LMFDB - Embedded newform 38.4.e.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,4,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.24207258022$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 135 x^{10} + 730 x^{9} + 7953 x^{8} - 36258 x^{7} - 262940 x^{6} + 918855 x^{5} + \cdots + 272110107 $ x^12 - 6x^11 - 135x^10 + 730x^9 + 7953x^8 - 36258x^7 - 262940x^6 + 918855x^5 + 5157591x^4 - 11890401x^3 - 56759508x^2 + 62864118*x + 272110107
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.1
Root			$5.05412 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	38.5
Dual form			38.4.e.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 + 0.684040i) q^{2} +(-1.54081 + 8.73839i) q^{3} +(3.06418 - 2.57115i) q^{4} +(-15.3487 - 12.8791i) q^{5} +(-3.08163 - 17.4768i) q^{6} +(4.71270 + 8.16264i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-48.6136 - 17.6939i) q^{9} +O(q^{10})$	\(q+(-1.87939 + 0.684040i) q^{2} +(-1.54081 + 8.73839i) q^{3} +(3.06418 - 2.57115i) q^{4} +(-15.3487 - 12.8791i) q^{5} +(-3.08163 - 17.4768i) q^{6} +(4.71270 + 8.16264i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-48.6136 - 17.6939i) q^{9} +(37.6558 + 13.7056i) q^{10} +(-24.7562 + 42.8791i) q^{11} +(17.7464 + 30.7376i) q^{12} +(3.93183 + 22.2985i) q^{13} +(-14.4406 - 12.1171i) q^{14} +(136.192 - 114.278i) q^{15} +(2.77837 - 15.7569i) q^{16} +(30.4142 - 11.0699i) q^{17} +103.467 q^{18} +(-28.5348 + 77.7481i) q^{19} -80.1450 q^{20} +(-78.5897 + 28.6043i) q^{21} +(17.1955 - 97.5206i) q^{22} +(-0.237340 + 0.199152i) q^{23} +(-54.3781 - 45.6286i) q^{24} +(48.0052 + 272.251i) q^{25} +(-22.6425 - 39.2180i) q^{26} +(109.733 - 190.063i) q^{27} +(35.4279 + 12.8947i) q^{28} +(-39.4741 - 14.3674i) q^{29} +(-177.785 + 307.933i) q^{30} +(-0.938479 - 1.62549i) q^{31} +(5.55674 + 31.5138i) q^{32} +(-336.549 - 282.398i) q^{33} +(-49.5877 + 41.6090i) q^{34} +(32.7934 - 185.981i) q^{35} +(-194.455 + 70.7757i) q^{36} +331.421 q^{37} +(0.445152 - 165.638i) q^{38} -200.911 q^{39} +(150.623 - 54.8224i) q^{40} +(-8.17216 + 46.3466i) q^{41} +(128.134 - 107.517i) q^{42} +(-293.235 - 246.054i) q^{43} +(34.3910 + 195.041i) q^{44} +(518.273 + 897.675i) q^{45} +(0.309825 - 0.536633i) q^{46} +(115.099 + 41.8927i) q^{47} +(133.409 + 48.5570i) q^{48} +(127.081 - 220.110i) q^{49} +(-276.451 - 478.827i) q^{50} +(49.8701 + 282.827i) q^{51} +(69.3807 + 58.2173i) q^{52} +(-71.6880 + 60.1534i) q^{53} +(-76.2196 + 432.263i) q^{54} +(932.217 - 339.299i) q^{55} -75.4033 q^{56} +(-635.426 - 369.144i) q^{57} +84.0149 q^{58} +(-517.526 + 188.364i) q^{59} +(123.489 - 700.338i) q^{60} +(-404.046 + 339.035i) q^{61} +(2.87567 + 2.41297i) q^{62} +(-84.6726 - 480.202i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(226.835 - 392.891i) q^{65} +(825.678 + 300.522i) q^{66} +(605.223 + 220.283i) q^{67} +(64.7322 - 112.119i) q^{68} +(-1.37457 - 2.38082i) q^{69} +(65.5868 + 371.961i) q^{70} +(468.607 + 393.208i) q^{71} +(317.042 - 266.030i) q^{72} +(-70.7704 + 401.359i) q^{73} +(-622.867 + 226.705i) q^{74} -2453.00 q^{75} +(112.466 + 311.601i) q^{76} -466.675 q^{77} +(377.590 - 137.431i) q^{78} +(70.3461 - 398.953i) q^{79} +(-245.578 + 206.065i) q^{80} +(421.750 + 353.890i) q^{81} +(-16.3443 - 92.6933i) q^{82} +(387.299 + 670.822i) q^{83} +(-167.267 + 289.715i) q^{84} +(-609.386 - 221.798i) q^{85} +(719.413 + 261.845i) q^{86} +(186.370 - 322.803i) q^{87} +(-198.050 - 343.033i) q^{88} +(-152.983 - 867.607i) q^{89} +(-1588.08 - 1332.56i) q^{90} +(-163.485 + 137.180i) q^{91} +(-0.215202 + 1.22047i) q^{92} +(15.6502 - 5.69621i) q^{93} -244.972 q^{94} +(1439.29 - 825.827i) q^{95} -283.942 q^{96} +(-1391.18 + 506.347i) q^{97} +(-88.2694 + 500.601i) q^{98} +(1962.19 - 1646.47i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) $ 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9} - 9 q^{11} + 36 q^{12} + 39 q^{13} - 138 q^{14} + 423 q^{15} + 69 q^{17} + 132 q^{18} - 462 q^{19} - 216 q^{20} - 279 q^{21} + 204 q^{22} - 66 q^{23} - 72 q^{24} + 342 q^{25} + 48 q^{26} + 189 q^{27} + 192 q^{28} + 159 q^{29} + 72 q^{31} - 1560 q^{33} + 408 q^{34} - 135 q^{35} - 108 q^{36} + 1116 q^{37} - 294 q^{38} - 1248 q^{39} + 147 q^{41} + 414 q^{42} - 117 q^{43} + 408 q^{44} + 1296 q^{45} + 528 q^{46} + 783 q^{47} + 288 q^{48} + 1413 q^{49} - 354 q^{50} - 2301 q^{51} - 348 q^{52} - 249 q^{53} - 540 q^{54} + 2187 q^{55} - 336 q^{56} - 2670 q^{57} - 1932 q^{58} - 4248 q^{59} + 324 q^{60} + 3114 q^{61} - 438 q^{62} + 363 q^{63} - 384 q^{64} + 495 q^{65} + 822 q^{66} + 3060 q^{67} + 408 q^{68} - 237 q^{69} - 270 q^{70} + 1686 q^{71} + 432 q^{72} + 1626 q^{73} + 90 q^{74} - 1854 q^{75} - 1416 q^{77} - 108 q^{78} - 327 q^{79} + 3483 q^{81} + 294 q^{82} + 927 q^{83} + 204 q^{84} - 3294 q^{85} + 1188 q^{86} + 2892 q^{87} - 72 q^{88} - 6366 q^{89} - 5076 q^{90} + 840 q^{91} - 156 q^{92} + 870 q^{93} + 3432 q^{94} + 513 q^{95} - 576 q^{96} - 8052 q^{97} + 378 q^{98} + 4494 q^{99}+O(q^{100}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9 - 9 * q^11 + 36 * q^12 + 39 * q^13 - 138 * q^14 + 423 * q^15 + 69 * q^17 + 132 * q^18 - 462 * q^19 - 216 * q^20 - 279 * q^21 + 204 * q^22 - 66 * q^23 - 72 * q^24 + 342 * q^25 + 48 * q^26 + 189 * q^27 + 192 * q^28 + 159 * q^29 + 72 * q^31 - 1560 * q^33 + 408 * q^34 - 135 * q^35 - 108 * q^36 + 1116 * q^37 - 294 * q^38 - 1248 * q^39 + 147 * q^41 + 414 * q^42 - 117 * q^43 + 408 * q^44 + 1296 * q^45 + 528 * q^46 + 783 * q^47 + 288 * q^48 + 1413 * q^49 - 354 * q^50 - 2301 * q^51 - 348 * q^52 - 249 * q^53 - 540 * q^54 + 2187 * q^55 - 336 * q^56 - 2670 * q^57 - 1932 * q^58 - 4248 * q^59 + 324 * q^60 + 3114 * q^61 - 438 * q^62 + 363 * q^63 - 384 * q^64 + 495 * q^65 + 822 * q^66 + 3060 * q^67 + 408 * q^68 - 237 * q^69 - 270 * q^70 + 1686 * q^71 + 432 * q^72 + 1626 * q^73 + 90 * q^74 - 1854 * q^75 - 1416 * q^77 - 108 * q^78 - 327 * q^79 + 3483 * q^81 + 294 * q^82 + 927 * q^83 + 204 * q^84 - 3294 * q^85 + 1188 * q^86 + 2892 * q^87 - 72 * q^88 - 6366 * q^89 - 5076 * q^90 + 840 * q^91 - 156 * q^92 + 870 * q^93 + 3432 * q^94 + 513 * q^95 - 576 * q^96 - 8052 * q^97 + 378 * q^98 + 4494 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$3$	−1.54081	+	8.73839i	−0.296530	+	1.68170i	0.364389	+	0.931247i	$0.381278\pi$
$3$	−1.54081	+	8.73839i	−0.296530	+	1.68170i	−0.660919	+	0.750457i	$0.729833\pi$
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	−15.3487	−	12.8791i	−1.37283	−	1.15194i	−0.971783	−	0.235878i	$-0.924203\pi$
$5$	−15.3487	−	12.8791i	−1.37283	−	1.15194i	−0.401043	−	0.916059i	$-0.631352\pi$
$6$	−3.08163	−	17.4768i	−0.209678	−	1.18914i
$7$	4.71270	+	8.16264i	0.254462	+	0.440741i	0.964749	−	0.263171i	$-0.0847683\pi$
$7$	4.71270	+	8.16264i	0.254462	+	0.440741i	−0.710287	+	0.703912i	$0.751435\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	−48.6136	−	17.6939i	−1.80051	−	0.655330i
$10$	37.6558	+	13.7056i	1.19078	+	0.433409i
$11$	−24.7562	+	42.8791i	−0.678572	+	1.17532i	0.296839	+	0.954927i	$0.404067\pi$
$11$	−24.7562	+	42.8791i	−0.678572	+	1.17532i	−0.975411	+	0.220393i	$0.929266\pi$
$12$	17.7464	+	30.7376i	0.426912	+	0.739433i
$13$	3.93183	+	22.2985i	0.0838841	+	0.475730i	0.997592	+	0.0693584i	$0.0220952\pi$
$13$	3.93183	+	22.2985i	0.0838841	+	0.475730i	−0.913708	+	0.406372i	$0.866794\pi$
$14$	−14.4406	−	12.1171i	−0.275672	−	0.231316i
$15$	136.192	−	114.278i	2.34430	−	1.96710i
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	30.4142	−	11.0699i	0.433913	−	0.157931i	−0.115823	−	0.993270i	$-0.536951\pi$
$17$	30.4142	−	11.0699i	0.433913	−	0.157931i	0.549736	+	0.835338i	$0.314728\pi$
$18$	103.467			1.35486
$19$	−28.5348	+	77.7481i	−0.344544	+	0.938770i
$19$	−28.5348	+	77.7481i	−0.344544	+	0.938770i
$20$	−80.1450			−0.896048
$21$	−78.5897	+	28.6043i	−0.816652	+	0.297237i
$22$	17.1955	−	97.5206i	0.166641	−	0.945066i
$23$	−0.237340	+	0.199152i	−0.00215169	+	0.00180548i	−0.643863	−	0.765141i	$-0.722669\pi$
