1.48434	−	1.07843i	0.976127	−	0.217200i	$-0.0696925\pi$
$158$	194.087	+	141.012i	0.0977260	+	0.0710021i
$159$	−205.889	−	633.662i	−0.102692	−	0.316054i
$160$	212.560	+	654.192i	0.105027	+	0.323240i
$161$	575.910	+	418.423i	0.281913	+	0.204822i
$162$	309.517	−	224.877i	0.150111	−	0.109062i
$163$	284.219	−	874.736i	0.136575	−	0.420335i	−0.859257	−	0.511545i	$-0.829073\pi$
$163$	284.219	−	874.736i	0.136575	−	0.420335i	0.995832	+	0.0912099i	$0.0290734\pi$
$164$	5408.35			2.57513
$165$	255.667	−	607.146i	0.120628	−	0.286462i
$166$	5780.52			2.70274
$167$	−713.424	+	2195.69i	−0.330577	+	1.01741i	0.638282	+	0.769802i	$0.279645\pi$
$167$	−713.424	+	2195.69i	−0.330577	+	1.01741i	−0.968860	+	0.247610i	$0.920355\pi$
$168$	720.361	−	523.373i	0.330816	−	0.240352i
$169$	−4809.17	−	3494.07i	−2.18897	−	1.59038i
$170$	−393.861	−	1212.18i	−0.177693	−	0.546883i
$171$	−381.205	−	1173.23i	−0.170476	−	0.524672i
$172$	−3195.62	−	2321.76i	−1.41665	−	1.02926i
$173$	370.871	−	269.454i	0.162987	−	0.118417i	−0.503302	−	0.864111i	$-0.667882\pi$
$173$	370.871	−	269.454i	0.162987	−	0.118417i	0.666289	+	0.745693i	$0.267882\pi$
$174$	647.323	−	1992.26i	0.282031	−	0.868003i
$175$	−884.159			−0.381921
$176$	−820.342	+	496.116i	−0.351338	+	0.212478i
$177$	507.402			0.215473
$178$	−1408.25	+	4334.16i	−0.592995	+	1.82505i
$179$	2880.70	−	2092.95i	1.20287	−	0.873935i	0.208304	−	0.978064i	$-0.433206\pi$
$179$	2880.70	−	2092.95i	1.20287	−	0.873935i	0.994564	+	0.104129i	$0.0332056\pi$
$180$	−627.110	−	455.622i	−0.259678	−	0.188667i
$181$	248.804	+	765.741i	0.102174	+	0.314459i	0.989057	−	0.147535i	$-0.0471340\pi$
$181$	248.804	+	765.741i	0.102174	+	0.314459i	−0.886883	+	0.461994i	$0.847134\pi$
$182$	1311.71	+	4037.01i	0.534231	+	1.64419i
$183$	−551.084	−	400.386i	−0.222608	−	0.161734i
$184$	−1723.07	+	1251.88i	−0.690360	+	0.501576i
$185$	18.8244	−	57.9355i	0.00748106	−	0.0230243i
$186$	−109.369			−0.0431146
$187$	−1399.57	+	846.413i	−0.547307	+	0.330994i
$188$	−3393.33			−1.31640
$189$	83.1013	−	255.759i	0.0319827	−	0.0984326i
$190$	−3152.56	+	2290.47i	−1.20374	+	0.874568i
$191$	1836.35	+	1334.19i	0.695674	+	0.505437i	0.878520	−	0.477705i	$-0.158531\pi$
$191$	1836.35	+	1334.19i	0.695674	+	0.505437i	−0.182847	+	0.983141i	$0.558531\pi$
$192$	−695.282	−	2139.86i	−0.261342	−	0.804328i
$193$	−1477.59	−	4547.55i	−0.551083	−	1.69606i	−0.706069	−	0.708143i	$-0.749533\pi$
$193$	−1477.59	−	4547.55i	−0.551083	−	1.69606i	0.154986	−	0.987917i	$-0.450467\pi$
$194$	974.983	+	708.367i	0.360823	+	0.262153i
$195$	1318.14	−	957.684i	0.484071	−	0.351698i
$196$	−1078.01	+	3317.79i	−0.392862	+	1.20911i
$197$	−2009.15			−0.726630			−0.363315	−	0.931666i	$-0.618355\pi$
$197$	−2009.15			−0.726630			−0.363315	+	0.931666i	$0.618355\pi$
$198$	−601.876	+	1429.31i	−0.216028	+	0.513012i
$199$	3250.22			1.15780			0.578900	−	0.815398i	$-0.303482\pi$
$199$	3250.22			1.15780			0.578900	+	0.815398i	$0.303482\pi$
$200$	817.450	−	2515.85i	0.289012	−	0.889488i
$201$	880.217	−	639.515i	0.308884	−	0.224417i
$202$	518.450	+	376.676i	0.180584	+	0.131202i
$203$	−455.009	−	1400.37i	−0.157317	−	0.484172i
$204$	594.710	+	1830.33i	0.204108	+	0.628180i
$205$	−1840.52	−	1337.22i	−0.627061	−	0.455586i
$206$	−2633.47	+	1913.33i	−0.890691	+	0.647125i
$207$	−198.774	+	611.764i	−0.0667428	+	0.205413i
$208$	−2371.05			−0.790399
$209$	3783.39	+	3269.86i	1.25216	+	1.08221i
$210$	−849.483			−0.279142
$211$	−95.3371	+	293.417i	−0.0311056	+	0.0957331i	−0.965404	−	0.260759i	$-0.916027\pi$
$211$	−95.3371	+	293.417i	−0.0311056	+	0.0957331i	0.934298	+	0.356492i	$0.116027\pi$
$212$	2570.99	−	1867.93i	0.832907	−	0.605143i
$213$	1727.27	+	1254.93i	0.555635	+	0.403693i
$214$	−1414.67	−	4353.89i	−0.451890	−	1.39078i
$215$	513.450	+	1580.24i	0.162870	+	0.501262i
$216$	650.925	+	472.925i	0.205046	+	0.148974i
$217$	−62.1943	+	45.1868i	−0.0194563	+	0.0141359i
$218$	344.294	−	1059.63i	0.106966	−	0.329207i
$219$	−3135.15			−0.967369
$220$	3131.01	+	264.888i	0.959511	+	0.0811762i
$221$	−4045.20			−1.23127
$222$	−44.3151	+	136.388i	−0.0133975	+	0.0412332i
$223$	−3744.98	+	2720.89i	−1.12458	+	0.817058i	−0.984898	−	0.173137i	$-0.944610\pi$
$223$	−3744.98	+	2720.89i	−1.12458	+	0.817058i	−0.139687	+	0.990196i	$0.544610\pi$
$224$	−920.846	−	669.033i	−0.274672	−	0.199561i
$225$	−246.884	−	759.832i	−0.0731510	−	0.225135i
$226$	−751.901	−	2314.11i	−0.221308	−	0.681117i
$227$	−2093.34	−	1520.90i	−0.612070	−	0.444695i	0.238073	−	0.971247i	$-0.423484\pi$
$227$	−2093.34	−	1520.90i	−0.612070	−	0.444695i	−0.850142	+	0.526553i	$0.823484\pi$
$228$	4760.20	−	3458.49i	1.38268	−	1.00458i
$229$	675.764	−	2079.79i	0.195003	−	0.600158i	−0.804973	−	0.593311i	$-0.797820\pi$
$229$	675.764	−	2079.79i	0.195003	−	0.600158i	0.999977	−	0.00684712i	$-0.00217952\pi$
$230$	2031.92			0.582526
$231$	248.265	+	1061.47i	0.0707128	+	0.302335i
$232$	4405.41			1.24668
$233$	2059.58	−	6338.75i	0.579090	−	1.78225i	−0.0427208	−	0.999087i	$-0.513603\pi$
$233$	2059.58	−	6338.75i	0.579090	−	1.78225i	0.621810	−	0.783168i	$-0.286397\pi$
$234$	−3103.08	+	2254.52i	−0.866899	+	0.629839i
$235$	1154.79	+	839.002i	0.320553	+	0.232895i
$236$	747.869	+	2301.71i	0.206280	+	0.634866i
$237$	47.0870	+	144.919i	0.0129056	+	0.0397194i
$238$	1706.28	+	1239.68i	0.464712	+	0.337633i
$239$	−1800.04	+	1307.80i	−0.487174	+	0.353953i	−0.804097	−	0.594499i	$-0.797350\pi$
$239$	−1800.04	+	1307.80i	−0.487174	+	0.353953i	0.316922	+	0.948451i	$0.397350\pi$
$240$	146.631	−	451.283i	0.0394374	−	0.121376i
$241$	745.650			0.199301			0.0996505	−	0.995023i	$-0.468228\pi$
$241$	745.650			0.199301			0.0996505	+	0.995023i	$0.468228\pi$
$242$	−910.600	−	6220.35i	−0.241883	−	1.65231i
$243$	243.000			0.0641500
$244$	1004.00	−	3090.00i	0.263420	−	0.810724i
$245$	1187.18	−	862.539i	0.309577	−	0.224921i
$246$	4332.83	+	3147.99i	1.12297	+	0.815888i
$247$	3821.79	+	11762.3i	0.984513	+	3.03002i
$248$	−71.0761	−	218.750i	−0.0181989	−	0.0560106i
$249$	2970.33	+	2158.07i	0.755972	+	0.549246i
$250$	−4916.74	+	3572.22i	−1.24385	+	0.903709i
$251$	−546.697	+	1682.56i	−0.137479	+	0.423116i	−0.995967	−	0.0897164i	$-0.971404\pi$
$251$	−546.697	+	1682.56i	−0.137479	+	0.423116i	0.858489	+	0.512833i	$0.171404\pi$
$252$	1282.68			0.320639
$253$	−593.839	−	2538.98i	−0.147566	−	0.630926i
$254$	−4877.86			−1.20498
$255$	250.163	−	769.923i	0.0614346	−	0.189076i
$256$	5188.69	−	3769.81i	1.26677	−	0.920363i
$257$	1942.61	+	1411.39i	0.471505	+	0.342569i	0.798028	−	0.602621i	$-0.205877\pi$
$257$	1942.61	+	1411.39i	0.471505	+	0.342569i	−0.326522	+	0.945189i	$0.605877\pi$
$258$	−1208.73	−	3720.09i	−0.291676	−	0.897686i
$259$	31.1495	+	95.8683i	0.00747311	+	0.0229999i
$260$	6287.13	+	4567.87i	1.49966	+	1.08957i
$261$	1076.41	−	782.055i	0.255279	−	0.185471i
$262$	−1993.99	+	6136.88i	−0.470188	+	1.44709i
$263$	−5999.10			−1.40654			−0.703270	−	0.710923i	$-0.748278\pi$
$263$	−5999.10			−1.40654			−0.703270	+	0.710923i	$0.748278\pi$
$264$	−3249.91	−	274.948i	−0.757644	−	0.0640979i
$265$	−1336.78			−0.309879
$266$	1992.59	−	6132.57i	0.459299	−	1.41358i
$267$	−2341.73	+	1701.36i	−0.536747	+	0.389969i
$268$	4198.37	+	3050.30i	0.956927	+	0.695248i
$269$	241.484	+	743.212i	0.0547344	+	0.168455i	0.974687	−	0.223575i	$-0.0717728\pi$
$269$	241.484	+	743.212i	0.0547344	+	0.168455i	−0.919952	+	0.392030i	$0.871773\pi$
