LMFDB - Embedded newform 201.4.e.a.163.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

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("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.4
Character	$\chi$	$=$	201.163
Dual form			201.4.e.a.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00589 + 3.47431i) q^{2} +3.00000 q^{3} +(-4.04720 - 7.00996i) q^{4} +19.8930 q^{5} +(-6.01767 + 10.4229i) q^{6} +(-14.1596 - 24.5251i) q^{7} +0.378714 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(-2.00589 + 3.47431i) q^{2} +3.00000 q^{3} +(-4.04720 - 7.00996i) q^{4} +19.8930 q^{5} +(-6.01767 + 10.4229i) q^{6} +(-14.1596 - 24.5251i) q^{7} +0.378714 q^{8} +9.00000 q^{9} +(-39.9031 + 69.1143i) q^{10} +(24.4131 + 42.2847i) q^{11} +(-12.1416 - 21.0299i) q^{12} +(32.8838 - 56.9564i) q^{13} +113.610 q^{14} +59.6789 q^{15} +(31.6179 - 54.7639i) q^{16} +(16.2993 - 28.2311i) q^{17} +(-18.0530 + 31.2688i) q^{18} +(-12.0080 + 20.7984i) q^{19} +(-80.5108 - 139.449i) q^{20} +(-42.4787 - 73.5753i) q^{21} -195.880 q^{22} +(73.9812 - 128.139i) q^{23} +1.13614 q^{24} +270.730 q^{25} +(131.923 + 228.497i) q^{26} +27.0000 q^{27} +(-114.613 + 198.516i) q^{28} +(9.06761 + 15.7056i) q^{29} +(-119.709 + 207.343i) q^{30} +(97.8998 + 169.567i) q^{31} +(128.359 + 222.325i) q^{32} +(73.2393 + 126.854i) q^{33} +(65.3891 + 113.257i) q^{34} +(-281.676 - 487.877i) q^{35} +(-36.4248 - 63.0896i) q^{36} +(-148.392 + 257.023i) q^{37} +(-48.1733 - 83.4387i) q^{38} +(98.6514 - 170.869i) q^{39} +7.53376 q^{40} +(159.947 + 277.036i) q^{41} +340.831 q^{42} -192.882 q^{43} +(197.609 - 342.270i) q^{44} +179.037 q^{45} +(296.796 + 514.066i) q^{46} +(-177.194 - 306.909i) q^{47} +(94.8538 - 164.292i) q^{48} +(-229.487 + 397.483i) q^{49} +(-543.055 + 940.600i) q^{50} +(48.8978 - 84.6934i) q^{51} -532.349 q^{52} -316.789 q^{53} +(-54.1591 + 93.8063i) q^{54} +(485.649 + 841.169i) q^{55} +(-5.36243 - 9.28801i) q^{56} +(-36.0239 + 62.3952i) q^{57} -72.7546 q^{58} -526.850 q^{59} +(-241.532 - 418.347i) q^{60} +(432.671 - 749.408i) q^{61} -785.506 q^{62} +(-127.436 - 220.726i) q^{63} -524.011 q^{64} +(654.156 - 1133.03i) q^{65} -587.640 q^{66} +(3.05957 + 548.410i) q^{67} -263.865 q^{68} +(221.943 - 384.417i) q^{69} +2260.04 q^{70} +(342.870 + 593.868i) q^{71} +3.40843 q^{72} +(54.0131 - 93.5534i) q^{73} +(-595.318 - 1031.12i) q^{74} +812.191 q^{75} +194.395 q^{76} +(691.358 - 1197.47i) q^{77} +(395.768 + 685.490i) q^{78} +(-365.029 - 632.250i) q^{79} +(628.975 - 1089.42i) q^{80} +81.0000 q^{81} -1283.35 q^{82} +(-164.509 + 284.938i) q^{83} +(-343.840 + 595.548i) q^{84} +(324.241 - 561.601i) q^{85} +(386.901 - 670.132i) q^{86} +(27.2028 + 47.1167i) q^{87} +(9.24559 + 16.0138i) q^{88} +1523.22 q^{89} +(-359.128 + 622.028i) q^{90} -1862.48 q^{91} -1197.67 q^{92} +(293.699 + 508.702i) q^{93} +1421.73 q^{94} +(-238.874 + 413.742i) q^{95} +(385.078 + 666.974i) q^{96} +(-624.942 + 1082.43i) q^{97} +(-920.651 - 1594.61i) q^{98} +(219.718 + 380.563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.00589	+	3.47431i	−0.709190	+	1.22835i	0.255968	+	0.966685i	$0.417606\pi$
$2$	−2.00589	+	3.47431i	−0.709190	+	1.22835i	−0.965158	+	0.261667i	$0.915728\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	−4.04720	−	7.00996i	−0.505900	−	0.876245i
$5$	19.8930			1.77928			0.889641	−	0.456661i	$-0.150955\pi$
$5$	19.8930			1.77928			0.889641	+	0.456661i	$0.150955\pi$
$6$	−6.01767	+	10.4229i	−0.409451	+	0.709190i
$7$	−14.1596	−	24.5251i	−0.764545	−	1.32423i	−0.940487	−	0.339830i	$-0.889630\pi$
$7$	−14.1596	−	24.5251i	−0.764545	−	1.32423i	0.175942	−	0.984401i	$-0.443703\pi$
$8$	0.378714			0.0167370
$9$	9.00000			0.333333
$10$	−39.9031	+	69.1143i	−1.26185	+	2.18558i
$11$	24.4131	+	42.2847i	0.669166	+	1.15903i	0.978138	+	0.207958i	$0.0666819\pi$
$11$	24.4131	+	42.2847i	0.669166	+	1.15903i	−0.308972	+	0.951071i	$0.599985\pi$
$12$	−12.1416	−	21.0299i	−0.292082	−	0.505900i
$13$	32.8838	−	56.9564i	0.701563	−	1.21514i	−0.266354	−	0.963875i	$-0.585819\pi$
$13$	32.8838	−	56.9564i	0.701563	−	1.21514i	0.967918	−	0.251268i	$-0.0808475\pi$
$14$	113.610			2.16883
$15$	59.6789			1.02727
$16$	31.6179	−	54.7639i	0.494030	−	0.855686i
$17$	16.2993	−	28.2311i	0.232538	−	0.402768i	−0.726016	−	0.687678i	$-0.758630\pi$
$17$	16.2993	−	28.2311i	0.232538	−	0.402768i	0.958554	+	0.284910i	$0.0919636\pi$
$18$	−18.0530	+	31.2688i	−0.236397	+	0.409451i
$19$	−12.0080	+	20.7984i	−0.144990	+	0.251131i	−0.929369	−	0.369151i	$-0.879648\pi$
$19$	−12.0080	+	20.7984i	−0.144990	+	0.251131i	0.784379	+	0.620282i	$0.212982\pi$
$20$	−80.5108	−	139.449i	−0.900138	−	1.55909i
$21$	−42.4787	−	73.5753i	−0.441410	−	0.764545i
$22$	−195.880			−1.89826
$23$	73.9812	−	128.139i	0.670702	−	1.16169i	−0.307004	−	0.951708i	$-0.599326\pi$
$23$	73.9812	−	128.139i	0.670702	−	1.16169i	0.977705	−	0.209981i	$-0.0673403\pi$
$24$	1.13614			0.00966310
$25$	270.730			2.16584
$26$	131.923	+	228.497i	0.995083	+	1.72353i
$27$	27.0000			0.192450
$28$	−114.613	+	198.516i	−0.773567	+	1.33986i
$29$	9.06761	+	15.7056i	0.0580625	+	0.100567i	0.893596	−	0.448873i	$-0.148174\pi$
$29$	9.06761	+	15.7056i	0.0580625	+	0.100567i	−0.835533	+	0.549440i	$0.814841\pi$
$30$	−119.709	+	207.343i	−0.728528	+	1.26185i
$31$	97.8998	+	169.567i	0.567204	+	0.982426i	0.996841	+	0.0794245i	$0.0253083\pi$
$31$	97.8998	+	169.567i	0.567204	+	0.982426i	−0.429637	+	0.903002i	$0.641358\pi$
$32$	128.359	+	222.325i	0.709091	+	1.22818i
$33$	73.2393	+	126.854i	0.386343	+	0.669166i
$34$	65.3891	+	113.257i	0.329827	+	0.571278i
$35$	−281.676	−	487.877i	−1.36034	−	2.35618i
$36$	−36.4248	−	63.0896i	−0.168633	−	0.292082i
$37$	−148.392	+	257.023i	−0.659339	+	1.14201i	0.321448	+	0.946927i	$0.395831\pi$
$37$	−148.392	+	257.023i	−0.659339	+	1.14201i	−0.980787	+	0.195082i	$0.937503\pi$
$38$	−48.1733	−	83.4387i	−0.205651	−	0.356198i
$39$	98.6514	−	170.869i	0.405048	−	0.701563i
$40$	7.53376			0.0297798
$41$	159.947	+	277.036i	0.609257	+	1.05526i	0.991363	+	0.131146i	$0.0418656\pi$
$41$	159.947	+	277.036i	0.609257	+	1.05526i	−0.382106	+	0.924118i	$0.624801\pi$
$42$	340.831			1.25217
$43$	−192.882			−0.684053			−0.342026	−	0.939690i	$-0.611113\pi$
$43$	−192.882			−0.684053			−0.342026	+	0.939690i	$0.611113\pi$
$44$	197.609	−	342.270i	0.677062	−	1.17271i
$45$	179.037			0.593094
$46$	296.796	+	514.066i	0.951309	+	1.64772i
$47$	−177.194	−	306.909i	−0.549924	−	0.952496i	−0.998279	−	0.0586407i	$-0.981323\pi$
$47$	−177.194	−	306.909i	−0.549924	−	0.952496i	0.448355	−	0.893855i	$-0.352010\pi$
$48$	94.8538	−	164.292i	0.285229	−	0.494030i
$49$	−229.487	+	397.483i	−0.669058	+	1.15884i
$50$	−543.055	+	940.600i	−1.53599	+	2.66042i
$51$	48.8978	−	84.6934i	0.134256	−	0.232538i
$52$	−532.349			−1.41968
$53$	−316.789			−0.821025			−0.410512	−	0.911855i	$-0.634650\pi$
$53$	−316.789			−0.821025			−0.410512	+	0.911855i	$0.634650\pi$
$54$	−54.1591	+	93.8063i	−0.136484	+	0.236397i
$55$	485.649	+	841.169i	1.19063	+	2.06224i
$56$	−5.36243	−	9.28801i	−0.0127962	−	0.0221636i
$57$	−36.0239	+	62.3952i	−0.0837102	+	0.144990i
$58$	−72.7546			−0.164709
$59$	−526.850			−1.16254			−0.581271	−	0.813710i	$-0.697445\pi$
$59$	−526.850			−1.16254			−0.581271	+	0.813710i	$0.697445\pi$
$60$	−241.532	−	418.347i	−0.519695	−	0.900138i
$61$	432.671	−	749.408i	0.908162	−	1.57298i	0.0915455	−	0.995801i	$-0.470819\pi$
$61$	432.671	−	749.408i	0.908162	−	1.57298i	0.816616	−	0.577181i	$-0.195847\pi$
$62$	−785.506			−1.60902
$63$	−127.436	−	220.726i	−0.254848	−	0.441410i
$64$	−524.011			−1.02346
$65$	654.156	−	1133.03i	1.24828	−	2.16208i
$66$	−587.640			−1.09596
$67$	3.05957	+	548.410i	0.00557890	+	0.999984i
$67$	3.05957	+	548.410i	0.00557890	+	0.999984i
$68$	−263.865			−0.470564
$69$	221.943	−	384.417i	0.387230	−	0.670702i
$70$	2260.04			3.85896
$71$	342.870	+	593.868i	0.573115	+	0.992664i	0.996244	+	0.0865947i	$0.0275985\pi$
$71$	342.870	+	593.868i	0.573115	+	0.992664i	−0.423129	+	0.906070i	$0.639068\pi$
$72$	3.40843			0.00557899
$73$	54.0131	−	93.5534i	0.0865993	−	0.149994i	−0.819472	−	0.573119i	$-0.805733\pi$
$73$	54.0131	−	93.5534i	0.0865993	−	0.149994i	0.906072	+	0.423124i	$0.139067\pi$
$74$	−595.318	−	1031.12i	−0.935193	−	1.61980i
$75$	812.191			1.25045