$23$	−0.237340	+	0.199152i	−0.00215169	+	0.00180548i	0.641711	+	0.766946i	$0.278225\pi$
$24$	−54.3781	−	45.6286i	−0.462495	−	0.388079i
$25$	48.0052	+	272.251i	0.384042	+	2.17801i
$26$	−22.6425	−	39.2180i	−0.170791	−	0.295818i
$27$	109.733	−	190.063i	0.782151	−	1.35473i
$28$	35.4279	+	12.8947i	0.239116	+	0.0870312i
$29$	−39.4741	−	14.3674i	−0.252764	−	0.0919986i	0.212531	−	0.977154i	$-0.431829\pi$
$29$	−39.4741	−	14.3674i	−0.252764	−	0.0919986i	−0.465295	+	0.885156i	$0.654052\pi$
$30$	−177.785	+	307.933i	−1.08197	+	1.87402i
$31$	−0.938479	−	1.62549i	−0.00543728	−	0.00941765i	0.863294	−	0.504701i	$-0.168397\pi$
$31$	−0.938479	−	1.62549i	−0.00543728	−	0.00941765i	−0.868731	+	0.495284i	$0.835064\pi$
$32$	5.55674	+	31.5138i	0.0306970	+	0.174091i
$33$	−336.549	−	282.398i	−1.77532	−	1.48967i
$34$	−49.5877	+	41.6090i	−0.250124	+	0.209879i
$35$	32.7934	−	185.981i	0.158374	−	0.898185i
$36$	−194.455	+	70.7757i	−0.900253	+	0.327665i
$37$	331.421			1.47257			0.736287	−	0.676670i	$-0.236578\pi$
$37$	331.421			1.47257			0.736287	+	0.676670i	$0.236578\pi$
$38$	0.445152	−	165.638i	0.00190035	−	0.707104i
$39$	−200.911			−0.824912
$40$	150.623	−	54.8224i	0.595391	−	0.216705i
$41$	−8.17216	+	46.3466i	−0.0311287	+	0.176540i	−0.996408	−	0.0846794i	$-0.973013\pi$
$41$	−8.17216	+	46.3466i	−0.0311287	+	0.176540i	0.965280	+	0.261219i	$0.0841245\pi$
$42$	128.134	−	107.517i	0.470750	−	0.395006i
$43$	−293.235	−	246.054i	−1.03995	−	0.872624i	−0.0479511	−	0.998850i	$-0.515269\pi$
$43$	−293.235	−	246.054i	−1.03995	−	0.872624i	−0.992002	+	0.126226i	$0.959714\pi$
$44$	34.3910	+	195.041i	0.117833	+	0.668263i
$45$	518.273	+	897.675i	1.71688	+	2.97372i
$46$	0.309825	−	0.536633i	0.000993070	−	0.00172005i
$47$	115.099	+	41.8927i	0.357212	+	0.130014i	0.514391	−	0.857556i	$-0.328018\pi$
$47$	115.099	+	41.8927i	0.357212	+	0.130014i	−0.157180	+	0.987570i	$0.550240\pi$
$48$	133.409	+	48.5570i	0.401166	+	0.146012i
$49$	127.081	−	220.110i	0.370498	−	0.641722i
$50$	−276.451	−	478.827i	−0.781922	−	1.35433i
$51$	49.8701	+	282.827i	0.136926	+	0.776544i
$52$	69.3807	+	58.2173i	0.185026	+	0.155256i
$53$	−71.6880	+	60.1534i	−0.185795	+	0.155900i	−0.730941	−	0.682441i	$-0.760919\pi$
$53$	−71.6880	+	60.1534i	−0.185795	+	0.155900i	0.545146	+	0.838341i	$0.316474\pi$
$54$	−76.2196	+	432.263i	−0.192077	+	1.08932i
$55$	932.217	−	339.299i	2.28546	−	0.831838i
$56$	−75.4033			−0.179932
$57$	−635.426	−	369.144i	−1.47657	−	0.857795i
$58$	84.0149			0.190202
$59$	−517.526	+	188.364i	−1.14197	+	0.415642i	−0.842624	−	0.538503i	$-0.818990\pi$
$59$	−517.526	+	188.364i	−1.14197	+	0.415642i	−0.299345	+	0.954145i	$0.596768\pi$
$60$	123.489	−	700.338i	0.265705	−	1.50689i