$270$	−237.202	−	730.032i	−0.0534654	−	0.164549i
$271$	−363.969	−	264.439i	−0.0815851	−	0.0592751i	0.546245	−	0.837625i	$-0.316057\pi$
$271$	−363.969	−	264.439i	−0.0815851	−	0.0592751i	−0.627830	+	0.778350i	$0.716057\pi$
$272$	−953.097	+	692.465i	−0.212463	+	0.154364i
$273$	−833.137	+	2564.13i	−0.184702	+	0.568455i
$274$	−7141.19			−1.57451
$275$	2450.28	+	2117.70i	0.537301	+	0.464372i
$276$	−3068.10			−0.669123
$277$	−1303.43	+	4011.55i	−0.282728	+	0.870147i	0.704342	+	0.709860i	$0.251242\pi$
$277$	−1303.43	+	4011.55i	−0.282728	+	0.870147i	−0.987070	+	0.160287i	$0.948758\pi$
$278$	−4005.83	+	2910.41i	−0.864223	+	0.627895i
$279$	−56.1994	−	40.8313i	−0.0120594	−	0.00876166i
$280$	−552.058	−	1699.06i	−0.117828	−	0.362636i
$281$	−945.957	−	2911.36i	−0.200822	−	0.618068i	−0.999859	−	0.0167855i	$-0.994657\pi$
$281$	−945.957	−	2911.36i	−0.200822	−	0.618068i	0.799037	−	0.601282i	$-0.205343\pi$
$282$	−2718.53	−	1975.12i	−0.574063	−	0.417081i
$283$	4714.18	−	3425.05i	0.990208	−	0.719428i	0.0302411	−	0.999543i	$-0.490372\pi$
$283$	4714.18	−	3425.05i	0.990208	−	0.719428i	0.959967	+	0.280115i	$0.0903725\pi$
$284$	−3146.85	+	9685.00i	−0.657504	+	2.02359i
$285$	−2475.06			−0.514420
$286$	6034.14	−	14329.6i	1.24757	−	2.96268i
$287$	3764.55			0.774267
$288$	317.828	−	978.175i	0.0650285	−	0.200137i
$289$	2348.64	−	1706.39i	0.478047	−	0.347321i
$290$	−3400.21	−	2470.40i	−0.688508	−	0.500230i
$291$	236.539	+	727.991i	0.0476499	+	0.146651i
$292$	−4620.96	−	14221.9i	−0.926100	−	2.85024i
$293$	370.485	+	269.173i	0.0738703	+	0.0536699i	0.624108	−	0.781338i	$-0.285463\pi$
$293$	370.485	+	269.173i	0.0738703	+	0.0536699i	−0.550237	+	0.835008i	$0.685463\pi$
$294$	−2794.79	+	2030.53i	−0.554406	+	0.402800i
$295$	314.589	−	968.206i	0.0620885	−	0.191089i
$296$	−301.590			−0.0592215
$297$	−842.885	+	509.750i	−0.164677	+	0.0995915i
$298$	1828.95			0.355531
$299$	1992.82	−	6133.28i	0.385445	−	1.18628i
$300$	3082.91	−	2239.86i	0.593306	−	0.431062i
$301$	−2224.36	−	1616.09i	−0.425946	−	0.309468i
$302$	−990.713	−	3049.10i	−0.188772	−	0.580980i
$303$	125.780	+	387.111i	0.0238478	+	0.0733959i
$304$	2913.94	+	2117.10i	0.549757	+	0.399422i
$305$	−1105.67	+	803.320i	−0.207576	+	0.150813i
$306$	−588.918	+	1812.50i	−0.110020	+	0.338608i
$307$	3941.62			0.732769			0.366385	−	0.930463i	$-0.380595\pi$
$307$	3941.62			0.732769			0.366385	+	0.930463i	$0.380595\pi$
$308$	−4449.17	+	2690.71i	−0.823100	+	0.497784i
$309$	−2067.52			−0.380638
$310$	−67.8088	+	208.694i	−0.0124235	+	0.0382356i
$311$	−2220.01	+	1612.93i	−0.404776	+	0.294087i	−0.771483	−	0.636249i	$-0.780485\pi$
$311$	−2220.01	+	1612.93i	−0.404776	+	0.294087i	0.366708	+	0.930336i	$0.380485\pi$
$312$	−6525.89	−	4741.34i	−1.18415	−	0.860338i
$313$	−607.584	−	1869.95i	−0.109721	−	0.337687i	0.881088	−	0.472952i	$-0.156811\pi$
$313$	−607.584	−	1869.95i	−0.109721	−	0.337687i	−0.990809	+	0.135265i	$0.956811\pi$
$314$	5268.02	+	16213.3i	0.946789	+	2.91392i
$315$	−436.508	−	317.142i	−0.0780776	−	0.0567267i
$316$	−587.987	+	427.197i	−0.104674	+	0.0760498i
$317$	1972.03	−	6069.28i	0.349401	−	1.07535i	−0.609784	−	0.792568i	$-0.708744\pi$
$317$	1972.03	−	6069.28i	0.349401	−	1.07535i	0.959185	−	0.282778i	$-0.0912561\pi$
$318$	3146.97			0.554947
$319$	−2093.15	+	4970.70i	−0.367378	+	0.872432i
$320$	−4514.28			−0.788612
$321$	898.533	−	2765.40i	0.156234	−	0.480840i
$322$	−2720.17	+	1976.32i	−0.470773	+	0.342037i
$323$	4971.41	+	3611.94i	0.856399	+	0.622210i
$324$	358.163	+	1102.31i	0.0614133	+	0.189011i
$325$	2475.16	+	7617.74i	0.422452	+	1.30017i
$326$	3514.55	+	2553.47i	0.597094	+	0.433814i
$327$	572.513	−	415.955i	0.0968197	−	0.0703436i
$328$	−3480.52	+	10711.9i	−0.585913	+	1.80326i
$329$	−2361.97			−0.395805
$330$	2354.19	+	2034.65i	0.392708	+	0.339405i
$331$	3351.60			0.556557			0.278279	−	0.960500i	$-0.410236\pi$
$331$	3351.60			0.556557			0.278279	+	0.960500i	$0.410236\pi$
$332$	−5411.54	+	16655.0i	−0.894569	+	2.75320i
$333$	−73.6898	+	53.5388i	−0.0121267	+	0.00881053i
$334$	−8821.95	−	6409.52i	−1.44526	−	1.05004i
$335$	−674.565	−	2076.10i	−0.110016	−	0.338595i
$336$	242.636	+	746.757i	0.0393955	+	0.121247i
$337$	2127.64	+	1545.82i	0.343916	+	0.249870i	0.746312	−	0.665596i	$-0.231823\pi$
$337$	2127.64	+	1545.82i	0.343916	+	0.249870i	−0.402396	+	0.915466i	$0.631823\pi$
$338$	22714.9	−	16503.4i	3.65541	−	2.65581i
$339$	477.574	−	1469.82i	0.0765140	−	0.235486i
$340$	3861.29			0.615906
$341$	280.590	+	23.7383i	0.0445595	+	0.00376981i
$342$	5826.62			0.921251
$343$	−1806.06	+	5558.48i	−0.284309	+	0.875014i
$344$	6655.07	−	4835.19i	1.04307	−	0.757837i
$345$	1044.11	+	758.588i	0.162936	+	0.118380i
$346$	669.097	+	2059.27i	0.103962	+	0.319962i
$347$	−2710.55	−	8342.20i	−0.419336	−	1.29058i	−0.908314	−	0.418288i	$-0.862630\pi$
$347$	−2710.55	−	8342.20i	−0.419336	−	1.29058i	0.488978	−	0.872296i	$-0.337370\pi$
$348$	5134.14	+	3730.17i	0.790859	+	0.574593i
$349$	5365.95	−	3898.59i	0.823017	−	0.597957i	−0.0945581	−	0.995519i	$-0.530144\pi$
$349$	5365.95	−	3898.59i	0.823017	−	0.597957i	0.917575	+	0.397563i	$0.130144\pi$
$350$	1290.49	−	3971.71i	0.197084	−	0.606563i
$351$	−2436.21			−0.370471
$352$	949.513	+	4059.68i	0.143776	+	0.614720i
$353$	722.467			0.108932			0.0544661	−	0.998516i	$-0.482654\pi$
$353$	722.467			0.108932			0.0544661	+	0.998516i	$0.482654\pi$
$354$	−740.586	+	2279.29i	−0.111191	+	0.342211i
$355$	3465.52	−	2517.85i	0.518115	−	0.376433i
$356$	−11169.4	−	8115.01i	−1.66285	−	1.20813i
$357$	413.956	+	1274.03i	0.0613694	+	0.188876i
$358$	5197.13	+	15995.1i	0.767254	+	2.36136i
$359$	−6597.95	−	4793.69i	−0.969990	−	0.704739i	−0.0145406	−	0.999894i	$-0.504629\pi$
$359$	−6597.95	−	4793.69i	−0.969990	−	0.704739i	−0.955449	+	0.295155i	$0.904629\pi$
$360$	1305.99	−	948.859i	0.191200	−	0.138915i
$361$	3686.08	−	11344.6i	0.537407	−	1.65397i
$362$	−3802.92			−0.552146
$363$	1854.36	−	3536.30i	0.268123	−	0.511315i
$364$	−12859.5			−1.85171
$365$	−1943.79	+	5982.39i	−0.278748	+	0.857897i
$366$	2602.91	−	1891.12i	0.371738	−	0.270084i
$367$	−9647.07	−	7009.00i	−1.37213	−	0.996913i	−0.997567	−	0.0697126i	$-0.977792\pi$
$367$	−9647.07	−	7009.00i	−1.37213	−	0.996913i	−0.374566	−	0.927200i	$-0.622208\pi$
$368$	−580.374	−	1786.21i	−0.0822122	−	0.253023i
$369$	1051.18	+	3235.20i	0.148299	+	0.456416i
$370$	232.775	+	169.121i	0.0327065	+	0.0237627i
$371$	1789.57	−	1300.20i	0.250431	−	0.181949i
$372$	102.388	−	315.117i	0.0142703	−	0.0439195i
$373$	−5520.95			−0.766391			−0.383195	−	0.923667i	$-0.625176\pi$
$373$	−5520.95			−0.766391			−0.383195	+	0.923667i	$0.625176\pi$
$374$	−1759.39	−	7522.36i	−0.243252	−	1.04003i
$375$	−3860.11			−0.531561
$376$	2183.76	−	6720.93i	0.299518	−	0.921823i
$377$	−10791.6	+	7840.54i	−1.47426	+	1.07111i
$378$	1027.60	+	746.595i	0.139825	+	0.101589i
$379$	2086.95	+	6422.98i	0.282848	+	0.870518i	0.987035	+	0.160503i	$0.0513117\pi$
$379$	2086.95	+	6422.98i	0.282848	+	0.870518i	−0.704187	+	0.710015i	$0.748688\pi$
$380$	−3648.04	−	11227.5i	−0.492475	−	1.51568i
$381$	−2506.50	−	1821.08i	−0.337039	−	0.244873i
$382$	−8673.55	+	6301.70i	−1.16172	+	0.844040i
$383$	−1642.23	+	5054.26i	−0.219097	+	0.674310i	0.779741	+	0.626102i	$0.215351\pi$
$383$	−1642.23	+	5054.26i	−0.219097	+	0.674310i	−0.998837	+	0.0482074i	$0.984649\pi$
$384$	7884.52			1.04780
$385$	2179.38	+	184.379i	0.288497	+	0.0244073i