$76$	194.395			0.293402
$77$	691.358	−	1197.47i	1.02321	−	1.77226i
$78$	395.768	+	685.490i	0.574511	+	0.995083i
$79$	−365.029	−	632.250i	−0.519861	−	0.900426i	−0.999733	−	0.0230875i	$-0.992650\pi$
$79$	−365.029	−	632.250i	−0.519861	−	0.900426i	0.479872	−	0.877338i	$-0.340683\pi$
$80$	628.975	−	1089.42i	0.879019	−	1.52251i
$81$	81.0000			0.111111
$82$	−1283.35			−1.72832
$83$	−164.509	+	284.938i	−0.217557	+	0.376820i	−0.954061	−	0.299614i	$-0.903142\pi$
$83$	−164.509	+	284.938i	−0.217557	+	0.376820i	0.736503	+	0.676434i	$0.236475\pi$
$84$	−343.840	+	595.548i	−0.446619	+	0.773567i
$85$	324.241	−	561.601i	0.413751	−	0.716638i
$86$	386.901	−	670.132i	0.485123	−	0.840258i
$87$	27.2028	+	47.1167i	0.0335224	+	0.0580625i
$88$	9.24559	+	16.0138i	0.0111998	+	0.0193986i
$89$	1523.22			1.81417			0.907086	−	0.420946i	$-0.138302\pi$
$89$	1523.22			1.81417			0.907086	+	0.420946i	$0.138302\pi$
$90$	−359.128	+	622.028i	−0.420616	+	0.728528i
$91$	−1862.48			−2.14551
$92$	−1197.67			−1.35723
$93$	293.699	+	508.702i	0.327475	+	0.567204i
$94$	1421.73			1.56000
$95$	−238.874	+	413.742i	−0.257979	+	0.446832i
$96$	385.078	+	666.974i	0.409394	+	0.709091i
$97$	−624.942	+	1082.43i	−0.654157	+	1.13303i	0.327948	+	0.944696i	$0.393643\pi$
$97$	−624.942	+	1082.43i	−0.654157	+	1.13303i	−0.982104	+	0.188337i	$0.939690\pi$
$98$	−920.651	−	1594.61i	−0.948978	−	1.64368i
$99$	219.718	+	380.563i	0.223055	+	0.386343i
$100$	−1095.70	−	1897.81i	−1.09570	−	1.89781i
$101$	307.224	+	532.128i	0.302673	+	0.524244i	0.976740	−	0.214425i	$-0.0687878\pi$
$101$	307.224	+	532.128i	0.302673	+	0.524244i	−0.674068	+	0.738669i	$0.735454\pi$
$102$	196.167	+	339.772i	0.190426	+	0.329827i
$103$	−175.210	−	303.472i	−0.167611	−	0.290310i	0.769969	−	0.638082i	$-0.220272\pi$
$103$	−175.210	−	303.472i	−0.167611	−	0.290310i	−0.937579	+	0.347771i	$0.886939\pi$
$104$	12.4536	−	21.5702i	0.0117420	−	0.0203378i
$105$	−845.028	−	1463.63i	−0.785393	−	1.36034i
$106$	635.444	−	1100.62i	0.582262	−	1.00851i
$107$	−287.284			−0.259558			−0.129779	−	0.991543i	$-0.541427\pi$
$107$	−287.284			−0.259558			−0.129779	+	0.991543i	$0.541427\pi$
$108$	−109.274	−	189.269i	−0.0973605	−	0.168633i
$109$	−536.172			−0.471156			−0.235578	−	0.971855i	$-0.575698\pi$
$109$	−536.172			−0.471156			−0.235578	+	0.971855i	$0.575698\pi$
$110$	−3896.64			−3.37754
$111$	−445.177	+	771.069i	−0.380670	+	0.659339i
$112$	−1790.79			−1.51083
$113$	−334.133	−	578.735i	−0.278164	−	0.481794i	0.692764	−	0.721164i	$-0.256393\pi$
$113$	−334.133	−	578.735i	−0.278164	−	0.481794i	−0.970929	+	0.239370i	$0.923059\pi$
$114$	−144.520	−	250.316i	−0.118733	−	0.205651i
$115$	1471.71	−	2549.07i	1.19337	−	2.06697i
$116$	73.3969	−	127.127i	0.0587477	−	0.101754i
$117$	295.954	−	512.608i	0.233854	−	0.405048i
$118$	1056.80	−	1830.44i	0.824463	−	1.42801i
$119$	−923.162			−0.711144
$120$	22.6013			0.0171934
$121$	−526.499	+	911.923i	−0.395566	+	0.685141i
$122$	1735.78	+	3006.46i	1.28812	+	2.23109i
$123$	479.841	+	831.109i	0.351755	+	0.609257i
$124$	792.440	−	1372.55i	0.573897	−	0.994019i
$125$	2899.01			2.07436
$126$	1022.49			0.722943
$127$	−263.368	−	456.167i	−0.184017	−	0.318727i	0.759228	−	0.650825i	$-0.225577\pi$
$127$	−263.368	−	456.167i	−0.184017	−	0.318727i	−0.943245	+	0.332098i	$0.892243\pi$
$128$	24.2360	−	41.9781i	0.0167358	−	0.0289873i
$129$	−578.647			−0.394938
$130$	2624.33	+	4545.48i	1.77053	+	3.06665i
$131$	−1761.63			−1.17492			−0.587460	−	0.809253i	$-0.699872\pi$
$131$	−1761.63			−1.17492			−0.587460	+	0.809253i	$0.699872\pi$
$132$	592.828	−	1026.81i	0.390902	−	0.677062i
$133$	680.110			0.443406
$134$	−1911.48	−	1089.42i	−1.23229	−	0.702326i
$135$	537.110			0.342423
$136$	6.17276	−	10.6915i	0.00389199	−	0.00674112i
$137$	−615.823			−0.384038			−0.192019	−	0.981391i	$-0.561504\pi$
$137$	−615.823			−0.384038			−0.192019	+	0.981391i	$0.561504\pi$
$138$	890.389	+	1542.20i	0.549239	+	0.951309i
$139$	−1268.57			−0.774092			−0.387046	−	0.922060i	$-0.626504\pi$
$139$	−1268.57			−0.774092			−0.387046	+	0.922060i	$0.626504\pi$
$140$	−2280.00	+	3949.07i	−1.37639	+	2.38398i
$141$	−531.582	−	920.728i	−0.317499	−	0.549924i
$142$	−2751.04			−1.62579
$143$	3211.18			1.87785
$144$	284.561	−	492.875i	0.164677	−	0.285229i
$145$	180.382	+	312.430i	0.103310	+	0.178937i
$146$	216.689	+	375.316i	0.122831	+	0.212749i
$147$	−688.460	+	1192.45i	−0.386281	+	0.669058i
$148$	2402.29			1.33424
$149$	714.859			0.393044			0.196522	−	0.980499i	$-0.437035\pi$
$149$	714.859			0.393044			0.196522	+	0.980499i	$0.437035\pi$
$150$	−1629.17	+	2821.80i	−0.886806	+	1.53599i
$151$	56.4096	−	97.7043i	0.0304010	−	0.0526561i	−0.850425	−	0.526097i	$-0.823655\pi$
$151$	56.4096	−	97.7043i	0.0304010	−	0.0526561i	0.880826	+	0.473441i	$0.156988\pi$
$152$	−4.54759	+	7.87666i	−0.00242670	+	0.00420317i
$153$	146.693	−	254.080i	0.0775128	−	0.134256i
$154$	2773.58	+	4803.98i	1.45131	+	2.51374i
$155$	1947.52	+	3373.20i	1.00922	+	1.74801i
$156$	−1597.05			−0.819655
$157$	1755.20	−	3040.10i	0.892232	−	1.54539i	0.0550379	−	0.998484i	$-0.482472\pi$
$157$	1755.20	−	3040.10i	0.892232	−	1.54539i	0.837194	−	0.546906i	$-0.184195\pi$
$158$	2928.84			1.47472
$159$	−950.367			−0.474019
$160$	2553.45	+	4422.70i	1.26167	+	2.18528i
$161$	−4190.17			−2.05113
$162$	−162.477	+	281.419i	−0.0787989	+	0.136484i
$163$	400.793	+	694.194i	0.192592	+	0.333580i	0.946109	−	0.323850i	$-0.104977\pi$
$163$	400.793	+	694.194i	0.192592	+	0.333580i	−0.753516	+	0.657429i	$0.771644\pi$
$164$	1294.68	−	2242.44i	0.616446	−	1.06772i
$165$	1456.95	+	2523.51i	0.687413	+	1.19063i
$166$	−659.975	−	1143.11i	−0.308578	−	0.534474i
$167$	−597.367	−	1034.67i	−0.276800	−	0.479432i	0.693787	−	0.720180i	$-0.255941\pi$
$167$	−597.367	−	1034.67i	−0.276800	−	0.479432i	−0.970588	+	0.240747i	$0.922607\pi$
$168$	−16.0873	−	27.8640i	−0.00738787	−	0.0127962i
$169$	−1064.19	−	1843.23i	−0.484382	−	0.838974i
$170$	1300.78	+	2253.02i	0.586856	+	1.01646i
$171$	−108.072	+	187.186i	−0.0483301	+	0.0837102i
$172$	780.633	+	1352.10i	0.346062	+	0.599397i
$173$	707.470	−	1225.37i	0.310913	−	0.538517i	−0.667647	−	0.744478i	$-0.732699\pi$
$173$	707.470	−	1225.37i	0.310913	−	0.538517i	0.978560	+	0.205961i	$0.0660319\pi$
$174$	−218.264			−0.0950950
$175$	−3833.42	−	6639.68i	−1.65588	−	2.86807i
$176$	3087.57			1.32235
$177$	−1580.55			−0.671194
$178$	−3055.42	+	5292.14i	−1.28659	+	2.22844i
$179$	−269.093			−0.112363			−0.0561815	−	0.998421i	$-0.517893\pi$
$179$	−269.093			−0.112363			−0.0561815	+	0.998421i	$0.517893\pi$
$180$	−724.597	−	1255.04i	−0.300046	−	0.519695i
$181$	635.113	+	1100.05i	0.260815	+	0.451745i	0.966459	−	0.256822i	$-0.0826753\pi$
$181$	635.113	+	1100.05i	0.260815	+	0.451745i	−0.705644	+	0.708567i	$0.749342\pi$
$182$	3735.93	−	6470.83i	1.52157	−	2.63544i
$183$	1298.01	−	2248.23i	0.524327	−	0.908162i
$184$	28.0177	−	48.5281i	0.0112255	−	0.0194432i
$185$	−2951.96	+	5112.95i	−1.17315	+	2.03196i
$186$	−2356.52			−0.928969
$187$	1591.66			0.622427
$188$	−1434.28	+	2484.25i	−0.556413	+	0.963736i
$189$	−382.308	−	662.177i	−0.147137	−	0.254848i
$190$	−958.311	−	1659.84i	−0.365911	−	0.633777i
$191$	−190.372	+	329.733i	−0.0721194	+	0.124915i	−0.899830	−	0.436241i	$-0.856310\pi$
$191$	−190.372	+	329.733i	−0.0721194	+	0.124915i	0.827711	+	0.561155i	$0.189643\pi$
$192$	−1572.03			−0.590894
$193$	−1126.88			−0.420284			−0.210142	−	0.977671i	$-0.567393\pi$
$193$	−1126.88			−0.420284			−0.210142	+	0.977671i	$0.567393\pi$
$194$	−2507.13	−	4342.48i	−0.927843	−	1.60707i
$195$	1962.47	−	3399.10i	0.720694	−	1.24828i
$196$	3715.12			1.35391
$197$	−2249.92	−	3896.98i	−0.813708	−	1.40938i	−0.910252	−	0.414055i	$-0.864112\pi$
$197$	−2249.92	−	3896.98i	−0.813708	−	1.40938i	0.0965437	−	0.995329i	$-0.469221\pi$
$198$	−1762.92			−0.632754
$199$	−510.477	+	884.172i	−0.181843	+	0.314961i	−0.942508	−	0.334183i	$-0.891540\pi$
$199$	−510.477	+	884.172i	−0.181843	+	0.314961i	0.760665	+	0.649144i	$0.224873\pi$
$200$	102.529			0.0362496
$201$	9.17872	+	1645.23i	0.00322098	+	0.577341i
$202$	−2465.03			−0.858609
$203$	256.787	−	444.768i	0.0887828	−	0.153776i
$204$	−791.596			−0.271681
$205$	3181.82	+	5511.08i	1.08404	+	1.87761i
$206$	1405.81			0.475471
$207$	665.830	−	1153.25i	0.223567	−	0.387230i