$61$	−404.046	+	339.035i	−0.848079	+	0.711623i	−0.959366	−	0.282166i	$-0.908947\pi$
$61$	−404.046	+	339.035i	−0.848079	+	0.711623i	0.111287	+	0.993788i	$0.464503\pi$
$62$	2.87567	+	2.41297i	0.00589048	+	0.00494270i
$63$	−84.6726	−	480.202i	−0.169329	−	0.960314i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	226.835	−	392.891i	0.432853	−	0.749724i
$66$	825.678	+	300.522i	1.53991	+	0.560480i
$67$	605.223	+	220.283i	1.10358	+	0.401670i	0.828634	−	0.559790i	$-0.189118\pi$
$67$	605.223	+	220.283i	1.10358	+	0.401670i	0.274945	+	0.961460i	$0.411340\pi$
$68$	64.7322	−	112.119i	0.115440	−	0.199948i
$69$	−1.37457	−	2.38082i	−0.00239824	−	0.00415388i
$70$	65.5868	+	371.961i	0.111988	+	0.635113i
$71$	468.607	+	393.208i	0.783288	+	0.657257i	0.944074	−	0.329732i	$-0.106959\pi$
$71$	468.607	+	393.208i	0.783288	+	0.657257i	−0.160786	+	0.986989i	$0.551403\pi$
$72$	317.042	−	266.030i	0.518940	−	0.435443i
$73$	−70.7704	+	401.359i	−0.113466	+	0.643500i	0.874032	+	0.485869i	$0.161497\pi$
$73$	−70.7704	+	401.359i	−0.113466	+	0.643500i	−0.987498	+	0.157631i	$0.949614\pi$
$74$	−622.867	+	226.705i	−0.978470	+	0.356134i
$75$	−2453.00			−3.77665
$76$	112.466	+	311.601i	0.169747	+	0.470304i
$77$	−466.675			−0.690683
$78$	377.590	−	137.431i	0.548123	−	0.199501i
$79$	70.3461	−	398.953i	0.100184	−	0.568173i	−0.892851	−	0.450353i	$-0.851298\pi$
$79$	70.3461	−	398.953i	0.100184	−	0.568173i	0.993035	−	0.117820i	$-0.0375907\pi$
$80$	−245.578	+	206.065i	−0.343206	+	0.287984i
$81$	421.750	+	353.890i	0.578532	+	0.485446i
$82$	−16.3443	−	92.6933i	−0.0220113	−	0.124832i
$83$	387.299	+	670.822i	0.512188	+	0.887136i	0.999900	+	0.0141312i	$0.00449824\pi$
$83$	387.299	+	670.822i	0.512188	+	0.887136i	−0.487712	+	0.873005i	$0.662168\pi$
$84$	−167.267	+	289.715i	−0.217266	+	0.376315i
$85$	−609.386	−	221.798i	−0.777614	−	0.283028i
$86$	719.413	+	261.845i	0.902050	+	0.328319i
$87$	186.370	−	322.803i	0.229666	−	0.397794i
$88$	−198.050	−	343.033i	−0.239911	−	0.415539i
$89$	−152.983	−	867.607i	−0.182204	−	1.03333i	−0.929496	−	0.368832i	$-0.879758\pi$
$89$	−152.983	−	867.607i	−0.182204	−	1.03333i	0.747292	−	0.664495i	$-0.231353\pi$
$90$	−1588.08	−	1332.56i	−1.85998	−	1.56071i
$91$	−163.485	+	137.180i	−0.188329	+	0.158027i
$92$	−0.215202	+	1.22047i	−0.000243874	+	0.00138308i
$93$	15.6502	−	5.69621i	0.0174500	−	0.00635129i
$94$	−244.972			−0.268797
$95$	1439.29	−	825.827i	1.55440	−	0.891874i
$96$	−283.942			−0.301872
$97$	−1391.18	+	506.347i	−1.45621	+	0.530018i	−0.944319	−	0.329031i	$-0.893278\pi$
$97$	−1391.18	+	506.347i	−1.45621	+	0.530018i	−0.511894	+	0.859049i	$0.671056\pi$