$386$	22584.6			2.97804
$387$	767.733	−	2362.84i	0.100843	−	0.310361i
$388$	−2953.72	+	2146.00i	−0.386475	+	0.280790i
$389$	92.0601	+	66.8856i	0.0119991	+	0.00871783i	0.593769	−	0.804636i	$-0.297639\pi$
$389$	92.0601	+	66.8856i	0.0119991	+	0.00871783i	−0.581770	+	0.813354i	$0.697639\pi$
$390$	2378.08	+	7318.98i	0.308766	+	0.950285i
$391$	−990.163	−	3047.41i	−0.128068	−	0.394154i
$392$	−5877.55	−	4270.29i	−0.757299	−	0.550210i
$393$	−3315.73	+	2409.02i	−0.425589	+	0.309208i
$394$	2932.49	−	9025.27i	0.374966	−	1.15403i
$395$	305.723			0.0389433
$396$	−3554.70	−	3072.21i	−0.451087	−	0.389860i
$397$	−4034.28			−0.510012			−0.255006	−	0.966940i	$-0.582077\pi$
$397$	−4034.28			−0.510012			−0.255006	+	0.966940i	$0.582077\pi$
$398$	−4743.91	+	14600.3i	−0.597465	+	1.83881i
$399$	3313.40	−	2407.32i	0.415733	−	0.302048i
$400$	1887.20	+	1371.13i	0.235899	+	0.171391i
$401$	3098.74	+	9536.93i	0.385894	+	1.18766i	0.935830	+	0.352452i	$0.114652\pi$
$401$	3098.74	+	9536.93i	0.385894	+	1.18766i	−0.549936	+	0.835207i	$0.685348\pi$
$402$	1588.02	+	4887.42i	0.197023	+	0.606374i
$403$	563.430	+	409.356i	0.0696438	+	0.0505992i
$404$	−1570.65	+	1141.14i	−0.193422	+	0.140529i
$405$	150.660	−	463.684i	0.0184848	−	0.0568905i
$406$	6954.71			0.850139
$407$	143.295	−	340.290i	0.0174517	−	0.0414436i
$408$	−4007.93			−0.486329
$409$	91.0554	−	280.240i	0.0110083	−	0.0338801i	−0.945401	−	0.325908i	$-0.894330\pi$
$409$	91.0554	−	280.240i	0.0110083	−	0.0338801i	0.956410	+	0.292028i	$0.0943300\pi$
$410$	8693.24	−	6316.01i	1.04714	−	0.760794i
$411$	−3669.51	−	2666.06i	−0.440398	−	0.319968i
$412$	−3047.36	−	9378.82i	−0.364400	−	1.12151i
$413$	520.564	+	1602.13i	0.0620225	+	0.190886i
$414$	−2457.97	−	1785.82i	−0.291794	−	0.212001i
$415$	5959.56	−	4329.87i	0.704924	−	0.512157i
$416$	−3186.41	+	9806.75i	−0.375544	+	1.15581i
$417$	−3144.96			−0.369327
$418$	−20210.6	+	12222.7i	−2.36491	+	1.43022i
$419$	−1094.76			−0.127643			−0.0638215	−	0.997961i	$-0.520329\pi$
$419$	−1094.76			−0.127643			−0.0638215	+	0.997961i	$0.520329\pi$
$420$	795.259	−	2447.56i	0.0923921	−	0.284354i
$421$	−10574.2	+	7682.63i	−1.22412	+	0.889379i	−0.996436	−	0.0843554i	$-0.973117\pi$
$421$	−10574.2	+	7682.63i	−1.22412	+	0.889379i	−0.227689	+	0.973734i	$0.573117\pi$
$422$	−1178.90	−	856.524i	−0.135991	−	0.0988031i
$423$	−659.535	−	2029.84i	−0.0758102	−	0.233320i
$424$	2045.14	+	6294.28i	0.234247	+	0.720937i
$425$	3219.70	+	2339.25i	0.367479	+	0.266989i
$426$	−8158.32	+	5927.36i	−0.927868	+	0.674136i
$427$	698.848	−	2150.83i	0.0792029	−	0.243761i
$428$	13868.9			1.56631
$429$	8450.39	−	5110.52i	0.951023	−	0.575148i
$430$	−7847.97			−0.880146
$431$	−455.301	+	1401.27i	−0.0508842	+	0.156605i	−0.973270	−	0.229665i	$-0.926237\pi$
$431$	−455.301	+	1401.27i	−0.0508842	+	0.156605i	0.922386	+	0.386271i	$0.126237\pi$
$432$	−574.000	+	417.035i	−0.0639273	+	0.0464459i
$433$	3285.04	+	2386.72i	0.364594	+	0.264893i	0.754966	−	0.655764i	$-0.227654\pi$
$433$	3285.04	+	2386.72i	0.364594	+	0.264893i	−0.390372	+	0.920657i	$0.627654\pi$
$434$	−112.206	−	345.335i	−0.0124103	−	0.0381949i
$435$	−824.918	−	2538.84i	−0.0909237	−	0.279834i
$436$	2730.72	+	1983.98i	0.299949	+	0.217926i
$437$	−7925.49	+	5758.21i	−0.867569	+	0.630326i
$438$	4575.96	−	14083.3i	0.499196	−	1.53637i
$439$	11732.1			1.27550			0.637749	−	0.770244i	$-0.279866\pi$
$439$	11732.1			1.27550			0.637749	+	0.770244i	$0.279866\pi$
$440$	−2539.59	+	6030.90i	−0.275160	+	0.653436i
$441$	−2194.18			−0.236927
$442$	5904.24	−	18171.4i	0.635375	−	1.95548i
$443$	738.883	−	536.830i	0.0792447	−	0.0575747i	−0.547458	−	0.836833i	$-0.684404\pi$
$443$	738.883	−	536.830i	0.0792447	−	0.0575747i	0.626702	+	0.779259i	$0.284404\pi$
$444$	−351.479	−	255.364i	−0.0375686	−	0.0272952i
$445$	1794.61	+	5523.25i	0.191175	+	0.588376i
$446$	−6756.40	−	20794.1i	−0.717320	−	2.20768i
$447$	939.808	+	682.810i	0.0994438	+	0.0722502i
$448$	6043.33	−	4390.74i	0.637323	−	0.463042i
$449$	4495.39	−	13835.4i	0.472495	−	1.45419i	−0.376810	−	0.926290i	$-0.622979\pi$
$449$	4495.39	−	13835.4i	0.472495	−	1.45419i	0.849306	−	0.527901i	$-0.177021\pi$
$450$	3773.57			0.395306
$451$	−10432.8	−	9016.71i	−1.08927	−	0.941419i
$452$	7371.40			0.767083
$453$	629.257	−	1936.65i	0.0652650	−	0.200865i
$454$	9887.37	−	7183.59i	1.02211	−	0.742605i
$455$	4376.24	+	3179.52i	0.450904	+	0.327601i
$456$	3786.58	+	11653.9i	0.388865	+	1.19680i
$457$	559.410	+	1721.69i	0.0572606	+	0.176230i	0.975596	−	0.219573i	$-0.0704663\pi$
$457$	559.410	+	1721.69i	0.0572606	+	0.176230i	−0.918335	+	0.395803i	$0.870466\pi$
$458$	8356.25	+	6071.17i	0.852537	+	0.619404i
$459$	−979.288	+	711.494i	−0.0995844	+	0.0723523i
$460$	−1902.22	+	5854.44i	−0.192808	+	0.593401i
$461$	15271.1			1.54284			0.771419	−	0.636328i	$-0.219547\pi$
$461$	15271.1			1.54284			0.771419	+	0.636328i	$0.219547\pi$
$462$	−5130.55	−	434.053i	−0.516656	−	0.0437099i
$463$	−12919.4			−1.29679			−0.648397	−	0.761302i	$-0.724560\pi$
$463$	−12919.4			−1.29679			−0.648397	+	0.761302i	$0.724560\pi$
$464$	−1200.46	+	3694.65i	−0.120108	+	0.369654i
$465$	−112.756	+	81.9223i	−0.0112451	+	0.00817002i
$466$	25468.1	+	18503.6i	2.53173	+	1.83941i
$467$	−1120.49	−	3448.51i	−0.111028	−	0.341709i	0.880070	−	0.474844i	$-0.157496\pi$
$467$	−1120.49	−	3448.51i	−0.111028	−	0.341709i	−0.991098	+	0.133135i	$0.957496\pi$
$468$	−3590.78	−	11051.3i	−0.354666	−	1.09155i
$469$	2922.33	+	2123.20i	0.287720	+	0.209041i
$470$	−5454.35	+	3962.82i	−0.535299	+	0.388917i
$471$	−3346.01	+	10298.0i	−0.327338	+	1.00744i
$472$	−5040.11			−0.491504
$473$	2293.60	+	9806.38i	0.222960	+	0.953273i
$474$	−719.713			−0.0697416
$475$	3759.97	−	11572.0i	0.363199	−	1.11781i
$476$	−5169.17	+	3755.62i	−0.497749	+	0.361636i
$477$	1617.07	+	1174.87i	0.155222	+	0.112775i
$478$	−3247.48	−	9994.73i	−0.310746	−	0.956377i
$479$	2325.95	+	7158.52i	0.221869	+	0.682842i	0.998594	+	0.0530027i	$0.0168792\pi$
$479$	2325.95	+	7158.52i	0.221869	+	0.682842i	−0.776726	+	0.629839i	$0.783121\pi$
$480$	−1669.47	−	1212.94i	−0.158751	−	0.115339i
$481$	738.782	−	536.756i	0.0700323	−	0.0508815i
$482$	−1088.32	+	3349.52i	−0.102846	+	0.316528i
$483$	−2135.59			−0.201186
$484$	18774.7	+	3199.65i	1.76322	+	0.300493i
$485$	1535.78			0.143786
$486$	−354.674	+	1091.58i	−0.0331036	+	0.101882i
$487$	8956.17	−	6507.04i	0.833353	−	0.605466i	−0.0871530	−	0.996195i	$-0.527777\pi$
$487$	8956.17	−	6507.04i	0.833353	−	0.605466i	0.920506	+	0.390729i	$0.127777\pi$
$488$	5474.02	+	3977.11i	0.507781	+	0.368925i
$489$	852.657	+	2624.21i	0.0788517	+	0.242680i
$490$	2141.82	+	6591.85i	0.197465	+	0.607734i
$491$	−12589.0	−	9146.43i	−1.15709	−	0.840678i	−0.167686	−	0.985840i	$-0.553629\pi$
$491$	−12589.0	−	9146.43i	−1.15709	−	0.840678i	−0.989408	+	0.145163i	$0.953629\pi$
$492$	−13126.3	+	9536.84i	−1.20281	+	0.873890i
$493$	−2048.08	+	6303.35i	−0.187102	+	0.575839i
$494$	−58415.2			−5.32029
$495$	450.097	+	1924.41i	0.0408694	+	0.174739i
$496$	202.825			0.0183611
$497$	−2190.40	+	6741.37i	−0.197692	+	0.608434i
$498$	−14029.6	+	10193.1i	−1.26241	+	0.917197i
$499$	6505.61	+	4726.61i	0.583630	+	0.424032i	0.840031	−	0.542539i	$-0.182537\pi$
$499$	6505.61	+	4726.61i	0.583630	+	0.424032i	−0.256401	+	0.966570i	$0.582537\pi$
$500$	−5689.50	−	17510.5i	−0.508884	−	1.56618i
$501$	−2140.27	−	6587.08i	−0.190859	−	0.587404i