$208$	−2079.44	−	3601.69i	−0.693187	−	1.20064i
$209$	−1172.61			−0.388090
$210$	6780.13			2.22797
$211$	−2262.19	+	3918.22i	−0.738083	+	1.27840i	0.215275	+	0.976553i	$0.430935\pi$
$211$	−2262.19	+	3918.22i	−0.738083	+	1.27840i	−0.953358	+	0.301843i	$0.902398\pi$
$212$	1282.11	+	2220.68i	0.415357	+	0.719419i
$213$	1028.61	+	1781.60i	0.330888	+	0.573115i
$214$	576.260	−	998.111i	0.184076	−	0.318829i
$215$	−3837.00			−1.21712
$216$	10.2253			0.00322103
$217$	2772.44	−	4802.00i	0.867306	−	1.50222i
$218$	1075.50	−	1862.83i	0.334139	−	0.578745i
$219$	162.039	−	280.660i	0.0499981	−	0.0865993i
$220$	3931.04	−	6808.76i	1.20468	−	2.08657i
$221$	−1071.96	−	1856.69i	−0.326281	−	0.565135i
$222$	−1785.95	−	3093.36i	−0.539934	−	0.935193i
$223$	2086.56			0.626576			0.313288	−	0.949658i	$-0.398570\pi$
$223$	2086.56			0.626576			0.313288	+	0.949658i	$0.398570\pi$
$224$	3635.02	−	6296.04i	1.08426	−	1.87800i
$225$	2436.57			0.721947
$226$	2680.93			0.789085
$227$	2939.66	+	5091.64i	0.859524	+	1.48874i	0.872383	+	0.488823i	$0.162573\pi$
$227$	2939.66	+	5091.64i	0.859524	+	1.48874i	−0.0128589	+	0.999917i	$0.504093\pi$
$228$	583.184			0.169396
$229$	−3065.16	+	5309.01i	−0.884503	+	1.53200i	−0.0382208	+	0.999269i	$0.512169\pi$
$229$	−3065.16	+	5309.01i	−0.884503	+	1.53200i	−0.846282	+	0.532735i	$0.821164\pi$
$230$	5904.16	+	10226.3i	1.69265	+	2.93175i
$231$	2074.07	−	3592.40i	0.590753	−	1.02321i
$232$	3.43404	+	5.94792i	0.000971791	+	0.00168319i
$233$	2177.36	+	3771.30i	0.612204	+	1.06037i	0.990868	+	0.134834i	$0.0430502\pi$
$233$	2177.36	+	3771.30i	0.612204	+	1.06037i	−0.378664	+	0.925534i	$0.623617\pi$
$234$	1187.30	+	2056.47i	0.331694	+	0.574511i
$235$	−3524.92	−	6105.34i	−0.978469	−	1.69476i
$236$	2132.27	+	3693.20i	0.588130	+	1.01867i
$237$	−1095.09	−	1896.75i	−0.300142	−	0.519861i
$238$	1851.76	−	3207.35i	0.504336	−	0.873535i
$239$	−1328.49	−	2301.01i	−0.359552	−	0.622762i	0.628334	−	0.777944i	$-0.283737\pi$
$239$	−1328.49	−	2301.01i	−0.359552	−	0.622762i	−0.987886	+	0.155182i	$0.950404\pi$
$240$	1886.92	−	3268.25i	0.507502	−	0.879019i
$241$	−5680.37			−1.51828			−0.759138	−	0.650929i	$-0.774379\pi$
$241$	−5680.37			−1.51828			−0.759138	+	0.650929i	$0.774379\pi$
$242$	−2112.20	−	3658.44i	−0.561063	−	0.971790i
$243$	243.000			0.0641500
$244$	−7004.43			−1.83776
$245$	−4565.17	+	7907.11i	−1.19044	+	2.06191i
$246$	−3850.04			−0.997843
$247$	789.735	+	1367.86i	0.203440	+	0.352368i
$248$	37.0761	+	64.2177i	0.00949328	+	0.0164428i
$249$	−493.528	+	854.815i	−0.125607	+	0.217557i
$250$	−5815.09	+	10072.0i	−1.47112	+	2.54805i
$251$	−370.134	+	641.090i	−0.0930782	+	0.161216i	−0.908805	−	0.417221i	$-0.863004\pi$
$251$	−370.134	+	641.090i	−0.0930782	+	0.161216i	0.815727	+	0.578437i	$0.196337\pi$
$252$	−1031.52	+	1786.64i	−0.257856	+	0.446619i
$253$	7224.44			1.79524
$254$	2113.15			0.522012
$255$	972.722	−	1684.80i	0.238879	−	0.413751i
$256$	−1998.81	−	3462.05i	−0.487992	−	0.845227i
$257$	923.007	+	1598.70i	0.224030	+	0.388031i	0.956028	−	0.293276i	$-0.0947454\pi$
$257$	923.007	+	1598.70i	0.224030	+	0.388031i	−0.731998	+	0.681306i	$0.761412\pi$
$258$	1160.70	−	2010.40i	0.280086	−	0.485123i
$259$	8404.69			2.01638
$260$	−10590.0			−2.52602
$261$	81.6085	+	141.350i	0.0193542	+	0.0335224i
$262$	3533.64	−	6120.45i	0.833241	−	1.44322i
$263$	−1857.51			−0.435510			−0.217755	−	0.976003i	$-0.569873\pi$
$263$	−1857.51			−0.435510			−0.217755	+	0.976003i	$0.569873\pi$
$264$	27.7368	+	48.0415i	0.00646622	+	0.0111998i
$265$	−6301.87			−1.46083
$266$	−1364.23	+	2362.91i	−0.314459	+	0.544659i
$267$	4569.67			1.04741
$268$	3831.95	−	2240.97i	0.873409	−	0.510781i
$269$	−1249.75			−0.283265			−0.141633	−	0.989919i	$-0.545235\pi$
$269$	−1249.75			−0.283265			−0.141633	+	0.989919i	$0.545235\pi$
$270$	−1077.38	+	1866.08i	−0.242843	+	0.420616i
$271$	−7132.89			−1.59886			−0.799432	−	0.600756i	$-0.794866\pi$
$271$	−7132.89			−1.59886			−0.799432	+	0.600756i	$0.794866\pi$
$272$	−1030.70	−	1785.22i	−0.229762	−	0.397959i
$273$	−5587.44			−1.23871
$274$	1235.27	−	2139.56i	0.272356	−	0.471735i
$275$	6609.36	+	11447.8i	1.44931	+	2.51027i
$276$	−3593.00			−0.783598
$277$	2714.90			0.588889			0.294445	−	0.955669i	$-0.404865\pi$
$277$	2714.90			0.588889			0.294445	+	0.955669i	$0.404865\pi$
$278$	2544.61	−	4407.40i	0.548978	−	0.950858i
$279$	881.098	+	1526.11i	0.189068	+	0.327475i
$280$	−106.675	−	184.766i	−0.0227680	−	0.0394353i
$281$	2767.14	−	4792.83i	0.587451	−	1.01750i	−0.407114	−	0.913377i	$-0.633465\pi$
$281$	2767.14	−	4792.83i	0.587451	−	1.01750i	0.994565	−	0.104118i	$-0.0332019\pi$
$282$	4265.19			0.900667
$283$	−7495.58			−1.57444			−0.787219	−	0.616673i	$-0.788480\pi$
$283$	−7495.58			−1.57444			−0.787219	+	0.616673i	$0.788480\pi$
$284$	2775.33	−	4807.01i	0.579878	−	1.00438i
$285$	−716.622	+	1241.23i	−0.148944	+	0.257979i
$286$	−6441.28	+	11156.6i	−1.33175	+	2.30666i
$287$	4529.56	−	7845.43i	0.931609	−	1.61359i
$288$	1155.23	+	2000.92i	0.236364	+	0.409394i
$289$	1925.17	+	3334.49i	0.391852	+	0.678707i
$290$	−1447.30			−0.293064
$291$	−1874.83	+	3247.29i	−0.377678	+	0.654157i
$292$	−874.407			−0.175242
$293$	5829.32			1.16230			0.581148	−	0.813798i	$-0.302604\pi$
$293$	5829.32			1.16230			0.581148	+	0.813798i	$0.302604\pi$
$294$	−2761.95	−	4783.84i	−0.547892	−	0.948978i
$295$	−10480.6			−2.06849
$296$	−56.1983	+	97.3384i	−0.0110353	+	0.0191138i
$297$	659.154	+	1141.69i	0.128781	+	0.223055i
$298$	−1433.93	+	2483.64i	−0.278743	+	0.482797i
$299$	−4865.56	−	8427.40i	−0.941079	−	1.63000i
$300$	−3287.10	−	5693.42i	−0.632602	−	1.09570i
$301$	2731.13	+	4730.45i	0.522989	+	0.905843i
$302$	226.303	+	391.969i	0.0431201	+	0.0746863i
$303$	921.672	+	1596.38i	0.174748	+	0.302673i
$304$	759.334	+	1315.21i	0.143259	+	0.248132i
$305$	8607.11	−	14908.0i	1.61587	−	2.79878i
$306$	588.502	+	1019.31i	0.109942	+	0.190426i
$307$	−413.312	+	715.878i	−0.0768370	+	0.133086i	−0.901884	−	0.431979i	$-0.857815\pi$
$307$	−413.312	+	715.878i	−0.0768370	+	0.133086i	0.825047	+	0.565065i	$0.191149\pi$
$308$	−11192.3			−2.07058
$309$	−525.629	−	910.415i	−0.0967701	−	0.167611i
$310$	−15626.0			−2.86290
$311$	2951.03			0.538062			0.269031	−	0.963131i	$-0.413297\pi$
$311$	2951.03			0.538062			0.269031	+	0.963131i	$0.413297\pi$
$312$	37.3607	−	64.7106i	0.00677927	−	0.0117420i
$313$	−4706.77			−0.849976			−0.424988	−	0.905199i	$-0.639722\pi$
$313$	−4706.77			−0.849976			−0.424988	+	0.905199i	$0.639722\pi$
$314$	7041.49	+	12196.2i	1.26552	+	2.19195i
$315$	−2535.08	−	4390.89i	−0.453447	−	0.785393i
$316$	−2954.69	+	5117.68i	−0.525995	+	0.911051i
$317$	4173.43	−	7228.59i	0.739442	−	1.28075i	−0.213304	−	0.976986i	$-0.568423\pi$
$317$	4173.43	−	7228.59i	0.739442	−	1.28075i	0.952747	−	0.303766i	$-0.0982441\pi$
$318$	1906.33	−	3301.87i	0.336169	−	0.582262i
$319$	−442.737	+	766.843i	−0.0777069	+	0.134592i
$320$	−10424.1			−1.82102
$321$	−861.851			−0.149856
$322$	8405.02	−	14557.9i	1.45464	−	2.51951i
$323$	391.442	+	677.997i	0.0674316	+	0.116795i
$324$	−327.823	−	567.806i	−0.0562111	−	0.0973605i
$325$	8902.64	−	15419.8i	1.51947	−	2.63181i
$326$	−3215.79			−0.546338
$327$	−1608.52			−0.272022
$328$	60.5743	+	104.918i	0.0101971	+	0.0176619i
$329$	−5017.99	+	8691.41i	−0.840883	+	1.45645i
$330$	−11689.9			−1.95003
$331$	1452.76	+	2516.26i	0.241242	+	0.417843i	0.961068	−	0.276311i	$-0.0891120\pi$
$331$	1452.76	+	2516.26i	0.241242	+	0.417843i	−0.719827	+	0.694154i	$0.755779\pi$
$332$	2663.21			0.440249
$333$	−1335.53	+	2313.21i	−0.219780	+	0.380670i
$334$	4793.02			0.785216
$335$	60.8640	+	10909.5i	0.00992644	+	1.77925i
$336$	−5372.36			−0.872280
$337$	1216.77	−	2107.51i	0.196682	−	0.340663i	−0.750769	−	0.660565i	$-0.770317\pi$
$337$	1216.77	−	2107.51i	0.196682	−	0.340663i	0.947450	+	0.319902i	$0.103650\pi$
$338$	8538.57			1.37407
$339$	−1002.40	−	1736.20i	−0.160598	−	0.278164i
$340$	−5249.07			−0.837267
$341$	−4780.08	+	8279.34i	−0.759107	+	1.31481i
$342$	−433.560	−	750.948i	−0.0685504	−	0.118733i
$343$	3284.27			0.517009
$344$	−73.0473			−0.0114490
$345$	4415.12	−	7647.20i	0.688991	−	1.19337i
$346$	2838.22	+	4915.93i	0.440992	+	0.763821i
$347$	354.715	+	614.384i	0.0548763	+	0.0950485i	0.892159	−	0.451722i	$-0.149190\pi$