$98$	−88.2694	+	500.601i	−0.0909853	+	0.516003i
$99$	1962.19	−	1646.47i	1.99199	−	1.67148i
$100$	847.096	+	710.798i	0.847096	+	0.710798i
$101$	105.822	+	600.144i	0.104254	+	0.591253i	0.991516	+	0.129987i	$0.0414935\pi$
$101$	105.822	+	600.144i	0.104254	+	0.591253i	−0.887262	+	0.461266i	$0.847395\pi$
$102$	−287.191	−	497.429i	−0.278785	−	0.482870i
$103$	−275.654	+	477.447i	−0.263699	+	0.456740i	−0.967222	−	0.253932i	$-0.918276\pi$
$103$	−275.654	+	477.447i	−0.263699	+	0.456740i	0.703523	+	0.710673i	$0.251609\pi$
$104$	−170.216	−	61.9536i	−0.160491	−	0.0584139i
$105$	1574.64	+	573.123i	1.46352	+	0.532677i
$106$	93.5821	−	162.089i	0.0857500	−	0.148523i
$107$	499.772	+	865.631i	0.451540	+	0.782091i	0.998482	−	0.0550801i	$-0.0175414\pi$
$107$	499.772	+	865.631i	0.451540	+	0.782091i	−0.546942	+	0.837171i	$0.684208\pi$
$108$	−152.439	−	864.526i	−0.135819	−	0.770269i
$109$	−229.462	−	192.542i	−0.201638	−	0.169194i	0.536378	−	0.843978i	$-0.319792\pi$
$109$	−229.462	−	192.542i	−0.201638	−	0.169194i	−0.738015	+	0.674784i	$0.764237\pi$
$110$	−1519.90	+	1275.35i	−1.31743	+	1.10545i
$111$	−510.657	+	2896.08i	−0.436662	+	2.47643i
$112$	141.712	−	51.5789i	0.119558	−	0.0435156i
$113$	1535.53			1.27833			0.639163	−	0.769071i	$-0.279281\pi$
$113$	1535.53			1.27833			0.639163	+	0.769071i	$0.279281\pi$
$114$	1446.72	+	259.107i	1.18858	+	0.212873i
$115$	6.20774			0.00503369
$116$	−157.896	+	57.4696i	−0.126382	+	0.0459993i
$117$	203.408	−	1153.58i	0.160727	−	0.911527i
$118$	843.782	−	708.017i	0.658275	−	0.552358i
$119$	233.692	+	196.091i	0.180021	+	0.151056i
$120$	246.977	+	1400.68i	0.187882	+	1.06553i
$121$	−560.243	−	970.370i	−0.420919	−	0.729053i
$122$	527.445	−	913.561i	0.391415	−	0.677951i
$123$	−392.403	−	142.823i	−0.287657	−	0.104699i
$124$	−7.05505	−	2.56783i	−0.00510937	−	0.00185966i
$125$	1517.26	−	2627.97i	1.08566	−	1.88042i
$126$	487.610	+	844.565i	0.344760	+	0.597142i
$127$	−179.708	−	1019.17i	−0.125563	−	0.712102i	−0.980972	−	0.194149i	$-0.937805\pi$
$127$	−179.708	−	1019.17i	−0.125563	−	0.712102i	0.855409	−	0.517953i	$-0.173306\pi$
$128$	98.0537	+	82.2768i	0.0677094	+	0.0568149i
$129$	2601.93	−	2183.28i	1.77587	−	1.49013i
$130$	−157.558	+	893.557i	−0.106298	+	0.602847i
$131$	−2320.30	+	844.519i	−1.54752	+	0.563252i	−0.967834	−	0.251588i	$-0.919047\pi$
$131$	−2320.30	+	844.519i	−1.54752	+	0.563252i	−0.579686	+	0.814840i	$0.696825\pi$
$132$	−1757.34			−1.15876
$133$	−769.106	+	133.484i	−0.501428	+	0.0870265i
$134$	−1288.13			−0.830429
$135$	−4132.08	+	1503.95i	−2.63432	+	0.958813i
$136$	−44.9625	+	254.995i	−0.0283493	+	0.160777i
$137$	−41.0660	+	34.4585i	−0.0256095	+	0.0214889i	−0.655503	−	0.755193i	$-0.727543\pi$