$502$	−6760.25	−	4911.61i	−0.601045	−	0.436685i
$503$	−2493.19	+	1811.41i	−0.221005	+	0.160570i	−0.692779	−	0.721150i	$-0.743614\pi$
$503$	−2493.19	+	1811.41i	−0.221005	+	0.160570i	0.471774	+	0.881720i	$0.343614\pi$
$504$	−825.460	+	2540.50i	−0.0729542	+	0.224530i
$505$	816.656			0.0719618
$506$	12272.0	+	1038.23i	1.07818	+	0.0912157i
$507$	17833.4			1.56215
$508$	4566.50	−	14054.2i	0.398830	−	1.22747i
$509$	9792.05	−	7114.34i	0.852701	−	0.619524i	−0.0731882	−	0.997318i	$-0.523317\pi$
$509$	9792.05	−	7114.34i	0.852701	−	0.619524i	0.925890	+	0.377794i	$0.123317\pi$
$510$	3093.43	+	2247.51i	0.268587	+	0.195140i
$511$	−3216.48	−	9899.31i	−0.278452	−	0.856986i
$512$	2863.84	+	8813.98i	0.247197	+	0.760794i
$513$	2994.02	+	2175.28i	0.257679	+	0.187215i
$514$	−9175.45	+	6666.36i	−0.787377	+	0.572063i
$515$	−1281.87	+	3945.18i	−0.109681	+	0.337563i
$516$	11850.0			1.01098
$517$	6545.77	+	5657.30i	0.556833	+	0.481253i
$518$	−476.113			−0.0403846
$519$	−424.980	+	1307.95i	−0.0359433	+	0.110622i
$520$	−13093.3	+	9512.85i	−1.10419	+	0.802242i
$521$	723.094	+	525.359i	0.0608048	+	0.0441773i	0.617772	−	0.786357i	$-0.288035\pi$
$521$	723.094	+	525.359i	0.0608048	+	0.0441773i	−0.556968	+	0.830534i	$0.688035\pi$
$522$	1941.97	+	5976.77i	0.162831	+	0.501142i
$523$	1461.97	+	4499.48i	0.122232	+	0.376193i	0.993387	−	0.114817i	$-0.0366281\pi$
$523$	1461.97	+	4499.48i	0.122232	+	0.376193i	−0.871154	+	0.491009i	$0.836628\pi$
$524$	−15815.0	−	11490.3i	−1.31848	−	0.957932i
$525$	2145.90	−	1559.09i	0.178390	−	0.129608i
$526$	8756.07	−	26948.4i	0.725823	−	2.23385i
$527$	346.035			0.0286025
$528$	1116.18	−	2650.65i	0.0919992	−	0.218475i
$529$	−7058.77			−0.580157
$530$	1951.12	−	6004.94i	0.159908	−	0.492147i
$531$	−1231.49	+	894.730i	−0.100644	+	0.0731223i
$532$	15803.9	+	11482.2i	1.28795	+	0.935748i
$533$	−10538.7	−	32434.7i	−0.856435	−	2.63584i
$534$	−4224.76	−	13002.5i	−0.342366	−	1.05369i
$535$	−4719.75	−	3429.10i	−0.381406	−	0.277108i
$536$	−8743.35	+	6352.42i	−0.704581	+	0.511908i
$537$	−3300.98	+	10159.4i	−0.265266	+	0.816406i
$538$	−3691.03			−0.295783
$539$	7610.86	−	4602.80i	0.608205	−	0.367823i
$540$	2325.45			0.185318
$541$	−5944.61	+	18295.6i	−0.472419	+	1.45396i	0.376987	+	0.926219i	$0.376960\pi$
$541$	−5944.61	+	18295.6i	−0.472419	+	1.45396i	−0.849407	+	0.527739i	$0.823040\pi$
$542$	1719.12	−	1249.01i	0.136241	−	0.0989847i
$543$	−1954.13	−	1419.76i	−0.154438	−	0.112206i
$544$	1583.21	+	4872.63i	0.124779	+	0.384030i
$545$	−438.753	−	1350.34i	−0.0344846	−	0.106133i
$546$	−10302.3	−	7485.03i	−0.807502	−	0.586685i
$547$	−1572.62	+	1142.57i	−0.122925	+	0.0893105i	−0.647549	−	0.762024i	$-0.724206\pi$
$547$	−1572.62	+	1142.57i	−0.122925	+	0.0893105i	0.524624	+	0.851334i	$0.324206\pi$
$548$	6685.36	−	20575.4i	0.521139	−	1.60390i
$549$	2043.53			0.158863
$550$	−13089.2	+	7915.95i	−1.01478	+	0.613704i
$551$	20263.3			1.56669
$552$	1974.46	−	6076.77i	0.152244	−	0.468559i
$553$	−409.276	+	297.356i	−0.0314723	+	0.0228660i
$554$	−16117.8	−	11710.2i	−1.23606	−	0.898052i
$555$	56.4731	+	173.806i	0.00431919	+	0.0132931i
$556$	−4635.42	−	14266.4i	−0.353571	−	1.08818i
$557$	11344.0	+	8241.91i	0.862947	+	0.626967i	0.928685	−	0.370869i	$-0.120940\pi$
$557$	11344.0	+	8241.91i	0.862947	+	0.626967i	−0.0657384	+	0.997837i	$0.520940\pi$
$558$	265.444	−	192.856i	0.0201382	−	0.0146313i
$559$	−7696.95	+	23688.8i	−0.582373	+	1.79236i
$560$	1575.37			0.118878
$561$	1904.29	−	4522.22i	0.143314	−	0.340336i
$562$	14458.7			1.08524
$563$	2766.65	−	8514.86i	0.207105	−	0.637404i	−0.792515	−	0.609852i	$-0.791229\pi$
$563$	2766.65	−	8514.86i	0.207105	−	0.637404i	0.999620	−	0.0275520i	$-0.00877120\pi$
$564$	8235.79	−	5983.65i	0.614874	−	0.446732i
$565$	−2508.57	−	1822.58i	−0.186790	−	0.135711i
$566$	8504.95	+	26175.6i	0.631607	+	1.94389i
$567$	249.304	+	767.278i	0.0184652	+	0.0568301i
$568$	−17157.3	−	12465.5i	−1.26743	−	0.920845i
$569$	−14526.8	+	10554.4i	−1.07029	+	0.777612i	−0.975965	−	0.217929i	$-0.930070\pi$
$569$	−14526.8	+	10554.4i	−1.07029	+	0.777612i	−0.0943269	+	0.995541i	$0.530070\pi$
$570$	3612.51	−	11118.2i	0.265458	−	0.816997i
$571$	−10089.5			−0.739464			−0.369732	−	0.929138i	$-0.620551\pi$
$571$	−10089.5			−0.739464			−0.369732	+	0.929138i	$0.620551\pi$
$572$	35637.9	+	30800.7i	2.60506	+	2.25147i
$573$	−6809.57			−0.496464
$574$	−5494.61	+	16910.7i	−0.399548	+	1.22968i
$575$	−5132.89	+	3729.26i	−0.372272	+	0.270471i
$576$	5460.82	+	3967.51i	0.395024	+	0.287002i
$577$	−6570.03	−	20220.5i	−0.474027	−	1.45891i	−0.847265	−	0.531170i	$-0.821752\pi$
$577$	−6570.03	−	20220.5i	−0.474027	−	1.45891i	0.373238	−	0.927736i	$-0.378248\pi$
$578$	4237.24	+	13040.9i	0.304924	+	0.938459i
$579$	11605.1	+	8431.61i	0.832975	+	0.605192i
$580$	10301.0	−	7484.08i	0.737455	−	0.535793i
$581$	−3766.77	+	11592.9i	−0.268971	+	0.827807i
$582$	−3615.44			−0.257499
$583$	−8073.66	−	683.044i	−0.573545	−	0.0485228i
$584$	31142.0			2.20662
$585$	−1510.45	+	4648.69i	−0.106751	+	0.328547i
$586$	−1749.90	+	1271.37i	−0.123358	+	0.0896245i
$587$	−6016.43	−	4371.19i	−0.423040	−	0.307357i	0.355820	−	0.934555i	$-0.384202\pi$
$587$	−6016.43	−	4371.19i	−0.423040	−	0.307357i	−0.778860	+	0.627198i	$0.784202\pi$
$588$	−3234.04	−	9953.36i	−0.226819	−	0.698077i
$589$	−326.924	−	1006.17i	−0.0228704	−	0.0703879i
$590$	3890.10	+	2826.32i	0.271445	+	0.197217i
$591$	4876.31	−	3542.85i	0.339399	−	0.246588i
$592$	82.1826	−	252.932i	0.00570555	−	0.0175599i
$593$	1727.95			0.119660			0.0598301	−	0.998209i	$-0.480944\pi$
$593$	1727.95			0.119660			0.0598301	+	0.998209i	$0.480944\pi$
$594$	−1059.59	−	4530.32i	−0.0731911	−	0.312931i
$595$	2687.70			0.185185
$596$	−1712.20	+	5269.62i	−0.117675	+	0.362168i
$597$	−7888.46	+	5731.30i	−0.540793	+	0.392909i
$598$	24642.5	+	17903.8i	1.68513	+	1.22432i
$599$	854.645	+	2630.33i	0.0582969	+	0.179419i	0.975965	−	0.217929i	$-0.0699303\pi$
$599$	854.645	+	2630.33i	0.0582969	+	0.179419i	−0.917668	+	0.397349i	$0.869930\pi$
$600$	2452.35	+	7547.55i	0.166861	+	0.513546i
$601$	9978.89	+	7250.09i	0.677283	+	0.492075i	0.872455	−	0.488694i	$-0.162527\pi$
$601$	9978.89	+	7250.09i	0.677283	+	0.492075i	−0.195172	+	0.980769i	$0.562527\pi$
$602$	10506.2	−	7633.20i	0.711297	−	0.516787i
$603$	−1008.64	+	3104.27i	−0.0681176	+	0.209645i
$604$	9712.64			0.654307
$605$	−5598.13	−	5730.93i	−0.376192	−	0.385117i
$606$	−1922.52			−0.128873
$607$	2570.13	−	7910.05i	0.171859	−	0.528928i	−0.827617	−	0.561293i	$-0.810304\pi$
$607$	2570.13	−	7910.05i	0.171859	−	0.528928i	0.999476	+	0.0323655i	$0.0103041\pi$
$608$	12672.4	−	9207.03i	0.845285	−	0.614136i
$609$	3573.69	+	2596.44i	0.237788	+	0.172763i
$610$	−1994.77	−	6139.28i	−0.132403	−	0.407495i
$611$	6612.21	+	20350.3i	0.437809	+	1.34744i
$612$	−4670.92	−	3393.62i	−0.308514	−	0.224149i
$613$	1049.66	−	762.620i	0.0691602	−	0.0502478i	−0.552668	−	0.833402i	$-0.686390\pi$
$613$	1049.66	−	762.620i	0.0691602	−	0.0502478i	0.621828	+	0.783154i	$0.286390\pi$
$614$	−5753.05	+	17706.1i	−0.378134	+	1.16378i
$615$	6825.02			0.447498
$616$	−2466.06	−	10543.7i	−0.161300	−	0.689642i
$617$	−13415.2			−0.875328			−0.437664	−	0.899139i	$-0.644194\pi$
$617$	−13415.2			−0.875328			−0.437664	+	0.899139i	$0.644194\pi$
$618$	3017.69	−	9287.48i	0.196422	−	0.604526i
$619$	−11943.5	+	8677.44i	−0.775523	+	0.563450i	−0.903632	−	0.428310i	$-0.859109\pi$