$347$	354.715	+	614.384i	0.0548763	+	0.0950485i	−0.837282	+	0.546771i	$0.815857\pi$
$348$	220.191	−	381.381i	0.0339180	−	0.0587477i
$349$	−8586.14			−1.31692			−0.658460	−	0.752615i	$-0.728792\pi$
$349$	−8586.14			−1.31692			−0.658460	+	0.752615i	$0.728792\pi$
$350$	30757.7			4.69734
$351$	887.862	−	1537.82i	0.135016	−	0.233854i
$352$	−6267.29	+	10855.3i	−0.948999	+	1.64371i
$353$	−5530.98	+	9579.93i	−0.833950	+	1.44444i	0.0609332	+	0.998142i	$0.480592\pi$
$353$	−5530.98	+	9579.93i	−0.833950	+	1.44444i	−0.894883	+	0.446301i	$0.852741\pi$
$354$	3170.41	−	5491.31i	0.476004	−	0.824463i
$355$	6820.70	+	11813.8i	1.01973	+	1.76623i
$356$	−6164.79	−	10677.7i	−0.917789	−	1.58966i
$357$	−2769.49			−0.410579
$358$	539.771	−	934.912i	0.0796866	−	0.138021i
$359$	−146.723			−0.0215703			−0.0107851	−	0.999942i	$-0.503433\pi$
$359$	−146.723			−0.0215703			−0.0107851	+	0.999942i	$0.503433\pi$
$360$	67.8038			0.00992659
$361$	3141.12	+	5440.58i	0.457956	+	0.793202i
$362$	−5095.87			−0.739870
$363$	−1579.50	+	2735.77i	−0.228380	+	0.395566i
$364$	7537.83	+	13055.9i	1.08541	+	1.87999i
$365$	1074.48	−	1861.05i	0.154085	−	0.266882i
$366$	5207.35	+	9019.39i	0.743695	+	1.28812i
$367$	1017.69	+	1762.69i	0.144750	+	0.250714i	0.929279	−	0.369377i	$-0.120429\pi$
$367$	1017.69	+	1762.69i	0.144750	+	0.250714i	−0.784530	+	0.620091i	$0.787096\pi$
$368$	−4678.26	−	8102.99i	−0.662694	−	1.14782i
$369$	1439.52	+	2493.33i	0.203086	+	0.351755i
$370$	−11842.6	−	20512.1i	−1.66397	−	2.88208i
$371$	4485.60	+	7769.28i	0.627710	+	1.08723i
$372$	2377.32	−	4117.64i	0.331340	−	0.573897i
$373$	2685.80	+	4651.94i	0.372830	+	0.645760i	0.990000	−	0.141070i	$-0.0450542\pi$
$373$	2685.80	+	4651.94i	0.372830	+	0.645760i	−0.617170	+	0.786830i	$0.711721\pi$
$374$	−3192.70	+	5529.92i	−0.441419	+	0.764560i
$375$	8697.02			1.19763
$376$	−67.1060	−	116.231i	−0.00920406	−	0.0159419i
$377$	1192.71			0.162938
$378$	3067.48			0.417391
$379$	4385.70	−	7596.25i	0.594401	−	1.02953i	−0.399230	−	0.916851i	$-0.630722\pi$
$379$	4385.70	−	7596.25i	0.594401	−	1.02953i	0.993631	−	0.112683i	$-0.0359443\pi$
$380$	3867.08			0.522045
$381$	−790.105	−	1368.50i	−0.106242	−	0.184017i
$382$	−763.730	−	1322.82i	−0.102293	−	0.177176i
$383$	−6470.69	+	11207.6i	−0.863282	+	1.49525i	0.00546105	+	0.999985i	$0.498262\pi$
$383$	−6470.69	+	11207.6i	−0.863282	+	1.49525i	−0.868743	+	0.495263i	$0.835072\pi$
$384$	72.7081	−	125.934i	0.00966242	−	0.0167358i
$385$	13753.2	−	23821.2i	1.82059	−	3.15335i
$386$	2260.40	−	3915.13i	0.298061	−	0.516256i
$387$	−1735.94			−0.228018
$388$	10117.1			1.32375
$389$	3769.82	−	6529.52i	0.491356	−	0.851054i	−0.508594	−	0.861006i	$-0.669835\pi$
$389$	3769.82	−	6529.52i	0.491356	−	0.851054i	0.999950	+	0.00995266i	$0.00316808\pi$
$390$	7873.00	+	13636.4i	1.02222	+	1.77053i
$391$	−2411.68	−	4177.15i	−0.311928	−	0.540274i
$392$	−86.9100	+	150.532i	−0.0111980	+	0.0193955i
$393$	−5284.89			−0.678340
$394$	18052.4			2.30829
$395$	−7261.52	−	12577.3i	−0.924979	−	1.60211i
$396$	1778.48	−	3080.43i	0.225687	−	0.390902i
$397$	−446.085			−0.0563938			−0.0281969	−	0.999602i	$-0.508977\pi$
$397$	−446.085			−0.0563938			−0.0281969	+	0.999602i	$0.508977\pi$
$398$	−2047.92	−	3547.11i	−0.257922	−	0.446735i
$399$	2040.33			0.256001
$400$	8559.93	−	14826.2i	1.06999	−	1.85328i
$401$	4754.86			0.592135			0.296067	−	0.955167i	$-0.404325\pi$
$401$	4754.86			0.592135			0.296067	+	0.955167i	$0.404325\pi$
$402$	−5734.44	−	3268.26i	−0.711463	−	0.405488i
$403$	12877.3			1.59172
$404$	2486.79	−	4307.25i	0.306244	−	0.530430i
$405$	1611.33			0.197698
$406$	1030.17	+	1784.31i	0.125928	+	0.218113i
$407$	−14490.9			−1.76483
$408$	18.5183	−	32.0746i	0.00224704	−	0.00389199i
$409$	−4420.12	−	7655.88i	−0.534379	−	0.925572i	−0.999193	−	0.0401635i	$-0.987212\pi$
$409$	−4420.12	−	7655.88i	−0.534379	−	0.925572i	0.464814	−	0.885408i	$-0.346121\pi$
$410$	−25529.6			−3.07516
$411$	−1847.47			−0.221725
$412$	−1418.22	+	2456.42i	−0.169589	+	0.293736i
$413$	7459.97	+	12921.0i	0.888816	+	1.53947i
$414$	2671.17	+	4626.60i	0.317103	+	0.549239i
$415$	−3272.58	+	5668.27i	−0.387095	+	0.670469i
$416$	16883.7			1.98989
$417$	−3805.71			−0.446922
$418$	2352.12	−	4073.99i	0.275230	−	0.476712i
$419$	−2655.11	+	4598.79i	−0.309572	+	0.536195i	−0.978269	−	0.207341i	$-0.933519\pi$
$419$	−2655.11	+	4598.79i	−0.309572	+	0.536195i	0.668697	+	0.743535i	$0.266853\pi$
$420$	−6839.99	+	11847.2i	−0.794661	+	1.37639i
$421$	−8398.89	+	14547.3i	−0.972297	+	1.68407i	−0.283714	+	0.958909i	$0.591567\pi$
$421$	−8398.89	+	14547.3i	−0.972297	+	1.68407i	−0.688582	+	0.725158i	$0.741767\pi$
$422$	−9075.41	−	15719.1i	−1.04688	−	1.81325i
$423$	−1594.75	−	2762.18i	−0.183308	−	0.317499i
$424$	−119.973			−0.0137415
$425$	4412.70	−	7643.02i	0.503641	−	0.872332i
$426$	−8253.12			−0.938650
$427$	−24505.7			−2.77732
$428$	1162.69	+	2013.85i	0.131311	+	0.227437i
$429$	9633.54			1.08418
$430$	7696.61	−	13330.9i	0.863170	−	1.49505i
$431$	1128.23	+	1954.15i	0.126090	+	0.218395i	0.922159	−	0.386812i	$-0.126424\pi$
$431$	1128.23	+	1954.15i	0.126090	+	0.218395i	−0.796068	+	0.605207i	$0.793090\pi$
$432$	853.684	−	1478.62i	0.0950762	−	0.164677i
$433$	−666.426	−	1154.28i	−0.0739640	−	0.128109i	0.826671	−	0.562685i	$-0.190232\pi$
$433$	−666.426	−	1154.28i	−0.0739640	−	0.128109i	−0.900635	+	0.434576i	$0.856898\pi$
$434$	11122.4	+	19264.6i	1.23017	+	2.13071i
$435$	541.145	+	937.291i	0.0596458	+	0.103310i
$436$	2170.00	+	3758.54i	0.238358	+	0.412848i
$437$	1776.73	+	3077.38i	0.194490	+	0.336867i
$438$	650.066	+	1125.95i	0.0709163	+	0.122831i
$439$	2609.84	−	4520.38i	0.283738	−	0.491449i	−0.688564	−	0.725175i	$-0.741759\pi$
$439$	2609.84	−	4520.38i	0.283738	−	0.491449i	0.972302	+	0.233726i	$0.0750920\pi$
$440$	183.922	+	318.563i	0.0199276	+	0.0345157i
$441$	−2065.38	+	3577.34i	−0.223019	+	0.386281i
$442$	8600.96			0.925579
$443$	4008.05	+	6942.15i	0.429861	+	0.744540i	0.996861	−	0.0791775i	$-0.0252294\pi$
$443$	4008.05	+	6942.15i	0.429861	+	0.744540i	−0.567000	+	0.823718i	$0.691896\pi$
$444$	7206.88			0.770323
$445$	30301.4			3.22792
$446$	−4185.41	+	7249.34i	−0.444361	+	0.769656i
$447$	2144.58			0.226924
$448$	7419.77	+	12851.4i	0.782480	+	1.35530i
$449$	793.859	+	1375.00i	0.0834399	+	0.144522i	0.904725	−	0.425995i	$-0.140076\pi$
$449$	793.859	+	1375.00i	0.0834399	+	0.144522i	−0.821285	+	0.570517i	$0.806743\pi$
$450$	−4887.50	+	8465.40i	−0.511998	+	0.886806i
$451$	−7809.61	+	13526.6i	−0.815388	+	1.41229i
$452$	−2704.60	+	4684.51i	−0.281446	+	0.487480i
$453$	169.229	−	293.113i	0.0175520	−	0.0304010i
$454$	−23586.5			−2.43826
$455$	−37050.3			−3.81746
$456$	−13.6428	+	23.6300i	−0.00140106	+	0.00242670i
$457$	2061.74	+	3571.05i	0.211038	+	0.365528i	0.952040	−	0.305975i	$-0.0989823\pi$
$457$	2061.74	+	3571.05i	0.211038	+	0.365528i	−0.741002	+	0.671503i	$0.765649\pi$
$458$	−12296.7	−	21298.6i	−1.25456	−	2.17296i
$459$	440.080	−	762.241i	0.0447520	−	0.0775128i
$460$	−23825.1			−2.41490
$461$	−8496.94			−0.858443			−0.429221	−	0.903199i	$-0.641212\pi$
$461$	−8496.94			−0.858443			−0.429221	+	0.903199i	$0.641212\pi$
$462$	8320.73	+	14411.9i	0.837912	+	1.45131i
$463$	−7715.35	+	13363.4i	−0.774433	+	1.34136i	0.160680	+	0.987007i	$0.448631\pi$
$463$	−7715.35	+	13363.4i	−0.774433	+	1.34136i	−0.935113	+	0.354351i	$0.884702\pi$
$464$	1146.80			0.114739
$465$	5842.55	+	10119.6i	0.582671	+	1.00922i
$466$	−17470.2			−1.73667
$467$	−1606.32	+	2782.23i	−0.159169	+	0.275688i	−0.934569	−	0.355782i	$-0.884215\pi$
$467$	−1606.32	+	2782.23i	−0.159169	+	0.275688i	0.775400	+	0.631470i	$0.217548\pi$
$468$	−4791.14			−0.473228
$469$	13406.5	−	7840.29i	1.31994	−	0.771921i
$470$	28282.4			2.77568
$471$	5265.61	−	9120.30i	0.515130	−	0.892232i
$472$	−199.526			−0.0194574
$473$	−4708.85	−	8155.97i	−0.457745	−	0.792837i
$474$	8786.51			0.851430
$475$	−3250.92	+	5630.76i	−0.314026	+	0.543909i
$476$	3736.22	+	6471.32i	0.359768	+	0.623136i
$477$	−2851.10			−0.273675
$478$	10659.2			1.01996
$479$	−5218.93	+	9039.45i	−0.497827	+	0.862261i	−0.999997	−	0.00250782i	$-0.999202\pi$
$479$	−5218.93	+	9039.45i	−0.497827	+	0.862261i	0.502170	+	0.864769i	$0.332535\pi$
$480$	7660.34	+	13268.1i	0.728427	+	1.26167i
$481$	9759.41	+	16903.8i	0.925136	+	1.60238i
$482$	11394.2	−	19735.3i	1.07675	−	1.86498i