$137$	−41.0660	+	34.4585i	−0.0256095	+	0.0214889i	0.629893	+	0.776682i	$0.283099\pi$
$138$	4.21193	+	3.53423i	0.00259814	+	0.00218010i
$139$	−66.6697	−	378.103i	−0.0406824	−	0.230721i	0.957687	−	0.287813i	$-0.0929283\pi$
$139$	−66.6697	−	378.103i	−0.0406824	−	0.230721i	−0.998369	+	0.0570921i	$0.981817\pi$
$140$	−377.700	−	654.195i	−0.228010	−	0.394925i
$141$	−543.421	+	941.233i	−0.324570	+	0.562171i
$142$	−1149.66	−	418.444i	−0.679420	−	0.247289i
$143$	−1053.48	−	383.434i	−0.616057	−	0.224226i
$144$	−413.868	+	716.841i	−0.239507	+	0.414839i
$145$	420.836	+	728.909i	0.241024	+	0.417466i
$146$	−141.541	−	802.718i	−0.0802329	−	0.455024i
$147$	1727.60	+	1449.63i	0.969322	+	0.813358i
$148$	1015.53	−	852.132i	0.564028	−	0.473276i
$149$	−360.258	+	2043.13i	−0.198077	+	1.12335i	0.709891	+	0.704312i	$0.248744\pi$
$149$	−360.258	+	2043.13i	−0.198077	+	1.12335i	−0.907968	+	0.419040i	$0.862367\pi$
$150$	4610.14	−	1677.95i	2.50944	−	0.913362i
$151$	−290.042			−0.156313			−0.0781566	−	0.996941i	$-0.524903\pi$
$151$	−290.042			−0.156313			−0.0781566	+	0.996941i	$0.524903\pi$
$152$	−424.515	−	508.687i	−0.226531	−	0.271447i
$153$	−1674.41			−0.884760
$154$	877.063	−	319.225i	0.458933	−	0.167038i
$155$	−6.53042	+	37.0358i	−0.00338410	+	0.0191922i
$156$	−615.628	+	516.573i	−0.315960	+	0.265122i
$157$	−2496.06	−	2094.44i	−1.26884	−	1.06468i	−0.994682	−	0.102994i	$-0.967158\pi$
$157$	−2496.06	−	2094.44i	−1.26884	−	1.06468i	−0.274154	−	0.961686i	$-0.588398\pi$
$158$	140.692	+	797.905i	0.0708410	+	0.401759i
$159$	−415.186	−	719.123i	−0.207084	−	0.358680i
$160$	320.580	−	555.261i	0.158400	−	0.274358i
$161$	−2.74412	−	0.998777i	−0.00134327	−	0.000488911i
$162$	−1034.70	−	376.602i	−0.501815	−	0.182646i
$163$	−134.000	+	232.095i	−0.0643908	+	0.111528i	−0.896424	−	0.443198i	$-0.853844\pi$
$163$	−134.000	+	232.095i	−0.0643908	+	0.111528i	0.832033	+	0.554726i	$0.187177\pi$
$164$	94.1232	+	163.026i	0.0448158	+	0.0776232i
$165$	1528.56	+	8668.87i	0.721199	+	4.09012i
$166$	−1186.75	−	995.804i	−0.554879	−	0.465599i
$167$	−1162.53	+	975.475i	−0.538676	+	0.452003i	−0.871085	−	0.491132i	$-0.836583\pi$
$167$	−1162.53	+	975.475i	−0.538676	+	0.452003i	0.332409	+	0.943135i	$0.392139\pi$
$168$	116.182	−	658.903i	0.0533551	−	0.302592i
$169$	1582.74	−	576.070i	0.720410	−	0.262208i
$170$	1296.99			0.585145
$171$	2762.85	−	3274.72i	1.23556	−	1.46447i
$172$	−1531.17			−0.678781
$173$	4176.94	−	1520.28i	1.83565	−	0.668121i	0.844465	−	0.535611i	$-0.179919\pi$
$173$	4176.94	−	1520.28i	1.83565	−	0.668121i	0.991182	−	0.132510i	$-0.0423036\pi$
$174$	−129.451	+	734.155i	−0.0564005	+	0.319863i