$619$	−11943.5	+	8677.44i	−0.775523	+	0.563450i	0.128109	+	0.991760i	$0.459109\pi$
$620$	−537.815	−	390.745i	−0.0348374	−	0.0253108i
$621$	−596.323	−	1835.29i	−0.0385340	−	0.118595i
$622$	−4005.17	−	12326.6i	−0.258188	−	0.794620i
$623$	−7774.57	−	5648.56i	−0.499971	−	0.363250i
$624$	5754.67	−	4181.01i	0.369185	−	0.268228i
$625$	1035.68	−	3187.49i	0.0662835	−	0.204000i
$626$	9286.78			0.592930
$627$	−14948.4	−	1264.66i	−0.952124	−	0.0805512i
$628$	−51646.0			−3.28169
$629$	140.210	−	431.522i	0.00888797	−	0.0273544i
$630$	2061.74	−	1497.94i	0.130384	−	0.0947292i
$631$	−20996.8	−	15255.1i	−1.32467	−	0.962432i	−0.999861	−	0.0166535i	$-0.994699\pi$
$631$	−20996.8	−	15255.1i	−1.32467	−	0.962432i	−0.324813	−	0.945778i	$-0.605301\pi$
$632$	−467.723	−	1439.50i	−0.0294384	−	0.0906019i
$633$	−286.011	−	880.252i	−0.0179588	−	0.0552715i
$634$	24385.4	+	17717.0i	1.52755	+	1.10983i
$635$	−5028.95	+	3653.74i	−0.314280	+	0.228338i
$636$	−2946.09	+	9067.14i	−0.183680	+	0.565307i
$637$	21997.9			1.36827
$638$	−19273.7	−	16657.6i	−1.19601	−	1.03367i
$639$	−6405.06			−0.396526
$640$	4888.41	−	15045.0i	0.301924	−	0.929226i
$641$	16063.7	−	11671.0i	0.989827	−	0.719152i	0.0299440	−	0.999552i	$-0.490467\pi$
$641$	16063.7	−	11671.0i	0.989827	−	0.719152i	0.959883	+	0.280400i	$0.0904671\pi$
$642$	11110.9	+	8072.56i	0.683043	+	0.496259i
$643$	−4581.91	−	14101.7i	−0.281015	−	0.864877i	−0.987565	−	0.157213i	$-0.949749\pi$
$643$	−4581.91	−	14101.7i	−0.281015	−	0.864877i	0.706549	−	0.707664i	$-0.250251\pi$
$644$	−3147.69	−	9687.59i	−0.192603	−	0.592771i
$645$	−4032.69	−	2929.92i	−0.246181	−	0.178861i
$646$	−23481.2	+	17060.1i	−1.43012	+	1.03904i
$647$	9349.60	−	28775.1i	0.568115	−	1.74848i	−0.0903934	−	0.995906i	$-0.528812\pi$
$647$	9349.60	−	28775.1i	0.568115	−	1.74848i	0.658509	−	0.752573i	$-0.271188\pi$
$648$	−2413.76			−0.146330
$649$	2394.71	−	5686.85i	0.144839	−	0.343958i
$650$	−37832.2			−2.28292
$651$	71.2683	−	219.341i	0.00429067	−	0.0132053i
$652$	−10647.3	+	7735.74i	−0.639543	+	0.464655i
$653$	7520.52	+	5463.98i	0.450690	+	0.327446i	0.789868	−	0.613277i	$-0.210149\pi$
$653$	7520.52	+	5463.98i	0.450690	+	0.327446i	−0.339178	+	0.940722i	$0.610149\pi$
$654$	1032.88	+	3178.89i	0.0617568	+	0.190068i
$655$	2541.05	+	7820.55i	0.151583	+	0.466525i
$656$	−8035.26	−	5837.96i	−0.478238	−	0.347460i
$657$	7609.17	−	5528.39i	0.451845	−	0.328284i
$658$	3447.45	−	10610.2i	0.204249	−	0.628613i
$659$	15034.4			0.888705			0.444353	−	0.895852i	$-0.353434\pi$
$659$	15034.4			0.888705			0.444353	+	0.895852i	$0.353434\pi$
$660$	−8066.21	+	4878.18i	−0.475722	+	0.287701i
$661$	18459.0			1.08619			0.543095	−	0.839671i	$-0.317252\pi$
$661$	18459.0			1.08619			0.543095	+	0.839671i	$0.317252\pi$
$662$	−4891.88	+	15055.6i	−0.287203	+	0.883919i
$663$	9817.91	−	7133.13i	0.575107	−	0.417840i
$664$	−29504.8	−	21436.5i	−1.72441	−	1.25286i
$665$	−2539.26	−	7815.05i	−0.148073	−	0.455721i
$666$	−132.945	−	409.164i	−0.00773503	−	0.0238060i
$667$	−8548.09	−	6210.55i	−0.496227	−	0.360530i
$668$	26726.1	−	19417.7i	1.54800	−	1.12469i
$669$	4291.36	−	13207.5i	0.248003	−	0.763273i
$670$	10310.6			0.594525
$671$	−7088.32	+	4286.79i	−0.407811	+	0.246631i
$672$	3414.68			0.196018
$673$	−4568.65	+	14060.8i	−0.261677	+	0.805358i	0.730764	+	0.682630i	$0.239164\pi$
$673$	−4568.65	+	14060.8i	−0.261677	+	0.805358i	−0.992440	+	0.122727i	$0.960836\pi$
$674$	−10049.4	+	7301.29i	−0.574313	+	0.417263i
$675$	1939.06	+	1408.81i	0.110569	+	0.0803333i
$676$	26285.0	+	80896.9i	1.49550	+	4.60269i
$677$	−9528.48	−	29325.6i	−0.540929	−	1.66481i	−0.730476	−	0.682938i	$-0.760702\pi$
$677$	−9528.48	−	29325.6i	−0.540929	−	1.66481i	0.189547	−	0.981872i	$-0.439298\pi$
$678$	5905.50	+	4290.60i	0.334513	+	0.243038i
$679$	−2055.97	+	1493.75i	−0.116202	+	0.0844255i
$680$	−2484.92	+	7647.79i	−0.140136	+	0.431293i
$681$	7762.53			0.436800
$682$	−516.174	+	1225.78i	−0.0289814	+	0.0688236i
$683$	7599.08			0.425726			0.212863	−	0.977082i	$-0.431721\pi$
$683$	7599.08			0.425726			0.212863	+	0.977082i	$0.431721\pi$
$684$	−5454.70	+	16787.8i	−0.304921	+	0.938449i
$685$	−7362.37	+	5349.08i	−0.410660	+	0.298362i
$686$	−22333.1	−	16225.9i	−1.24297	−	0.903074i
$687$	2027.29	+	6239.36i	0.112585	+	0.346501i
$688$	2241.60	+	6898.93i	0.124215	+	0.382296i
$689$	−16212.1	−	11778.8i	−0.896417	−	0.651285i
$690$	−4931.58	+	3583.00i	−0.272090	+	0.197685i
$691$	−795.657	+	2448.78i	−0.0438035	+	0.134813i	−0.970567	−	0.240833i	$-0.922579\pi$
$691$	−795.657	+	2448.78i	−0.0438035	+	0.134813i	0.926763	+	0.375647i	$0.122579\pi$
$692$	−6559.61			−0.360345
$693$	−2474.30	−	2138.45i	−0.135629	−	0.117220i
$694$	41430.1			2.26609
$695$	−1949.88	+	6001.11i	−0.106422	+	0.327532i
$696$	−10692.1	+	7768.30i	−0.582306	+	0.423070i
$697$	−13708.8	−	9960.01i	−0.744988	−	0.541266i
$698$	9680.84	+	29794.5i	0.524964	+	1.61567i
$699$	6178.75	+	19016.3i	0.334338	+	1.02899i
$700$	10235.3	+	7436.38i	0.552655	+	0.401527i
$701$	−15435.4	+	11214.5i	−0.831652	+	0.604231i	−0.920026	−	0.391857i	$-0.871833\pi$
$701$	−15435.4	+	11214.5i	−0.831652	+	0.604231i	0.0883741	+	0.996087i	$0.471833\pi$
$702$	3555.81	−	10943.7i	0.191176	−	0.588379i
$703$	−1387.20			−0.0744231
$704$	−27264.5	−	2306.62i	−1.45962	−	0.123486i
$705$	−4282.19			−0.228761
$706$	−1054.49	+	3245.38i	−0.0562127	+	0.173005i
$707$	−1093.27	+	794.307i	−0.0581565	+	0.0422531i
$708$	−5873.84	−	4267.60i	−0.311797	−	0.226534i
$709$	4345.14	+	13373.0i	0.230162	+	0.708367i	0.997726	+	0.0673949i	$0.0214687\pi$
$709$	4345.14	+	13373.0i	0.230162	+	0.708367i	−0.767564	+	0.640972i	$0.778531\pi$
$710$	6252.23	+	19242.4i	0.330482	+	1.01712i
$711$	−369.826	−	268.694i	−0.0195071	−	0.0141727i
$712$	23260.8	−	16900.0i	1.22435	−	0.889541i
$713$	−170.470	+	524.654i	−0.00895395	+	0.0275574i
$714$	−6327.22			−0.331639
$715$	−4512.48	−	19293.3i	−0.236024	−	1.00913i
$716$	−50951.0			−2.65940
$717$	2062.66	−	6348.20i	0.107436	−	0.330653i
$718$	31163.8	−	22641.8i	1.61981	−	1.17686i
$719$	9313.93	+	6766.96i	0.483103	+	0.350995i	0.802526	−	0.596618i	$-0.203489\pi$
$719$	9313.93	+	6766.96i	0.483103	+	0.350995i	−0.319423	+	0.947612i	$0.603489\pi$
$720$	439.892	+	1353.85i	0.0227692	+	0.0700763i
$721$	−2121.16	−	6528.25i	−0.109565	−	0.337205i
$722$	45580.7	+	33116.3i	2.34950	+	1.70701i
$723$	−1809.73	+	1314.85i	−0.0930907	+	0.0676344i
$724$	3560.17	−	10957.1i	0.182752	−	0.562454i
$725$	13123.4			0.672261
$726$	13178.8	+	13491.4i	0.673705	+	0.689687i
$727$	23297.3			1.18851			0.594257	−	0.804275i	$-0.297446\pi$
$727$	23297.3			1.18851			0.594257	+	0.804275i	$0.297446\pi$
$728$	8275.70	−	25470.0i	0.421316	−	1.29668i
$729$	−589.773	+	428.495i	−0.0299636	+	0.0217698i
$730$	−24036.3	−	17463.4i	−1.21866	−	0.885408i
$731$	3824.34	+	11770.1i	0.193500	+	0.595531i
$732$	3012.00	+	9269.99i	0.152086	+	0.468072i
$733$	10078.1	+	7322.20i	0.507837	+	0.368965i	0.812003	−	0.583654i	$-0.198377\pi$
$733$	10078.1	+	7322.20i	0.507837	+	0.368965i	−0.304165	+	0.952619i	$0.598377\pi$
$734$	45565.5	−	33105.3i	2.29136	−	1.66477i
$735$	−1360.39	+	4186.85i	−0.0682704	+	0.210115i
$736$	−8167.76			−0.409059
$737$	−3013.31	−	12883.5i	−0.150606	−	0.643922i
$738$	−16067.0			−0.801403
$739$	6903.68	−	21247.4i	0.343648	−	1.05764i	−0.618655	−	0.785663i	$-0.712322\pi$