$483$	−12570.5			−1.18422
$484$	8523.39			0.800468
$485$	−12431.9	+	21532.8i	−1.16393	+	2.01598i
$486$	−487.432	+	844.256i	−0.0454945	+	0.0787989i
$487$	−3507.16	+	6074.59i	−0.326334	+	0.565227i	−0.981781	−	0.190014i	$-0.939147\pi$
$487$	−3507.16	+	6074.59i	−0.326334	+	0.565227i	0.655447	+	0.755241i	$0.272480\pi$
$488$	163.859	−	283.812i	0.0151999	−	0.0263270i
$489$	1202.38	+	2082.58i	0.111193	+	0.192592i
$490$	−18314.5	−	31721.6i	−1.68850	−	2.92456i
$491$	17265.5			1.58693			0.793465	−	0.608616i	$-0.208275\pi$
$491$	17265.5			1.58693			0.793465	+	0.608616i	$0.208275\pi$
$492$	3884.03	−	6727.33i	0.355905	−	0.616446i
$493$	591.181			0.0540070
$494$	−6336.49			−0.577109
$495$	4370.84	+	7570.52i	0.396878	+	0.687413i
$496$	12381.6			1.12086
$497$	9709.78	−	16817.8i	0.876344	−	1.51787i
$498$	−1979.93	−	3429.33i	−0.178158	−	0.308578i
$499$	8055.91	−	13953.2i	0.722710	−	1.25177i	−0.237200	−	0.971461i	$-0.576230\pi$
$499$	8055.91	−	13953.2i	0.722710	−	1.25177i	0.959910	−	0.280309i	$-0.0904369\pi$
$500$	−11732.9	−	20321.9i	−1.04942	−	1.81765i
$501$	−1792.10	−	3104.01i	−0.159811	−	0.276800i
$502$	−1484.90	−	2571.91i	−0.132020	−	0.228666i
$503$	5580.62	+	9665.91i	0.494687	+	0.856822i	0.999981	−	0.00612457i	$-0.00194952\pi$
$503$	5580.62	+	9665.91i	0.494687	+	0.856822i	−0.505295	+	0.862947i	$0.668616\pi$
$504$	−48.2619	−	83.5921i	−0.00426539	−	0.00738787i
$505$	6111.60	+	10585.6i	0.538540	+	0.932778i
$506$	−14491.4	+	25099.9i	−1.27317	+	2.20519i
$507$	−3192.56	−	5529.68i	−0.279658	−	0.484382i
$508$	−2131.81	+	3692.40i	−0.186188	+	0.322488i
$509$	−10733.6			−0.934697			−0.467348	−	0.884073i	$-0.654791\pi$
$509$	−10733.6			−0.934697			−0.467348	+	0.884073i	$0.654791\pi$
$510$	3902.35	+	6759.07i	0.338821	+	0.586856i
$511$	−3059.21			−0.264836
$512$	16425.4			1.41779
$513$	−324.215	+	561.557i	−0.0279034	+	0.0483301i
$514$	−7405.81			−0.635518
$515$	−3485.44	−	6036.95i	−0.298227	−	0.516544i
$516$	2341.90	+	4056.29i	0.199799	+	0.346062i
$517$	8651.72	−	14985.2i	0.735981	−	1.27476i
$518$	−16858.9	+	29200.5i	−1.42999	+	2.47682i
$519$	2122.41	−	3676.12i	0.179506	−	0.310913i
$520$	247.738	−	429.096i	0.0208924	−	0.0361867i
$521$	12509.7			1.05194			0.525969	−	0.850504i	$-0.323703\pi$
$521$	12509.7			1.05194			0.525969	+	0.850504i	$0.323703\pi$
$522$	−654.791			−0.0549031
$523$	5007.54	−	8673.32i	0.418670	−	0.725158i	−0.577136	−	0.816648i	$-0.695830\pi$
$523$	5007.54	−	8673.32i	0.418670	−	0.725158i	0.995806	+	0.0914901i	$0.0291630\pi$
$524$	7129.67	+	12349.0i	0.594392	+	1.02952i
$525$	−11500.3	−	19919.1i	−0.956025	−	1.65588i
$526$	3725.97	−	6453.56i	0.308859	−	0.534960i
$527$	6382.78			0.527587
$528$	9262.70			0.763461
$529$	−4862.93	−	8422.83i	−0.399682	−	0.692269i
$530$	12640.9	−	21894.6i	1.03601	−	1.79442i
$531$	−4741.65			−0.387514
$532$	−2752.54	−	4767.54i	−0.224319	−	0.388532i
$533$	21038.7			1.70973
$534$	−9166.26	+	15876.4i	−0.742814	+	1.28659i
$535$	−5714.92			−0.461827
$536$	1.15871	+	207.691i	9.33740e−5	+	0.0167367i
$537$	−807.279			−0.0648728
$538$	2506.85	−	4342.00i	0.200889	−	0.347949i
$539$	−22409.9			−1.79084
$540$	−2173.79	−	3765.12i	−0.173232	−	0.300046i
$541$	13954.7			1.10898			0.554492	−	0.832189i	$-0.312912\pi$
$541$	13954.7			1.10898			0.554492	+	0.832189i	$0.312912\pi$
$542$	14307.8	−	24781.8i	1.13390	−	1.96397i
$543$	1905.34	+	3300.14i	0.150582	+	0.260815i
$544$	8368.64			0.659563
$545$	−10666.1			−0.838318
$546$	11207.8	−	19412.5i	0.878479	−	1.52157i
$547$	3436.91	+	5952.90i	0.268650	+	0.465316i	0.968514	−	0.248961i	$-0.0800891\pi$
$547$	3436.91	+	5952.90i	0.268650	+	0.465316i	−0.699863	+	0.714277i	$0.746756\pi$
$548$	2492.36	+	4316.89i	0.194285	+	0.336512i
$549$	3894.04	−	6744.68i	0.302721	−	0.524327i
$550$	−53030.7			−4.11134
$551$	−435.534			−0.0336740
$552$	84.0532	−	145.584i	0.00648106	−	0.0112255i
$553$	−10337.3	+	17904.8i	−0.794914	+	1.37683i
$554$	−5445.79	+	9432.38i	−0.417634	+	0.723364i
$555$	−8855.89	+	15338.9i	−0.677319	+	1.17315i
$556$	5134.16	+	8892.62i	0.391613	+	0.678294i
$557$	−2936.54	−	5086.24i	−0.223385	−	0.386914i	0.732449	−	0.680822i	$-0.238377\pi$
$557$	−2936.54	−	5086.24i	−0.223385	−	0.386914i	−0.955834	+	0.293908i	$0.905044\pi$
$558$	−7069.55			−0.536340
$559$	−6342.70	+	10985.9i	−0.479906	+	0.831222i
$560$	−35624.0			−2.68820
$561$	4774.98			0.359358
$562$	11101.2	+	19227.8i	0.833229	+	1.44319i
$563$	−4771.82			−0.357209			−0.178604	−	0.983921i	$-0.557158\pi$
$563$	−4771.82			−0.357209			−0.178604	+	0.983921i	$0.557158\pi$
$564$	−4302.84	+	7452.74i	−0.321245	+	0.556413i
$565$	−6646.89	−	11512.7i	−0.494932	−	0.857248i
$566$	15035.3	−	26041.9i	1.11658	−	1.93397i
$567$	−1146.93	−	1986.53i	−0.0849494	−	0.147137i
$568$	129.850	+	224.906i	0.00959221	+	0.0166142i
$569$	4999.63	+	8659.61i	0.368358	+	0.638014i	0.989309	−	0.145835i	$-0.0465869\pi$
$569$	4999.63	+	8659.61i	0.368358	+	0.638014i	−0.620951	+	0.783849i	$0.713254\pi$
$570$	−2874.93	−	4979.53i	−0.211259	−	0.365911i
$571$	−4237.95	−	7340.35i	−0.310600	−	0.537976i	0.667892	−	0.744258i	$-0.267197\pi$
$571$	−4237.95	−	7340.35i	−0.310600	−	0.537976i	−0.978493	+	0.206282i	$0.933863\pi$
$572$	−12996.3	−	22510.2i	−0.950004	−	1.64546i
$573$	−571.115	+	989.200i	−0.0416382	+	0.0721194i
$574$	18171.6	+	31474.2i	1.32137	+	2.28869i
$575$	20028.9	−	34691.1i	1.45263	−	2.51604i
$576$	−4716.10			−0.341153
$577$	−9833.10	−	17031.4i	−0.709458	−	1.22882i	−0.965058	−	0.262035i	$-0.915607\pi$
$577$	−9833.10	−	17031.4i	−0.709458	−	1.22882i	0.255601	−	0.966782i	$-0.417727\pi$
$578$	−15446.7			−1.11159
$579$	−3380.65			−0.242651
$580$	1460.08	−	2528.94i	0.104529	−	0.181049i
$581$	9317.52			0.665329
$582$	−7521.39	−	13027.4i	−0.535690	−	0.927843i
$583$	−7733.80	−	13395.3i	−0.549402	−	0.951592i
$584$	20.4555	−	35.4300i	0.00144941	−	0.00251045i
$585$	5887.41	−	10197.3i	0.416093	−	0.720694i
$586$	−11693.0	+	20252.9i	−0.824289	+	1.42771i
$587$	5955.78	−	10315.7i	0.418776	−	0.725341i	−0.577041	−	0.816715i	$-0.695793\pi$
$587$	5955.78	−	10315.7i	0.418776	−	0.725341i	0.995817	+	0.0913744i	$0.0291260\pi$
$588$	11145.3			0.781677
$589$	−4702.31			−0.328956
$590$	21023.0	−	36412.8i	1.46695	−	2.54084i
$591$	−6749.77	−	11691.0i	−0.469795	−	0.813708i
$592$	9383.72	+	16253.1i	0.651467	+	1.12837i
$593$	−1232.09	+	2134.05i	−0.0853222	+	0.147782i	−0.905528	−	0.424286i	$-0.860525\pi$
$593$	−1232.09	+	2134.05i	−0.0853222	+	0.147782i	0.820206	+	0.572068i	$0.193859\pi$
$594$	−5288.76			−0.365321
$595$	−18364.4			−1.26532
$596$	−2893.18	−	5011.13i	−0.198841	−	0.344403i
$597$	−1531.43	+	2652.52i	−0.104987	+	0.181843i
$598$	39039.2			2.66961
$599$	−14399.0	−	24939.8i	−0.982182	−	1.70119i	−0.653846	−	0.756628i	$-0.726846\pi$
$599$	−14399.0	−	24939.8i	−0.982182	−	1.70119i	−0.328336	−	0.944561i	$-0.606488\pi$
$600$	307.588			0.0209287
$601$	392.512	−	679.851i	0.0266404	−	0.0461426i	−0.852398	−	0.522894i	$-0.824852\pi$
$601$	392.512	−	679.851i	0.0266404	−	0.0461426i	0.879038	+	0.476751i	$0.158186\pi$
$602$	−21913.4			−1.48359
$603$	27.5362	+	4935.69i	0.00185963	+	0.333328i
$604$	−913.204			−0.0615195
$605$	−10473.6	+	18140.9i	−0.703824	+	1.21906i
$606$	−7395.10			−0.495718
$607$	−4806.98	−	8325.93i	−0.321432	−	0.556737i	0.659352	−	0.751835i	$-0.270831\pi$
$607$	−4806.98	−	8325.93i	−0.321432	−	0.556737i	−0.980784	+	0.195098i	$0.937498\pi$
$608$	−6165.33			−0.411245
$609$	770.361	−	1334.30i	0.0512588	−	0.0887828i
$610$	34529.9	+	59807.5i	2.29192	+	3.96973i
$611$	−23307.3			−1.54323
$612$	−2374.79			−0.156855
$613$	10088.9	−	17474.5i	0.664744	−	1.15137i	−0.314611	−	0.949221i	$-0.601874\pi$
$613$	10088.9	−	17474.5i	0.664744	−	1.15137i	0.979355	−	0.202149i	$-0.0647926\pi$
$614$	−1658.12	−	2871.95i	−0.108984	−	0.188766i
$615$	9545.47	+	16533.2i	0.625871	+	1.08404i
$616$	261.827	−	453.498i	0.0171255	−	0.0296623i
$617$	9571.54			0.624531			0.312265	−	0.949995i	$-0.398912\pi$
$617$	9571.54			0.624531			0.312265	+	0.949995i	$0.398912\pi$
$618$	4217.42			0.274513
$619$	2099.86	−	3637.07i	0.136350	−	0.236165i	−0.789762	−	0.613413i	$-0.789796\pi$
$619$	2099.86	−	3637.07i	0.136350	−	0.236165i	0.926112	+	0.377248i	$0.123129\pi$
$620$	15764.0	−	27304.0i	1.02112	−	1.76864i
$621$	1997.49	−	3459.76i	0.129077	−	0.223567i
$622$	−5919.44	+	10252.8i	−0.381588	+	0.660930i
$623$	−21568.2	−	37357.2i	−1.38702	−	2.40238i
$624$	−6238.31	−	10805.1i	−0.400212	−	0.693187i
$625$	23828.6			1.52503
$626$	9441.27	−	16352.8i	0.602794	−	1.04407i
$627$	−3517.82			−0.224064
$628$	−28414.6			−1.80552
$629$	4837.37	+	8378.57i	0.306643	+	0.531122i
$630$	20340.4			1.28632
$631$	8816.64	−	15270.9i	0.556236	−	0.963429i	−0.441570	−	0.897227i	$-0.645578\pi$
$631$	8816.64	−	15270.9i	0.556236	−	0.963429i	0.997806	−	0.0662021i	$-0.0210882\pi$
$632$	−138.242	−	239.442i	−0.00870090	−	0.0150704i
$633$	−6786.56	+	11754.7i	−0.426132	+	0.738083i
$634$	16742.9	+	28999.5i	1.04881	+	1.81659i
$635$	−5239.18	−	9074.52i	−0.327418	−	0.567105i
$636$	3846.33	+	6662.03i	0.239806	+	0.415357i
$637$	15092.8	+	26141.5i	0.938772	+	1.62600i
$638$	−1776.16	−	3076.41i	−0.110218	−	0.190903i
$639$	3085.83	+	5344.81i	0.191038	+	0.330888i
$640$	482.127	−	835.068i	0.0297777	−	0.0515765i
$641$	−6302.66	−	10916.5i	−0.388362	−	0.672663i	0.603867	−	0.797085i	$-0.293626\pi$
$641$	−6302.66	−	10916.5i	−0.388362	−	0.672663i	−0.992229	+	0.124422i	$0.960292\pi$
$642$	1728.78	−	2994.33i	0.106276	−	0.184076i
$643$	9291.31			0.569850			0.284925	−	0.958550i	$-0.408031\pi$
$643$	9291.31			0.569850			0.284925	+	0.958550i	$0.408031\pi$
$644$	16958.4	+	29372.9i	1.03766	+	1.79729i
$645$	−11511.0			−0.702706
$646$	−3140.76			−0.191287
$647$	−12364.3	+	21415.6i	−0.751300	+	1.30129i	0.195892	+	0.980625i	$0.437240\pi$
$647$	−12364.3	+	21415.6i	−0.751300	+	1.30129i	−0.947193	+	0.320665i	$0.896094\pi$
$648$	30.6759			0.00185966
$649$	−12862.0	−	22277.7i	−0.777934	−	1.34742i
$650$	35715.4	+	61861.0i	2.15519	+	3.73290i
$651$	8317.32	−	14406.0i	0.500739	−	0.867306i
$652$	3244.18	−	5619.08i	0.194865	−	0.337516i
$653$	−2214.19	+	3835.09i	−0.132692	+	0.229830i	−0.924714	−	0.380664i	$-0.875696\pi$
$653$	−2214.19	+	3835.09i	−0.132692	+	0.229830i	0.792021	+	0.610494i	$0.209029\pi$
$654$	3226.51	−	5588.48i	0.192915	−	0.334139i
$655$	−35044.1			−2.09051
$656$	20228.8			1.20397
$657$	486.118	−	841.980i	0.0288664	−	0.0499981i
$658$	−20131.1	−	34868.0i	−1.19269	−	2.06580i
$659$	−2310.93	−	4002.64i	−0.136602	−	0.236602i	0.789606	−	0.613614i	$-0.210285\pi$
$659$	−2310.93	−	4002.64i	−0.136602	−	0.236602i	−0.926208	+	0.377012i	$0.876952\pi$
$660$	11793.1	−	20426.3i	0.695525	−	1.20468i
$661$	5167.94			0.304099			0.152050	−	0.988373i	$-0.451413\pi$
$661$	5167.94			0.304099			0.152050	+	0.988373i	$0.451413\pi$
$662$	−11656.3			−0.684345
$663$	−3215.89	−	5570.08i	−0.188378	−	0.326281i
$664$	−62.3020	+	107.910i	−0.00364125	+	0.00630682i
$665$	13529.4			0.788945
$666$	−5357.86	−	9280.09i	−0.311731	−	0.539934i
$667$	2683.33			0.155771
$668$	−4835.33	+	8375.04i	−0.280067	+	0.485090i
$669$	6259.68			0.361754
$670$	−38025.0	−	21671.8i	−2.19259	−	1.24964i
$671$	42251.4			2.43084
$672$	10905.1	−	18888.1i	0.626000	−	1.08426i
$673$	−14628.6			−0.837877			−0.418938	−	0.908015i	$-0.637598\pi$
$673$	−14628.6			−0.837877			−0.418938	+	0.908015i	$0.637598\pi$
$674$	4881.42	+	8454.87i	0.278969	+	0.483189i
$675$	7309.72			0.416816
$676$	−8613.95	+	14919.8i	−0.490098	+	0.848874i
$677$	4299.48	+	7446.92i	0.244080	+	0.422760i	0.961873	−	0.273498i	$-0.0881806\pi$
$677$	4299.48	+	7446.92i	0.244080	+	0.422760i	−0.717792	+	0.696257i	$0.754847\pi$
$678$	8042.80			0.455578
$679$	35395.6			2.00053
$680$	122.795	−	212.687i	0.00692494	−	0.0119943i
$681$	8818.98	+	15274.9i	0.496247	+	0.859524i
$682$	−19176.6	−	33214.9i	−1.07670	−	1.86490i
$683$	2341.79	−	4056.09i	0.131195	−	0.227236i	−0.792943	−	0.609296i	$-0.791452\pi$
$683$	2341.79	−	4056.09i	0.131195	−	0.227236i	0.924137	+	0.382060i	$0.124785\pi$
$684$	1749.55			0.0978008
$685$	−12250.5			−0.683312
$686$	−6587.89	+	11410.6i	−0.366657	+	0.635069i
$687$	−9195.47	+	15927.0i	−0.510668	+	0.884503i
$688$	−6098.54	+	10563.0i	−0.337943	+	0.585334i
$689$	−10417.2	+	18043.2i	−0.576001	+	0.997663i
$690$	17712.5	+	30678.9i	0.977250	+	1.69265i
$691$	−4263.95	−	7385.38i	−0.234744	−	0.406589i	0.724454	−	0.689323i	$-0.242092\pi$
$691$	−4263.95	−	7385.38i	−0.234744	−	0.406589i	−0.959198	+	0.282734i	$0.908759\pi$
$692$	−11453.1			−0.629163
$693$	6222.22	−	10777.2i	0.341072	−	0.590753i
$694$	−2846.08			−0.155671
$695$	−25235.6			−1.37733
$696$	10.3021	+	17.8438i	0.000561064	+	0.000971791i
$697$	10428.1			0.566702
$698$	17222.9	−	29830.9i	0.933947	−	1.61764i
$699$	6532.08	+	11313.9i	0.353456	+	0.612204i
$700$	−31029.3	+	53744.3i	−1.67542	+	2.90192i
$701$	8517.18	+	14752.2i	0.458901	+	0.794839i	0.998903	−	0.0468241i	$-0.0149100\pi$
$701$	8517.18	+	14752.2i	0.458901	+	0.794839i	−0.540002	+	0.841663i	$0.681577\pi$
$702$	3561.91	+	6169.41i	0.191504	+	0.331694i
$703$	−3563.78	−	6172.65i	−0.191196	−	0.331160i
$704$	−12792.7	−	22157.7i	−0.684864	−	1.18622i
$705$	−10574.8	−	18316.0i	−0.564920	−	0.978469i
$706$	−22189.1	−	38432.6i	−1.18286	−	2.04877i
$707$	8700.32	−	15069.4i	0.462814	−	0.801617i
$708$	6396.80	+	11079.6i	0.339557	+	0.588130i
$709$	−11851.3	+	20527.1i	−0.627766	+	1.08732i	0.360233	+	0.932862i	$0.382697\pi$
$709$	−11851.3	+	20527.1i	−0.627766	+	1.08732i	−0.987999	+	0.154460i	$0.950636\pi$
$710$	−54726.3			−2.89274
$711$	−3285.27	−	5690.25i	−0.173287	−	0.300142i
$712$	576.866			0.0303637
$713$	28971.0			1.52170
$714$	5555.29	−	9622.04i	0.291178	−	0.504336i
$715$	63879.9			3.34122
$716$	1089.07	+	1886.33i	0.0568444	+	0.0984574i
$717$	−3985.47	−	6903.04i	−0.207587	−	0.359552i
$718$	294.310	−	509.760i	0.0152974	−	0.0264959i
$719$	−2708.69	+	4691.58i	−0.140497	+	0.243347i	−0.927684	−	0.373367i	$-0.878203\pi$
$719$	−2708.69	+	4691.58i	−0.140497	+	0.243347i	0.787187	+	0.616714i	$0.211537\pi$
$720$	5660.77	−	9804.75i	0.293006	−	0.507502i
$721$	−4961.78	+	8594.06i	−0.256292	+	0.443911i
$722$	−25203.0			−1.29911
$723$	−17041.1			−0.876578
$724$	5140.86	−	8904.23i	0.263893	−	0.457076i
$725$	2454.88	+	4251.97i	0.125754	+	0.217813i
$726$	−6336.60	−	10975.3i	−0.323930	−	0.561063i
$727$	13106.2	−	22700.5i	0.668612	−	1.15807i	−0.309681	−	0.950841i	$-0.600222\pi$
$727$	13106.2	−	22700.5i	0.668612	−	1.15807i	0.978293	−	0.207229i	$-0.0664444\pi$
$728$	−705.349			−0.0359093
$729$	729.000			0.0370370
$730$	4310.58	+	7466.15i	0.218550	+	0.378540i
$731$	−3143.84	+	5445.29i	−0.159068	+	0.275515i
$732$	−21013.3			−1.06103
$733$	3226.40	+	5588.29i	0.162578	+	0.281594i	0.935793	−	0.352551i	$-0.114686\pi$
$733$	3226.40	+	5588.29i	0.162578	+	0.281594i	−0.773214	+	0.634145i	$0.781352\pi$
$734$	−8165.52			−0.410620
$735$	−13695.5	+	23721.3i	−0.687302	+	1.19044i
$736$	37984.6			1.90235
$737$	−23114.7	+	13517.8i	−1.15528	+	0.675622i
$738$	−11550.1			−0.576105
$739$	−6586.56	+	11408.3i	−0.327863	+	0.567875i	−0.982088	−	0.188425i	$-0.939662\pi$
$739$	−6586.56	+	11408.3i	−0.327863	+	0.567875i	0.654225	+	0.756300i	$0.272995\pi$
$740$	47788.8			2.37399
$741$	2369.20	+	4103.58i	0.117456	+	0.203440i
$742$	−35990.5			−1.78066
$743$	−7205.11	+	12479.6i	−0.355760	+	0.616195i	−0.987248	−	0.159191i	$-0.949111\pi$
$743$	−7205.11	+	12479.6i	−0.355760	+	0.616195i	0.631488	+	0.775386i	$0.282445\pi$
$744$	111.228	+	192.653i	0.00548095	+	0.00949328i
$745$	14220.7			0.699336
$746$	−21549.7			−1.05763
$747$	−1480.58	+	2564.45i	−0.0725190	+	0.125607i
$748$	−6441.77	−	11157.5i	−0.314886	−	0.545398i
$749$	4067.81	+	7045.66i	0.198444	+	0.343715i
$750$	−17445.3	+	30216.1i	−0.849349	+	1.47112i
$751$	10637.5			0.516868			0.258434	−	0.966029i	$-0.416794\pi$
$751$	10637.5			0.516868			0.258434	+	0.966029i	$0.416794\pi$
$752$	−22410.1			−1.08672
$753$	−1110.40	+	1923.27i	−0.0537387	+	0.0930782i
$754$	−2392.45	+	4143.84i	−0.115554	+	0.200145i
$755$	1122.15	−	1943.63i	0.0540919	−	0.0936899i
$756$	−3094.56	+	5359.93i	−0.148873	+	0.257856i
$757$	−8767.26	−	15185.3i	−0.420940	−	0.729089i	0.575092	−	0.818089i	$-0.304966\pi$
$757$	−8767.26	−	15185.3i	−0.420940	−	0.729089i	−0.996032	+	0.0889999i	$0.971633\pi$
$758$	17594.5	+	30474.5i	0.843087	+	1.46027i
$759$	21673.3			1.03648
$760$	−90.4651	+	156.690i	−0.00431778	+	0.00747861i
$761$	22462.1			1.06997			0.534987	−	0.844860i	$-0.320317\pi$
$761$	22462.1			1.06997			0.534987	+	0.844860i	$0.320317\pi$
$762$	6339.46			0.301384
$763$	7591.97	+	13149.7i	0.360220	+	0.623919i