$739$	6903.68	−	21247.4i	0.343648	−	1.05764i	0.962303	−	0.271978i	$-0.0876778\pi$
$740$	−705.194	+	512.354i	−0.0350317	+	0.0254520i
$741$	−30016.7	−	21808.4i	−1.48811	−	1.08118i
$742$	3228.61	+	9936.63i	0.159738	+	0.491624i
$743$	10596.5	+	32612.5i	0.523212	+	1.61028i	0.767825	+	0.640659i	$0.221339\pi$
$743$	10596.5	+	32612.5i	0.523212	+	1.61028i	−0.244614	+	0.969621i	$0.578661\pi$
$744$	558.239	+	405.584i	0.0275081	+	0.0199858i
$745$	1885.60	−	1369.97i	0.0927287	−	0.0673714i
$746$	8058.18	−	24800.5i	0.395484	−	1.21717i
$747$	−11014.6			−0.539495
$748$	23320.7	+	1972.97i	1.13996	+	0.0964425i
$749$	9653.65			0.470944
$750$	5634.09	−	17339.9i	0.274304	−	0.844220i
$751$	15565.4	−	11308.9i	0.756312	−	0.549493i	−0.141465	−	0.989943i	$-0.545181\pi$
$751$	15565.4	−	11308.9i	0.756312	−	0.549493i	0.897777	+	0.440450i	$0.145181\pi$
$752$	5041.52	+	3662.88i	0.244475	+	0.177622i
$753$	−1640.09	−	5047.68i	−0.0793734	−	0.244286i
$754$	−19469.3	−	59920.4i	−0.940360	−	2.89413i
$755$	−3305.31	−	2401.45i	−0.159328	−	0.115759i
$756$	−3113.12	+	2261.81i	−0.149766	+	0.108811i
$757$	−4457.45	+	13718.6i	−0.214014	+	0.658668i	0.785208	+	0.619232i	$0.212556\pi$
$757$	−4457.45	+	13718.6i	−0.214014	+	0.658668i	−0.999222	+	0.0394359i	$0.987444\pi$
$758$	−31898.6			−1.52851
$759$	5918.40	+	5115.08i	0.283036	+	0.244619i
$760$	24585.2			1.17342
$761$	−7973.32	+	24539.4i	−0.379806	+	1.16892i	0.560372	+	0.828241i	$0.310658\pi$
$761$	−7973.32	+	24539.4i	−0.379806	+	1.16892i	−0.940178	+	0.340683i	$0.889342\pi$
$762$	11838.8	−	8601.41i	0.562828	−	0.408919i
$763$	1900.75	+	1380.98i	0.0901859	+	0.0655239i
$764$	−10036.8	−	30890.0i	−0.475284	−	1.46277i
$765$	750.490	+	2309.77i	0.0354693	+	0.109163i
$766$	−20307.2	−	14754.1i	−0.957871	−	0.695934i
$767$	12346.4	−	8970.17i	0.581228	−	0.422287i
$768$	−5945.71	+	18299.0i	−0.279359	+	0.859778i
$769$	−1832.44			−0.0859291			−0.0429646	−	0.999077i	$-0.513680\pi$
$769$	−1832.44			−0.0859291			−0.0429646	+	0.999077i	$0.513680\pi$
$770$	−4009.19	+	9520.83i	−0.187638	+	0.445593i
$771$	−7203.60			−0.336487
$772$	−21143.0	+	65071.4i	−0.985689	+	3.03364i
$773$	−30476.8	+	22142.7i	−1.41808	+	1.03030i	−0.425995	+	0.904725i	$0.640076\pi$
$773$	−30476.8	+	22142.7i	−1.41808	+	1.03030i	−0.992085	+	0.125570i	$0.959924\pi$
$774$	9493.50	+	6897.43i	0.440875	+	0.320314i
$775$	−211.730	−	651.638i	−0.00981364	−	0.0302033i
$776$	−2349.58	−	7231.27i	−0.108692	−	0.334520i
$777$	−244.651	−	177.750i	−0.0112958	−	0.00820686i
$778$	−434.823	+	315.918i	−0.0200375	+	0.0145581i
$779$	−16009.1	+	49271.0i	−0.736311	+	2.26613i
$780$	−23314.0			−1.07022
$781$	22217.0	−	13436.1i	1.01791	−	0.615598i
$782$	15134.4			0.692079
$783$	−1233.45	+	3796.18i	−0.0562963	+	0.173262i
$784$	5182.95	−	3765.63i	0.236104	−	0.171539i
$785$	17575.7	+	12769.5i	0.799113	+	0.580590i
$786$	−5981.98	−	18410.6i	−0.271463	−	0.835478i
$787$	9808.52	+	30187.5i	0.444264	+	1.36730i	0.883289	+	0.468830i	$0.155324\pi$
$787$	9808.52	+	30187.5i	0.444264	+	1.36730i	−0.439024	+	0.898475i	$0.644676\pi$
$788$	23258.6	+	16898.3i	1.05146	+	0.763932i
$789$	14560.1	−	10578.5i	0.656976	−	0.477321i
$790$	−446.223	+	1373.33i	−0.0200961	+	0.0618493i
$791$	5130.96			0.230639
$792$	8372.53	−	5063.44i	0.375637	−	0.227173i
$793$	−20487.6			−0.917446
$794$	5888.29	−	18122.3i	0.263184	−	0.809996i
$795$	3244.44	−	2357.22i	0.144740	−	0.105160i
$796$	−37625.6	−	27336.6i	−1.67538	−	1.21724i
$797$	−9351.45	−	28780.8i	−0.415615	−	1.27913i	−0.911699	−	0.410858i	$-0.865229\pi$
$797$	−9351.45	−	28780.8i	−0.415615	−	1.27913i	0.496084	−	0.868275i	$-0.334771\pi$
$798$	5977.77	+	18397.7i	0.265177	+	0.816130i
$799$	8601.22	+	6249.15i	0.380838	+	0.276695i
$800$	8207.19	−	5962.87i	0.362710	−	0.263524i
$801$	2683.38	−	8258.60i	0.118368	−	0.364299i
$802$	−47363.4			−2.08536
$803$	−14796.5	+	35138.1i	−0.650260	+	1.54421i
$804$	−15568.4			−0.682906
$805$	−1324.07	+	4075.06i	−0.0579717	+	0.178419i
$806$	−2661.22	+	1933.49i	−0.116300	+	0.0844967i
$807$	−1896.64	−	1377.99i	−0.0827322	−	0.0601085i
$808$	−1249.40	−	3845.25i	−0.0543980	−	0.167420i
$809$	−2434.74	−	7493.36i	−0.105811	−	0.325652i	0.884109	−	0.467281i	$-0.154766\pi$
$809$	−2434.74	−	7493.36i	−0.105811	−	0.325652i	−0.989920	+	0.141628i	$0.954766\pi$
$810$	1863.01	+	1353.55i	0.0808141	+	0.0587149i
$811$	−33536.1	+	24365.4i	−1.45205	+	1.05498i	−0.466704	+	0.884413i	$0.654559\pi$
$811$	−33536.1	+	24365.4i	−1.45205	+	1.05498i	−0.985347	+	0.170564i	$0.945441\pi$
$812$	−6510.78	+	20038.1i	−0.281384	+	0.866010i
$813$	1349.67			0.0582227
$814$	1319.46	+	1140.37i	0.0568146	+	0.0491030i
$815$	5536.07			0.237939
$816$	1092.15	−	3361.30i	0.0468541	−	0.144202i
$817$	30610.9	−	22240.1i	1.31082	−	0.952366i
$818$	1125.96	+	818.056i	0.0481274	+	0.0349666i
$819$	−2499.41	−	7692.39i	−0.106638	−	0.328198i
$820$	10059.5	+	30960.1i	0.428408	+	1.31850i
$821$	14844.6	+	10785.2i	0.631034	+	0.458473i	0.856758	−	0.515718i	$-0.172475\pi$
$821$	14844.6	+	10785.2i	0.631034	+	0.458473i	−0.225724	+	0.974191i	$0.572475\pi$
$822$	17332.0	−	12592.5i	0.735431	−	0.534322i
$823$	−8201.31	+	25241.0i	−0.347363	+	1.06907i	0.612944	+	0.790126i	$0.289985\pi$
$823$	−8201.31	+	25241.0i	−0.347363	+	1.06907i	−0.960307	+	0.278946i	$0.910015\pi$
$824$	20537.1			0.868256
$825$	−9681.23	−	819.048i	−0.408554	−	0.0345643i
$826$	−7956.70			−0.335168
$827$	−2363.74	+	7274.85i	−0.0993898	+	0.305890i	−0.988373	−	0.152050i	$-0.951413\pi$
$827$	−2363.74	+	7274.85i	−0.0993898	+	0.305890i	0.888983	+	0.457940i	$0.151413\pi$
$828$	7446.43	−	5410.15i	0.312538	−	0.227072i
$829$	23147.8	+	16817.9i	0.969791	+	0.704595i	0.955404	−	0.295302i	$-0.0954202\pi$
$829$	23147.8	+	16817.9i	0.969791	+	0.704595i	0.0143874	+	0.999896i	$0.495420\pi$
$830$	10751.8	+	33090.6i	0.449638	+	1.38384i
$831$	−3910.30	−	12034.7i	−0.163233	−	0.502380i
$832$	−54747.7	−	39776.6i	−2.28129	−	1.65746i
$833$	8842.52	−	6424.46i	0.367797	−	0.267220i
$834$	4590.28	−	14127.4i	0.190585	−	0.586562i
$835$	−13896.2			−0.575926
$836$	−16295.9	−	69673.8i	−0.674171	−	2.88244i
$837$	208.399			0.00860611
$838$	1597.87	−	4917.74i	0.0658682	−	0.202721i
$839$	−10416.9	+	7568.35i	−0.428644	+	0.311428i	−0.781107	−	0.624398i	$-0.785344\pi$
$839$	−10416.9	+	7568.35i	−0.428644	+	0.311428i	0.352462	+	0.935826i	$0.385344\pi$
$840$	4335.92	+	3150.23i	0.178099	+	0.129397i
$841$	−783.022	−	2409.89i	−0.0321055	−	0.0988107i
$842$	−19077.2	−	58713.6i	−0.780812	−	2.40309i
$843$	7429.64	+	5397.95i	0.303548	+	0.220540i
$844$	3571.49	−	2594.84i	0.145659	−	0.105827i
$845$	11056.7	−	34029.0i	0.450133	−	1.38537i
$846$	10080.8			0.409677
$847$	13068.4	+	2227.16i	0.530148	+	0.0903495i
$848$	−5836.07			−0.236334
$849$	−5401.97	+	16625.5i	−0.218369	+	0.672070i
$850$	−15207.5	+	11048.9i	−0.613661	+	0.445851i
$851$	585.195	+	425.169i	0.0235725	+	0.0171264i
$852$	−9440.54	−	29055.0i	−0.379610	−	1.16832i
$853$	−196.513	−	604.804i	−0.00788800	−	0.0242768i	0.947035	−	0.321130i	$-0.104063\pi$
$853$	−196.513	−	604.804i	−0.00788800	−	0.0242768i	−0.954923	+	0.296853i	$0.904063\pi$
$854$	8641.70	+	6278.56i	0.346268	+	0.251578i
$855$	6007.09	−	4364.41i	0.240279	−	0.174573i
$856$	−8925.29	+	27469.2i	−0.356379	+	1.09682i
$857$	−7820.86			−0.311733			−0.155867	−	0.987778i	$-0.549817\pi$
$857$	−7820.86			−0.311733			−0.155867	+	0.987778i	$0.549817\pi$
$858$	10623.0	+	45419.0i	0.422684	+	1.80720i