$764$	3081.89			0.145941
$765$	2918.17	−	5054.41i	0.137917	−	0.238879i
$766$	−25959.0	−	44962.3i	−1.22446	−	2.12083i
$767$	−17324.8	+	30007.5i	−0.815597	+	1.41266i
$768$	−5996.44	−	10386.1i	−0.281742	−	0.487992i
$769$	20187.2	+	34965.3i	0.946645	+	1.63964i	0.752423	+	0.658680i	$0.228885\pi$
$769$	20187.2	+	34965.3i	0.946645	+	1.63964i	0.194222	+	0.980958i	$0.437782\pi$
$770$	55174.7	+	95565.4i	2.58228	+	4.47265i
$771$	2769.02	+	4796.09i	0.129344	+	0.224030i
$772$	4560.72	+	7899.39i	0.212621	+	0.368271i
$773$	−14546.1	−	25194.5i	−0.676825	−	1.17230i	−0.975932	−	0.218076i	$-0.930022\pi$
$773$	−14546.1	−	25194.5i	−0.676825	−	1.17230i	0.299107	−	0.954220i	$-0.403311\pi$
$774$	3482.11	−	6031.19i	0.161708	−	0.280086i
$775$	26504.4	+	45907.0i	1.22847	+	2.12778i
$776$	−236.674	+	409.932i	−0.0109486	+	0.0189635i
$777$	25214.1			1.16416
$778$	15123.7	+	26195.0i	0.696929	+	1.20712i
$779$	−7682.55			−0.353345
$780$	−31770.0			−1.45840
$781$	−16741.0	+	28996.3i	−0.767018	+	1.32851i
$782$	19350.2			0.884863
$783$	244.826	+	424.050i	0.0111741	+	0.0193542i
$784$	14511.8	+	25135.2i	0.661070	+	1.14501i
$785$	34916.2	−	60476.6i	1.58753	−	2.74968i
$786$	10600.9	−	18361.3i	0.481072	−	0.833241i
$787$	4291.03	−	7432.28i	0.194357	−	0.336636i	−0.752333	−	0.658783i	$-0.771071\pi$
$787$	4291.03	−	7432.28i	0.194357	−	0.336636i	0.946689	+	0.322148i	$0.104405\pi$
$788$	−18211.8	+	31543.7i	−0.823310	+	1.42601i
$789$	−5572.54			−0.251442
$790$	58263.3			2.62394
$791$	−9462.35	+	16389.3i	−0.425338	+	0.736707i
$792$	83.2104	+	144.125i	0.00373327	+	0.00646622i
$793$	−28455.7	−	49286.8i	−1.27427	−	2.20709i
$794$	894.798	−	1549.84i	0.0399939	−	0.0692715i
$795$	−18905.6			−0.843413
$796$	8264.01			0.367978
$797$	−2027.67	−	3512.02i	−0.0901174	−	0.156088i	0.817443	−	0.576010i	$-0.195391\pi$
$797$	−2027.67	−	3512.02i	−0.0901174	−	0.156088i	−0.907560	+	0.419922i	$0.862058\pi$
$798$	−4092.68	+	7088.73i	−0.181553	+	0.314459i
$799$	−11552.5			−0.511513
$800$	34750.7	+	60190.0i	1.53578	+	2.66005i
$801$	13709.0			0.604724
$802$	−9537.72	+	16519.8i	−0.419936	+	0.727351i
$803$	5274.51			0.231797
$804$	11495.8	−	6722.92i	0.504263	−	0.294899i
$805$	−83354.8			−3.64953
$806$	−25830.4	+	44739.6i	−1.12883	+	1.95519i
$807$	−3749.24			−0.163543
$808$	116.350	+	201.524i	0.00506582	+	0.00877426i
$809$	29194.9			1.26877			0.634386	−	0.773016i	$-0.281253\pi$
$809$	29194.9			1.26877			0.634386	+	0.773016i	$0.281253\pi$
$810$	−3232.15	+	5598.25i	−0.140205	+	0.242843i
$811$	14514.2	+	25139.3i	0.628436	+	1.08848i	0.987866	+	0.155311i	$0.0496379\pi$
$811$	14514.2	+	25139.3i	0.628436	+	1.08848i	−0.359430	+	0.933172i	$0.617029\pi$
$812$	−4157.07			−0.179661
$813$	−21398.7			−0.923105
$814$	29067.1	−	50345.7i	1.25160	−	2.16783i
$815$	7972.96	+	13809.6i	0.342676	+	0.593532i
$816$	−3092.09	−	5355.66i	−0.132653	−	0.229762i
$817$	2316.12	−	4011.64i	0.0991810	−	0.171787i
$818$	35465.2			1.51590
$819$	−16762.3			−0.715169
$820$	25754.9	−	44608.9i	1.09683	−	1.89977i
$821$	16602.5	−	28756.4i	0.705764	−	1.22242i	−0.260651	−	0.965433i	$-0.583937\pi$
$821$	16602.5	−	28756.4i	0.705764	−	1.22242i	0.966415	−	0.256986i	$-0.0827293\pi$
$822$	3705.82	−	6418.67i	0.157245	−	0.272356i
$823$	17566.5	−	30426.1i	0.744022	−	1.28868i	−0.206628	−	0.978420i	$-0.566249\pi$
$823$	17566.5	−	30426.1i	0.744022	−	1.28868i	0.950650	−	0.310265i	$-0.100418\pi$
$824$	−66.3544	−	114.929i	−0.00280530	−	0.00485892i
$825$	19828.1	+	34343.3i	0.836758	+	1.44931i
$826$	−59855.5			−2.52136
$827$	−15384.5	+	26646.7i	−0.646882	+	1.12043i	0.336982	+	0.941511i	$0.390594\pi$
$827$	−15384.5	+	26646.7i	−0.646882	+	1.12043i	−0.983863	+	0.178921i	$0.942739\pi$
$828$	−10779.0			−0.452411
$829$	−27014.1			−1.13177			−0.565886	−	0.824483i	$-0.691466\pi$
$829$	−27014.1			−1.13177			−0.565886	+	0.824483i	$0.691466\pi$
$830$	−13128.9	−	22739.9i	−0.549048	−	0.950979i
$831$	8144.69			0.339995
$832$	−17231.5	+	29845.8i	−0.718021	+	1.24365i
$833$	7480.93	+	12957.3i	0.311163	+	0.538950i
$834$	7633.84	−	13222.2i	0.316953	−	0.548978i
$835$	−11883.4	−	20582.7i	−0.492506	−	0.853045i
$836$	4745.77	+	8219.92i	0.196335	+	0.340062i
$837$	2643.30	+	4578.32i	0.109158	+	0.189068i
$838$	−10651.7	−	18449.3i	−0.439091	−	0.760528i
$839$	−13632.7	−	23612.5i	−0.560968	−	0.971625i	−0.997412	−	0.0718940i	$-0.977096\pi$
$839$	−13632.7	−	23612.5i	−0.560968	−	0.971625i	0.436444	−	0.899731i	$-0.356238\pi$
$840$	−320.024	−	554.298i	−0.0131451	−	0.0227680i
$841$	12030.1	−	20836.7i	0.493257	−	0.854347i
$842$	−33694.5	−	58360.6i	−1.37909	−	2.38865i
$843$	8301.42	−	14378.5i	0.339165	−	0.587451i
$844$	36622.1			1.49358
$845$	−21169.8	−	36667.2i	−0.861852	−	1.49277i
$846$	12795.6			0.520001
$847$	29820.0			1.20971
$848$	−10016.2	+	17348.6i	−0.405611	+	0.702539i
$849$	−22486.7			−0.909002
$850$	17702.8	+	30662.1i	0.714354	+	1.23730i
$851$	21956.5	+	38029.7i	0.884440	+	1.53190i
$852$	8325.98	−	14421.0i	0.334793	−	0.579878i
$853$	6674.11	−	11559.9i	0.267898	−	0.464013i	−0.700421	−	0.713730i	$-0.747004\pi$
$853$	6674.11	−	11559.9i	0.267898	−	0.464013i	0.968319	+	0.249717i	$0.0803376\pi$
$854$	49155.9	−	85140.5i	1.96965	−	3.41153i
$855$	−2149.87	+	3723.68i	−0.0859928	+	0.148944i
$856$	−108.798			−0.00434422
$857$	20946.0			0.834891			0.417446	−	0.908702i	$-0.362925\pi$
$857$	20946.0			0.834891			0.417446	+	0.908702i	$0.362925\pi$
$858$	−19323.8	+	33469.9i	−0.768887	+	1.33175i
$859$	−7937.12	−	13747.5i	−0.315263	−	0.546052i	0.664230	−	0.747528i	$-0.268759\pi$
$859$	−7937.12	−	13747.5i	−0.315263	−	0.546052i	−0.979493	+	0.201476i	$0.935426\pi$
$860$	15529.1	+	26897.2i	0.615742	+	1.06650i
$861$	13588.7	−	23536.3i	0.537864	−	0.931609i
$862$	−9052.42			−0.357687
$863$	−5824.93			−0.229760			−0.114880	−	0.993379i	$-0.536648\pi$
$863$	−5824.93			−0.229760			−0.114880	+	0.993379i	$0.536648\pi$
$864$	3465.70	+	6002.76i	0.136465	+	0.236364i
$865$	14073.7	−	24376.3i	0.553202	−	0.958173i
$866$	5347.12			0.209818
$867$	5775.51	+	10003.5i	0.226236	+	0.391852i
$868$	−44882.5			−1.75508
$869$	17823.0	−	30870.3i	0.695747	−	1.20507i
$870$	−4341.91			−0.169201
$871$	31336.1	+	17859.5i	1.21904	+	0.694773i
$872$	−203.056			−0.00788572
$873$	−5624.48	+	9741.88i	−0.218052	+	0.377678i
$874$	−14255.7			−0.551723
$875$	−41048.7	−	71098.4i	−1.58594	−	2.74693i
$876$	−2623.22			−0.101176
$877$	3481.97	−	6030.94i	0.134068	−	0.232213i	−0.791173	−	0.611592i	$-0.790529\pi$
$877$	3481.97	−	6030.94i	0.134068	−	0.232213i	0.925241	+	0.379380i	$0.123863\pi$
$878$	10470.1	+	18134.8i	0.402448	+	0.697061i
$879$	17488.0			0.671052
$880$	61420.9			2.35284
$881$	−8335.31	+	14437.2i	−0.318756	+	0.552101i	−0.980229	−	0.197868i	$-0.936598\pi$
$881$	−8335.31	+	14437.2i	−0.318756	+	0.552101i	0.661473	+	0.749969i	$0.269932\pi$
$882$	−8285.86	−	14351.5i	−0.316326	−	0.547892i
$883$	−5970.86	−	10341.8i	−0.227560	−	0.394146i	0.729524	−	0.683955i	$-0.239741\pi$
$883$	−5970.86	−	10341.8i	−0.227560	−	0.394146i	−0.957084	+	0.289809i	$0.906408\pi$
$884$	−8676.89	+	15028.8i	−0.330131	+	0.571803i
$885$	−31441.8			−1.19424
$886$	−32158.9			−1.21941
$887$	−4192.26	+	7261.21i	−0.158695	+	0.274868i	−0.934398	−	0.356230i	$-0.884062\pi$
$887$	−4192.26	+	7261.21i	−0.158695	+	0.274868i	0.775703	+	0.631098i	$0.217395\pi$
$888$	−168.595	+	292.015i	−0.00637126	+	0.0110353i
$889$	−7458.37	+	12918.3i	−0.281379	+	0.487362i
$890$	−60781.3	+	105276.i	−2.28921	+	3.96503i
$891$	1977.46	+	3425.06i	0.0743518	+	0.128781i
$892$	−8444.72	−	14626.7i	−0.316985	−	0.549033i
$893$	8510.96			0.318935
$894$	−4301.79	+	7450.92i	−0.160932	+	0.278743i
$895$	−5353.06			−0.199925
$896$	−1372.69			−0.0511811
$897$	−14596.7	−	25282.2i	−0.543332	−	0.941079i
$898$	−6369.58			−0.236699
$899$	−1775.44	+	3075.14i	−0.0658666	+	0.114084i
$900$	−9861.30	−	17080.3i	−0.365233	−	0.632602i
$901$	−5163.43	+	8943.32i	−0.190920	+	0.330683i
$902$	−31330.5	−	54265.9i	−1.15653	−	2.00317i
$903$	8193.39	+	14191.4i	0.301948	+	0.522989i
$904$	−126.541	−	219.175i	−0.00465563	−	0.00806378i
$905$	12634.3	+	21883.2i	0.464064	+	0.803782i
$906$	678.909	+	1175.91i	0.0248954	+	0.0431201i
$907$	−6952.92	−	12042.8i	−0.254540	−	0.440876i	0.710230	−	0.703969i	$-0.248591\pi$
$907$	−6952.92	−	12042.8i	−0.254540	−	0.440876i	−0.964770	+	0.263093i	$0.915257\pi$
$908$	23794.8	−	41213.8i	0.869667	−	1.50631i
$909$	2765.02	+	4789.15i	0.100891	+	0.174748i
$910$	74318.8	−	128724.i	2.70730	−	4.68919i
$911$	−26165.8			−0.951604			−0.475802	−	0.879552i	$-0.657842\pi$
$911$	−26165.8			−0.951604			−0.475802	+	0.879552i	$0.657842\pi$
$912$	2278.00	+	3945.62i	0.0827107	+	0.143259i
$913$	−16064.7			−0.582327
$914$	−16542.5			−0.598664
$915$	25821.3	−	44723.9i	0.932926	−	1.61587i
$916$	49621.2			1.78988
$917$	24943.9	+	43204.2i	0.898279	+	1.55586i
$918$	1765.51	+	3057.94i	0.0634753	+	0.109942i
$919$	18979.6	−	32873.6i	0.681260	−	1.17998i	−0.293336	−	0.956009i	$-0.594766\pi$
$919$	18979.6	−	32873.6i	0.681260	−	1.17998i	0.974596	−	0.223968i	$-0.0719011\pi$
$920$	557.356	−	965.369i	0.0199734	−	0.0345949i
$921$	−1239.94	+	2147.63i	−0.0443619	+	0.0768370i
$922$	17043.9	−	29521.0i	0.608799	−	1.05447i
$923$	45099.4			1.60831
$924$	−33576.8			−1.19545
$925$	−40174.3	+	69583.9i	−1.42802	+	2.47341i
$926$	−30952.3	−	53610.9i	−1.09844	−	1.90255i
$927$	−1576.89	−	2731.25i	−0.0558702	−	0.0967701i
$928$	−2327.82	+	4031.91i	−0.0823432	+	0.142623i
$929$	4513.07			0.159385			0.0796927	−	0.996819i	$-0.474606\pi$
$929$	4513.07			0.159385			0.0796927	+	0.996819i	$0.474606\pi$
$930$	−46878.1			−1.65290
$931$	−5511.34	−	9545.92i	−0.194014	−	0.336042i
$932$	17624.4	−	30526.4i	0.619428	−	1.07288i
$933$	8853.08			0.310650
$934$	−6444.22	−	11161.7i	−0.225762	−	0.391031i
$935$	31662.9			1.10747
$936$	112.082	−	194.132i	0.00391401	−	0.00677927i
$937$	−26634.1			−0.928599			−0.464300	−	0.885678i	$-0.653694\pi$
$937$	−26634.1			−0.928599			−0.464300	+	0.885678i	$0.653694\pi$
$938$	347.599	+	62305.0i	0.0120997	+	2.16880i
$939$	−14120.3			−0.490734
$940$	−28532.1	+	49419.0i	−0.990015	+	1.71476i
$941$	16372.9			0.567205			0.283602	−	0.958942i	$-0.408470\pi$
$941$	16372.9			0.567205			0.283602	+	0.958942i	$0.408470\pi$
$942$	21124.5	+	36588.7i	0.730650	+	1.26552i
$943$	47332.3			1.63452
$944$	−16657.9	+	28852.3i	−0.574331	+	0.994771i
$945$	−7605.25	−	13172.7i	−0.261798	−	0.453447i
$946$	37781.8			1.29851
$947$	53831.2			1.84718			0.923589	−	0.383383i	$-0.125241\pi$
$947$	53831.2			1.84718			0.923589	+	0.383383i	$0.125241\pi$
$948$	−8864.08	+	15353.0i	−0.303684	+	0.525995i
$949$	−3552.31	−	6152.78i	−0.121510	−	0.210461i
$950$	−13042.0	−	22589.4i	−0.445408	−	0.771469i
$951$	12520.3	−	21685.8i	0.426917	−	0.739442i
$952$	−349.615			−0.0119024
$953$	−26400.2			−0.897363			−0.448682	−	0.893692i	$-0.648106\pi$
$953$	−26400.2			−0.897363			−0.448682	+	0.893692i	$0.648106\pi$
$954$	5719.00	−	9905.60i	0.194087	−	0.336169i
$955$	−3787.06	+	6559.38i	−0.128321	+	0.222258i
$956$	−10753.3	+	18625.3i	−0.363795	+	0.630111i
$957$	−1328.21	+	2300.53i	−0.0448641	+	0.0777069i
$958$	−20937.2	−	36264.3i	−0.706107	−	1.22301i
$959$	8719.78	+	15103.1i	0.293615	+	0.508555i
$960$	−31272.4			−1.05137
$961$	−4273.25	+	7401.49i	−0.143441	+	0.248447i
$962$	−78305.2			−2.62439
$963$	−2585.55			−0.0865195
$964$	22989.6	+	39819.1i	0.768096	+	1.33038i
$965$	−22417.0			−0.747803
$966$	25215.1	−	43673.7i	0.839835	−	1.45464i
$967$	559.902	+	969.778i	0.0186197	+	0.0322502i	0.875185	−	0.483788i	$-0.160739\pi$
$967$	559.902	+	969.778i	0.0186197	+	0.0322502i	−0.856565	+	0.516038i	$0.827406\pi$
$968$	−199.393	+	345.358i	−0.00662058	+	0.0114672i
$969$	1174.33	+	2033.99i	0.0389316	+	0.0674316i
$970$	−49874.3	−	86384.8i	−1.65089	−	2.85943i
$971$	−23583.3	−	40847.5i	−0.779429	−	1.35001i	−0.932271	−	0.361760i	$-0.882176\pi$
$971$	−23583.3	−	40847.5i	−0.779429	−	1.35001i	0.152843	−	0.988251i	$-0.451157\pi$
$972$	−983.470	−	1703.42i	−0.0324535	−	0.0562111i
$973$	17962.4	+	31111.8i	0.591828	+	1.02508i
$974$	−14070.0	−	24369.9i	−0.462866	−	0.801707i
$975$	26707.9	−	46259.4i	0.877269	−	1.51947i
$976$	−27360.3	−	47389.5i	−0.897319	−	1.55420i
$977$	8488.40	−	14702.3i	0.277961	−	0.481443i	−0.692917	−	0.721017i	$-0.743675\pi$
$977$	8488.40	−	14702.3i	0.277961	−	0.481443i	0.970878	+	0.239575i	$0.0770081\pi$
$978$	−9647.37			−0.315428
$979$	37186.6	+	64409.0i	1.21398	+	2.10268i
$980$	73904.7			2.40898
$981$	−4825.55			−0.157052
$982$	−34632.8	+	59985.7i	−1.12543	+	1.94931i
$983$	46351.4			1.50395			0.751973	−	0.659193i	$-0.229102\pi$
$983$	46351.4			1.50395			0.751973	+	0.659193i	$0.229102\pi$
$984$	181.723	+	314.753i	0.00588731	+	0.0101971i
$985$	−44757.7	−	77522.6i	−1.44782	−	2.50769i
$986$	−1185.85	+	2053.94i	−0.0383012	+	0.0663397i
$987$	−15054.0	+	26074.2i	−0.485484	+	0.840883i
$988$	6392.43	−	11072.0i	0.205840	−	0.356526i
$989$	−14269.7	+	24715.8i	−0.458795	+	0.794657i
$990$	−35069.7			−1.12585
$991$	−4243.61			−0.136027			−0.0680135	−	0.997684i	$-0.521666\pi$
$991$	−4243.61			−0.136027			−0.0680135	+	0.997684i	$0.521666\pi$
$992$	−25132.7	+	43531.1i	−0.804399	+	1.39326i
$993$	4358.29	+	7548.77i	0.139281	+	0.241242i
$994$	38953.5	+	67469.5i	1.24299	+	2.15292i
$995$	−10154.9	+	17588.8i	−0.323550	+	0.560405i
$996$	7989.62			0.254178
$997$	43637.5			1.38617			0.693086	−	0.720854i	$-0.256250\pi$
$997$	43637.5			1.38617			0.693086	+	0.720854i	$0.256250\pi$
$998$	32318.6	+	55977.4i	1.02508	+	1.77548i
$999$	−4006.59	+	6939.62i	−0.126890	+	0.219780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.a.163.4	yes	32
67.37	even	3	inner	201.4.e.a.37.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.a.37.4	✓	32	67.37	even	3	inner
201.4.e.a.163.4	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00589 + 3.47431i) q^{2} +3.00000 q^{3} +(-4.04720 - 7.00996i) q^{4} +19.8930 q^{5} +(-6.01767 + 10.4229i) q^{6} +(-14.1596 - 24.5251i) q^{7} +0.378714 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(-2.00589 + 3.47431i) q^{2} +3.00000 q^{3} +(-4.04720 - 7.00996i) q^{4} +19.8930 q^{5} +(-6.01767 + 10.4229i) q^{6} +(-14.1596 - 24.5251i) q^{7} +0.378714 q^{8} +9.00000 q^{9} +(-39.9031 + 69.1143i) q^{10} +(24.4131 + 42.2847i) q^{11} +(-12.1416 - 21.0299i) q^{12} +(32.8838 - 56.9564i) q^{13} +113.610 q^{14} +59.6789 q^{15} +(31.6179 - 54.7639i) q^{16} +(16.2993 - 28.2311i) q^{17} +(-18.0530 + 31.2688i) q^{18} +(-12.0080 + 20.7984i) q^{19} +(-80.5108 - 139.449i) q^{20} +(-42.4787 - 73.5753i) q^{21} -195.880 q^{22} +(73.9812 - 128.139i) q^{23} +1.13614 q^{24} +270.730 q^{25} +(131.923 + 228.497i) q^{26} +27.0000 q^{27} +(-114.613 + 198.516i) q^{28} +(9.06761 + 15.7056i) q^{29} +(-119.709 + 207.343i) q^{30} +(97.8998 + 169.567i) q^{31} +(128.359 + 222.325i) q^{32} +(73.2393 + 126.854i) q^{33} +(65.3891 + 113.257i) q^{34} +(-281.676 - 487.877i) q^{35} +(-36.4248 - 63.0896i) q^{36} +(-148.392 + 257.023i) q^{37} +(-48.1733 - 83.4387i) q^{38} +(98.6514 - 170.869i) q^{39} +7.53376 q^{40} +(159.947 + 277.036i) q^{41} +340.831 q^{42} -192.882 q^{43} +(197.609 - 342.270i) q^{44} +179.037 q^{45} +(296.796 + 514.066i) q^{46} +(-177.194 - 306.909i) q^{47} +(94.8538 - 164.292i) q^{48} +(-229.487 + 397.483i) q^{49} +(-543.055 + 940.600i) q^{50} +(48.8978 - 84.6934i) q^{51} -532.349 q^{52} -316.789 q^{53} +(-54.1591 + 93.8063i) q^{54} +(485.649 + 841.169i) q^{55} +(-5.36243 - 9.28801i) q^{56} +(-36.0239 + 62.3952i) q^{57} -72.7546 q^{58} -526.850 q^{59} +(-241.532 - 418.347i) q^{60} +(432.671 - 749.408i) q^{61} -785.506 q^{62} +(-127.436 - 220.726i) q^{63} -524.011 q^{64} +(654.156 - 1133.03i) q^{65} -587.640 q^{66} +(3.05957 + 548.410i) q^{67} -263.865 q^{68} +(221.943 - 384.417i) q^{69} +2260.04 q^{70} +(342.870 + 593.868i) q^{71} +3.40843 q^{72} +(54.0131 - 93.5534i) q^{73} +(-595.318 - 1031.12i) q^{74} +812.191 q^{75} +194.395 q^{76} +(691.358 - 1197.47i) q^{77} +(395.768 + 685.490i) q^{78} +(-365.029 - 632.250i) q^{79} +(628.975 - 1089.42i) q^{80} +81.0000 q^{81} -1283.35 q^{82} +(-164.509 + 284.938i) q^{83} +(-343.840 + 595.548i) q^{84} +(324.241 - 561.601i) q^{85} +(386.901 - 670.132i) q^{86} +(27.2028 + 47.1167i) q^{87} +(9.24559 + 16.0138i) q^{88} +1523.22 q^{89} +(-359.128 + 622.028i) q^{90} -1862.48 q^{91} -1197.67 q^{92} +(293.699 + 508.702i) q^{93} +1421.73 q^{94} +(-238.874 + 413.742i) q^{95} +(385.078 + 666.974i) q^{96} +(-624.942 + 1082.43i) q^{97} +(-920.651 - 1594.61i) q^{98} +(219.718 + 380.563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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