$859$	119.816			0.00475910			0.00237955	−	0.999997i	$-0.499243\pi$
$859$	119.816			0.00475910			0.00237955	+	0.999997i	$0.499243\pi$
$860$	7347.02	−	22611.8i	0.291315	−	0.896577i
$861$	−9136.76	+	6638.24i	−0.361649	+	0.262754i
$862$	−5630.09	−	4090.50i	−0.222461	−	0.161628i
$863$	−9940.00	−	30592.2i	−0.392076	−	1.20669i	−0.931215	−	0.364469i	$-0.881250\pi$
$863$	−9940.00	−	30592.2i	−0.392076	−	1.20669i	0.539139	−	0.842217i	$-0.318750\pi$
$864$	953.485	+	2934.52i	0.0375442	+	0.115549i
$865$	2232.31	+	1621.87i	0.0877465	+	0.0637515i
$866$	−15516.1	+	11273.1i	−0.608843	+	0.442351i
$867$	−2691.31	+	8282.99i	−0.105423	+	0.324458i
$868$	1100.03			0.0430156
$869$	1846.45	+	156.213i	0.0720788	+	0.00609799i
$870$	12608.7			0.491350
$871$	10112.2	−	31122.0i	0.393384	−	1.21071i
$872$	−5686.88	+	4131.76i	−0.220851	+	0.160458i
$873$	−1857.80	−	1349.77i	−0.0720240	−	0.0523285i
$874$	−14298.6	−	44006.4i	−0.553382	−	1.70313i
$875$	−3960.25	−	12188.4i	−0.153007	−	0.470906i
$876$	36293.5	+	26368.8i	1.39982	+	1.01703i
$877$	−6320.86	+	4592.37i	−0.243375	+	0.176822i	−0.702786	−	0.711402i	$-0.748061\pi$
$877$	−6320.86	+	4592.37i	−0.243375	+	0.176822i	0.459410	+	0.888224i	$0.348061\pi$
$878$	−17123.8	+	52701.6i	−0.658201	+	2.02573i
$879$	−1373.84			−0.0527171
$880$	−4365.85	−	3773.26i	−0.167242	−	0.144542i
$881$	−11759.7			−0.449709			−0.224855	−	0.974392i	$-0.572191\pi$
$881$	−11759.7			−0.449709			−0.224855	+	0.974392i	$0.572191\pi$
$882$	3202.54	−	9856.42i	0.122262	−	0.376284i
$883$	7639.22	−	5550.22i	0.291144	−	0.211529i	−0.432619	−	0.901577i	$-0.642411\pi$
$883$	7639.22	−	5550.22i	0.291144	−	0.211529i	0.723764	+	0.690048i	$0.242411\pi$
$884$	46828.5	+	34022.9i	1.78169	+	1.29447i
$885$	943.768	+	2904.62i	0.0358468	+	0.110325i
$886$	1333.04	+	4102.66i	0.0505465	+	0.155566i
$887$	−30976.4	−	22505.6i	−1.17259	−	0.851934i	−0.181270	−	0.983433i	$-0.558021\pi$
$887$	−30976.4	−	22505.6i	−1.17259	−	0.851934i	−0.991316	+	0.131499i	$0.958021\pi$
$888$	731.975	−	531.811i	0.0276616	−	0.0200973i
$889$	3178.57	−	9782.64i	0.119917	−	0.369066i
$890$	−27430.2			−1.03311
$891$	1146.85	−	2723.49i	0.0431213	−	0.102402i
$892$	66237.6			2.48632
$893$	10044.5	−	30913.8i	0.376402	−	1.15845i
$894$	−4438.95	+	3225.09i	−0.166063	+	0.120652i
$895$	17339.2	+	12597.6i	0.647581	+	0.470495i
$896$	8089.05	+	24895.5i	0.301603	+	0.928239i
$897$	5978.47	+	18399.8i	0.222537	+	0.684897i
$898$	55588.3	+	40387.3i	2.06571	+	1.50083i
$899$	923.135	−	670.697i	0.0342473	−	0.0248821i
$900$	−3532.70	+	10872.5i	−0.130841	+	0.402686i
$901$	−9956.78			−0.368156
$902$	55731.1	−	33704.4i	2.05725	−	1.24416i
$903$	8248.37			0.303974
$904$	−4743.83	+	14600.0i	−0.174533	+	0.537156i
$905$	−3920.70	+	2848.56i	−0.144010	+	0.104629i
$906$	7781.16	+	5653.34i	0.285333	+	0.207307i
$907$	12422.6	+	38232.9i	0.454782	+	1.39967i	0.871391	+	0.490588i	$0.163218\pi$
$907$	12422.6	+	38232.9i	0.454782	+	1.39967i	−0.416610	+	0.909085i	$0.636782\pi$
$908$	11441.3	+	35212.8i	0.418166	+	1.28698i
$909$	−987.889	−	717.743i	−0.0360464	−	0.0261893i
$910$	−20670.1	+	15017.7i	−0.752974	+	0.547068i
$911$	6470.55	−	19914.3i	0.235323	−	0.724249i	−0.761756	−	0.647864i	$-0.775662\pi$
$911$	6470.55	−	19914.3i	0.235323	−	0.724249i	0.997078	−	0.0763845i	$-0.0243376\pi$
$912$	−10805.5			−0.392331
$913$	38205.9	−	23105.7i	1.38492	−	0.837553i
$914$	−8550.45			−0.309435
$915$	1266.99	−	3899.40i	0.0457764	−	0.140885i
$916$	−25315.3	+	18392.6i	−0.913145	+	0.663439i
$917$	−11008.3	−	7997.98i	−0.396429	−	0.288022i
$918$	−1766.76	−	5437.51i	−0.0635203	−	0.195495i
$919$	−14412.6	−	44357.6i	−0.517333	−	1.59219i	−0.778996	−	0.627029i	$-0.784271\pi$
$919$	−14412.6	−	44357.6i	−0.517333	−	1.59219i	0.261663	−	0.965159i	$-0.415729\pi$
$920$	−10371.3	−	7535.20i	−0.371665	−	0.270031i
$921$	−9566.51	+	6950.48i	−0.342266	+	0.248671i
$922$	−22289.2	+	68599.2i	−0.796157	+	2.45032i
$923$	64214.3			2.28997
$924$	6053.67	−	14376.0i	0.215531	−	0.511834i
$925$	−898.413			−0.0319348
$926$	18856.7	−	58035.0i	0.669190	−	2.05956i
$927$	5017.98	−	3645.78i	0.177791	−	0.129173i
$928$	13667.9	+	9930.31i	0.483481	+	0.351270i
$929$	15712.4	+	48357.8i	0.554906	+	1.70782i	0.696192	+	0.717856i	$0.254876\pi$
$929$	15712.4	+	48357.8i	0.554906	+	1.70782i	−0.141286	+	0.989969i	$0.545124\pi$
$930$	−203.426	−	626.082i	−0.00717270	−	0.0220753i
$931$	−27034.6	−	19641.8i	−0.951690	−	0.691443i
$932$	−77155.7	+	56056.9i	−2.71171	+	1.97018i
$933$	2543.91	−	7829.34i	0.0892645	−	0.274728i
$934$	17126.4			0.599993
$935$	−7448.48	−	6437.48i	−0.260525	−	0.225164i
$936$	24199.3			0.845064
$937$	5230.89	−	16099.0i	0.182375	−	0.561293i	−0.817518	−	0.575903i	$-0.804651\pi$
$937$	5230.89	−	16099.0i	0.182375	−	0.561293i	0.999893	+	0.0146096i	$0.00465055\pi$
$938$	−13802.9	+	10028.4i	−0.480470	+	0.349082i
$939$	4772.03	+	3467.08i	0.165846	+	0.120494i
$940$	−6311.60	−	19425.1i	−0.219002	−	0.674018i
$941$	−6371.09	−	19608.2i	−0.220714	−	0.679287i	−0.998698	−	0.0510038i	$-0.983758\pi$
$941$	−6371.09	−	19608.2i	−0.220714	−	0.679287i	0.777985	−	0.628283i	$-0.216242\pi$
$942$	−41375.6	−	30061.1i	−1.43109	−	1.03975i
$943$	21854.7	−	15878.4i	0.754705	−	0.548325i
$944$	1373.42	−	4226.95i	0.0473528	−	0.145737i
$945$	1618.66			0.0557197
$946$	−47398.7	−	4010.01i	−1.62903	−	0.137819i
$947$	−46642.8			−1.60052			−0.800258	−	0.599656i	$-0.795304\pi$
$947$	−46642.8			−1.60052			−0.800258	+	0.599656i	$0.795304\pi$
$948$	673.773	−	2073.66i	0.0230835	−	0.0710436i
$949$	−76286.2	+	55425.2i	−2.60944	+	1.89587i
$950$	46494.4	+	33780.2i	1.58787	+	1.15366i
$951$	5916.09	+	18207.8i	0.201727	+	0.620851i
$952$	−4111.90	−	12655.1i	−0.139987	−	0.430835i
$953$	12290.8	+	8929.79i	0.417773	+	0.303530i	0.776741	−	0.629820i	$-0.216871\pi$
$953$	12290.8	+	8929.79i	0.417773	+	0.303530i	−0.358968	+	0.933350i	$0.616871\pi$
$954$	−7637.85	+	5549.23i	−0.259208	+	0.188326i
$955$	−4221.93	+	12993.8i	−0.143056	+	0.440281i
$956$	31837.3			1.07708
$957$	−3684.94	−	15755.1i	−0.124469	−	0.532174i
$958$	−35551.5			−1.19897
$959$	4653.43	−	14321.8i	0.156691	−	0.482247i
$960$	10956.4	−	7960.28i	0.368350	−	0.267622i
$961$	24053.2	+	17475.7i	0.807399	+	0.586610i
$962$	1332.85	+	4102.10i	0.0446704	+	0.137481i
$963$	2695.60	+	8296.20i	0.0902019	+	0.277613i
$964$	−8631.88	−	6271.43i	−0.288396	−	0.209532i
$965$	23284.1	−	16916.9i	0.776727	−	0.564325i
$966$	3117.03	−	9593.24i	0.103819	−	0.319521i
$967$	−31663.0			−1.05296			−0.526481	−	0.850187i	$-0.676489\pi$
$967$	−31663.0			−1.05296			−0.526481	+	0.850187i	$0.676489\pi$
$968$	−18419.7	+	35126.7i	−0.611603	+	1.16634i
$969$	−18435.0			−0.611164
$970$	−2241.57	+	6898.85i	−0.0741985	+	0.228359i
$971$	18374.8	−	13350.1i	0.607287	−	0.441220i	−0.241171	−	0.970483i	$-0.577531\pi$
$971$	18374.8	−	13350.1i	0.607287	−	0.441220i	0.848458	+	0.529263i	$0.177531\pi$
$972$	−2813.05	−	2043.80i	−0.0928276	−	0.0674432i
$973$	−3226.55	−	9930.29i	−0.106309	−	0.327184i
$974$	16158.0	+	49729.3i	0.531557	+	1.63596i
$975$	−19440.1	−	14124.1i	−0.638546	−	0.463931i
$976$	−4827.11	+	3507.10i	−0.158311	+	0.115020i
$977$	17034.6	−	52427.1i	0.557815	−	1.71678i	−0.130575	−	0.991438i	$-0.541682\pi$
$977$	17034.6	−	52427.1i	0.557815	−	1.71678i	0.688390	−	0.725340i	$-0.258318\pi$
$978$	−13032.7			−0.426113
$979$	8016.61	+	34275.3i	0.261708	+	1.11894i
$980$	−20997.8			−0.684437
$981$	−656.042	+	2019.09i	−0.0213515	+	0.0657131i
$982$	59461.0	−	43200.9i	1.93226	−	1.40387i
$983$	−41726.4	−	30316.0i	−1.35388	−	0.983653i	−0.998808	−	0.0488155i	$-0.984455\pi$
$983$	−41726.4	−	30316.0i	−1.35388	−	0.983653i	−0.355075	−	0.934838i	$-0.615545\pi$
$984$	−10441.6	−	32135.8i	−0.338277	−	1.04111i
$985$	−3737.03	−	11501.4i	−0.120885	−	0.372045i
$986$	−25325.9	−	18400.3i	−0.817991	−	0.594306i
$987$	5732.63	−	4165.00i	0.184875	−	0.134319i
$988$	54686.4	−	168308.i	1.76094	−	5.41961i
$989$	−19729.7			−0.634346
$990$	−9301.54	−	786.925i	−0.298608	−	0.0252628i
$991$	8219.68			0.263478			0.131739	−	0.991284i	$-0.457944\pi$
$991$	8219.68			0.263478			0.131739	+	0.991284i	$0.457944\pi$
$992$	272.572	−	838.891i	0.00872397	−	0.0268496i
$993$	−8134.50	+	5910.06i	−0.259960	+	0.188872i
$994$	−27085.7	−	19678.9i	−0.864293	−	0.627946i
$995$	6045.42	+	18605.9i	0.192616	+	0.592811i
$996$	−16234.6	−	49965.0i	−0.516479	−	1.58956i
$997$	22916.4	+	16649.7i	0.727952	+	0.528888i	0.888915	−	0.458072i	$-0.151460\pi$
$997$	22916.4	+	16649.7i	0.727952	+	0.528888i	−0.160963	+	0.986960i	$0.551460\pi$
$998$	−30727.7	+	22325.0i	−0.974616	+	0.708100i
$999$	84.4410	−	259.883i	0.00267427	−	0.00823056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.e.b.31.1	yes	8
3.2	odd	2		99.4.f.b.64.2		8
11.4	even	5		363.4.a.p.1.1		4
11.5	even	5	inner	33.4.e.b.16.1	✓	8
11.7	odd	10		363.4.a.t.1.4		4
33.5	odd	10		99.4.f.b.82.2		8
33.26	odd	10		1089.4.a.bg.1.4		4
33.29	even	10		1089.4.a.z.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.b.16.1	✓	8	11.5	even	5	inner
33.4.e.b.31.1	yes	8	1.1	even	1	trivial
99.4.f.b.64.2		8	3.2	odd	2
99.4.f.b.82.2		8	33.5	odd	10
363.4.a.p.1.1		4	11.4	even	5
363.4.a.t.1.4		4	11.7	odd	10
1089.4.a.z.1.1		4	33.29	even	10
1089.4.a.bg.1.4		4	33.26	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45957 + 4.49208i) q^{2} +(-2.42705 + 1.76336i) q^{3} +(-11.5763 - 8.41069i) q^{4} +(1.86000 + 5.72450i) q^{5} +(-4.37870 - 13.4762i) q^{6} +(-8.05785 - 5.85437i) q^{7} +(24.1083 - 17.5157i) q^{8} +(2.78115 - 8.55951i) q^{9} +O(q^{10})\)	\(q+(-1.45957 + 4.49208i) q^{2} +(-2.42705 + 1.76336i) q^{3} +(-11.5763 - 8.41069i) q^{4} +(1.86000 + 5.72450i) q^{5} +(-4.37870 - 13.4762i) q^{6} +(-8.05785 - 5.85437i) q^{7} +(24.1083 - 17.5157i) q^{8} +(2.78115 - 8.55951i) q^{9} -28.4297 q^{10} +(8.30870 + 35.5242i) q^{11} +42.9273 q^{12} +(-27.8826 + 85.8139i) q^{13} +(38.0593 - 27.6517i) q^{14} +(-14.6086 - 10.6138i) q^{15} +(8.12031 + 24.9917i) q^{16} +(13.8539 + 42.6379i) q^{17} +(34.3907 + 24.9863i) q^{18} +(110.890 - 80.5660i) q^{19} +(26.6150 - 81.9125i) q^{20} +29.8801 q^{21} +(-171.704 - 14.5265i) q^{22} -71.4719 q^{23} +(-27.6257 + 85.0232i) q^{24} +(71.8169 - 52.1780i) q^{25} +(-344.786 - 250.502i) q^{26} +(8.34346 + 25.6785i) q^{27} +(44.0409 + 135.544i) q^{28} +(119.601 + 86.8950i) q^{29} +(69.0003 - 50.1317i) q^{30} +(2.38514 - 7.34071i) q^{31} +114.279 q^{32} +(-82.8074 - 71.5677i) q^{33} -211.753 q^{34} +(18.5257 - 57.0163i) q^{35} +(-104.187 + 75.6962i) q^{36} +(-8.18776 - 5.94875i) q^{37} +(200.058 + 615.716i) q^{38} +(-83.6479 - 257.442i) q^{39} +(145.110 + 105.429i) q^{40} +(-305.780 + 222.162i) q^{41} +(-43.6120 + 134.224i) q^{42} +276.048 q^{43} +(202.598 - 481.121i) q^{44} +54.1718 q^{45} +(104.318 - 321.057i) q^{46} +(191.854 - 139.390i) q^{47} +(-63.7778 - 46.3373i) q^{48} +(-75.3376 - 231.865i) q^{49} +(129.566 + 398.764i) q^{50} +(-108.810 - 79.0549i) q^{51} +(1044.53 - 758.897i) q^{52} +(-68.6297 + 211.221i) q^{53} -127.528 q^{54} +(-187.904 + 113.638i) q^{55} -296.805 q^{56} +(-127.068 + 391.076i) q^{57} +(-564.905 + 410.427i) q^{58} +(-136.832 - 99.4144i) q^{59} +(79.8449 + 245.737i) q^{60} +(70.1651 + 215.946i) q^{61} +(29.4938 + 21.4285i) q^{62} +(-72.5206 + 52.6893i) q^{63} +(-231.761 + 713.286i) q^{64} -543.103 q^{65} +(442.351 - 267.520i) q^{66} -362.669 q^{67} +(198.237 - 610.110i) q^{68} +(173.466 - 126.030i) q^{69} +(229.082 + 166.438i) q^{70} +(-219.919 - 676.841i) q^{71} +(-82.8771 - 255.070i) q^{72} +(845.463 + 614.265i) q^{73} +(38.6729 - 28.0975i) q^{74} +(-82.2948 + 253.277i) q^{75} -1961.31 q^{76} +(141.021 - 334.890i) q^{77} +1278.54 q^{78} +(15.6957 - 48.3063i) q^{79} +(-127.961 + 92.9694i) q^{80} +(-65.5304 - 47.6106i) q^{81} +(-551.665 - 1697.85i) q^{82} +(-378.188 - 1163.94i) q^{83} +(-345.902 - 251.313i) q^{84} +(-218.312 + 158.613i) q^{85} +(-402.911 + 1240.03i) q^{86} -443.504 q^{87} +(822.541 + 710.895i) q^{88} +964.845 q^{89} +(-79.0673 + 243.344i) q^{90} +(727.060 - 528.240i) q^{91} +(827.381 + 601.128i) q^{92} +(7.15542 + 22.0221i) q^{93} +(346.128 + 1065.27i) q^{94} +(667.455 + 484.934i) q^{95} +(-277.362 + 201.515i) q^{96} +(78.8462 - 242.664i) q^{97} +1151.52 q^{98} +(327.177 + 27.6797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9} + 8 q^{10} - 87 q^{11} - 18 q^{12} + 171 q^{13} + 12 q^{14} - 63 q^{15} + 44 q^{16} + 36 q^{17} + 81 q^{18} + 324 q^{19} - 87 q^{20} - 66 q^{21} - 521 q^{22} - 84 q^{23} + 18 q^{24} + 263 q^{25} - 774 q^{26} - 54 q^{27} + 387 q^{28} + 393 q^{29} + 204 q^{30} + 15 q^{31} + 102 q^{32} - 216 q^{33} - 712 q^{34} + 1002 q^{35} - 144 q^{36} - 747 q^{37} - 36 q^{38} + 513 q^{39} + 41 q^{40} + 159 q^{41} + 396 q^{42} - 644 q^{43} + 219 q^{44} + 216 q^{45} + 753 q^{46} - 351 q^{47} - 423 q^{48} - 1967 q^{49} + 330 q^{50} + 63 q^{51} + 2871 q^{52} - 531 q^{53} - 162 q^{54} - 716 q^{55} + 1470 q^{56} - 453 q^{57} - 1205 q^{58} - 1002 q^{59} - 261 q^{60} + 1449 q^{61} + 99 q^{62} + 27 q^{63} - 1118 q^{64} - 954 q^{65} + 897 q^{66} - 518 q^{67} + 873 q^{68} + 693 q^{69} + 26 q^{70} + 429 q^{71} + 54 q^{72} + 2547 q^{73} + 468 q^{74} - 231 q^{75} - 2276 q^{76} - 2697 q^{77} + 1638 q^{78} + 2805 q^{79} - 1620 q^{80} - 162 q^{81} - 1631 q^{82} - 2553 q^{83} - 1509 q^{84} - 197 q^{85} - 1713 q^{86} - 3906 q^{87} + 2866 q^{88} + 1788 q^{89} - 648 q^{90} + 2885 q^{91} + 423 q^{92} + 45 q^{93} + 1159 q^{94} + 3009 q^{95} - 504 q^{96} + 9 q^{97} + 5550 q^{98} + 27 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9 + 8 * q^10 - 87 * q^11 - 18 * q^12 + 171 * q^13 + 12 * q^14 - 63 * q^15 + 44 * q^16 + 36 * q^17 + 81 * q^18 + 324 * q^19 - 87 * q^20 - 66 * q^21 - 521 * q^22 - 84 * q^23 + 18 * q^24 + 263 * q^25 - 774 * q^26 - 54 * q^27 + 387 * q^28 + 393 * q^29 + 204 * q^30 + 15 * q^31 + 102 * q^32 - 216 * q^33 - 712 * q^34 + 1002 * q^35 - 144 * q^36 - 747 * q^37 - 36 * q^38 + 513 * q^39 + 41 * q^40 + 159 * q^41 + 396 * q^42 - 644 * q^43 + 219 * q^44 + 216 * q^45 + 753 * q^46 - 351 * q^47 - 423 * q^48 - 1967 * q^49 + 330 * q^50 + 63 * q^51 + 2871 * q^52 - 531 * q^53 - 162 * q^54 - 716 * q^55 + 1470 * q^56 - 453 * q^57 - 1205 * q^58 - 1002 * q^59 - 261 * q^60 + 1449 * q^61 + 99 * q^62 + 27 * q^63 - 1118 * q^64 - 954 * q^65 + 897 * q^66 - 518 * q^67 + 873 * q^68 + 693 * q^69 + 26 * q^70 + 429 * q^71 + 54 * q^72 + 2547 * q^73 + 468 * q^74 - 231 * q^75 - 2276 * q^76 - 2697 * q^77 + 1638 * q^78 + 2805 * q^79 - 1620 * q^80 - 162 * q^81 - 1631 * q^82 - 2553 * q^83 - 1509 * q^84 - 197 * q^85 - 1713 * q^86 - 3906 * q^87 + 2866 * q^88 + 1788 * q^89 - 648 * q^90 + 2885 * q^91 + 423 * q^92 + 45 * q^93 + 1159 * q^94 + 3009 * q^95 - 504 * q^96 + 9 * q^97 + 5550 * q^98 + 27 * q^99

Introduction

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