$175$	−1996.06	+	1674.89i	−0.862215	+	0.723484i
$176$	606.860	+	509.216i	0.259908	+	0.218089i
$177$	−848.587	−	4812.58i	−0.360360	−	2.04370i
$178$	880.991	+	1525.92i	0.370972	+	0.642543i
$179$	425.753	−	737.426i	0.177778	−	0.307921i	−0.763341	−	0.645996i	$-0.776442\pi$
$179$	425.753	−	737.426i	0.177778	−	0.307921i	0.941119	+	0.338075i	$0.109776\pi$
$180$	3896.14	+	1418.08i	1.61334	+	0.587208i
$181$	1429.42	+	520.267i	0.587006	+	0.213653i	0.618412	−	0.785854i	$-0.287776\pi$
$181$	1429.42	+	520.267i	0.587006	+	0.213653i	−0.0314058	+	0.999507i	$0.509998\pi$
$182$	213.415	−	369.645i	0.0869196	−	0.150549i
$183$	−2340.06	−	4053.10i	−0.945258	−	1.63724i
$184$	−0.430405	−	2.44095i	−0.000172445	−	0.000977983i
$185$	−5086.86	−	4268.38i	−2.02159	−	1.69631i
$186$	−25.5163	+	21.4107i	−0.0100589	+	0.00844039i
$187$	−278.276	+	1578.18i	−0.108821	+	0.617155i
$188$	460.397	−	167.571i	0.178606	−	0.0650072i
$189$	2068.55			0.796112
$190$	−2140.09	+	2536.58i	−0.817149	+	0.968542i
$191$	4238.50			1.60569			0.802846	−	0.596187i	$-0.203318\pi$
$191$	4238.50			1.60569			0.802846	+	0.596187i	$0.203318\pi$
$192$	533.637	−	194.228i	0.200583	−	0.0730062i
$193$	157.454	−	892.967i	0.0587243	−	0.333042i	−0.941265	−	0.337669i	$-0.890362\pi$
$193$	157.454	−	892.967i	0.0587243	−	0.333042i	0.999989	+	0.00462659i	$0.00147269\pi$
$194$	2268.20	−	1903.24i	0.839418	−	0.704355i
$195$	3083.72	+	2587.55i	1.13246	+	0.950247i
$196$	−176.539	−	1001.20i	−0.0643363	−	0.364869i
$197$	2153.26	+	3729.55i	0.778747	+	1.34883i	0.932664	+	0.360746i	$0.117478\pi$
$197$	2153.26	+	3729.55i	0.778747	+	1.34883i	−0.153917	+	0.988084i	$0.549189\pi$
$198$	−2561.46	+	4436.57i	−0.919368	+	1.59239i
$199$	−2260.36	−	822.705i	−0.805190	−	0.293065i	−0.0935547	−	0.995614i	$-0.529823\pi$
$199$	−2260.36	−	822.705i	−0.805190	−	0.293065i	−0.711636	+	0.702549i	$0.752045\pi$
$200$	−2078.23	−	756.415i	−0.734766	−	0.267433i
$201$	−2857.46	+	4949.26i	−1.00273	+	1.73679i
$202$	−609.402	−	1055.51i	−0.212264	−	0.367652i
$203$	−68.7538	−	389.922i	−0.0237713	−	0.134814i
$204$	880.003	+	738.410i	0.302022	+	0.253427i
$205$	722.333	−	606.109i	0.246097	−	0.206500i
$206$	191.467	−	1085.87i	0.0647581	−	0.367261i
$207$	15.0617	−	5.48202i	0.00505731	−	0.00184071i
$208$	362.280			0.120767
$209$	−2627.35	−	3148.30i	−0.869558	−	1.04197i
$210$	−3351.40			−1.10128
$211$	5367.64	−	1953.66i	1.75130	−	0.637419i	0.751544	−	0.659683i	$-0.229310\pi$
$211$	5367.64	−	1953.66i	1.75130	−	0.637419i	0.999752	+	0.0222640i	$0.00708744\pi$
$212$	−65.0014	+	368.641i	−0.0210581	+	0.119426i
$213$	−4158.04	+	3489.01i	−1.33758	+	1.12236i
$214$	−1531.39	−	1284.99i	−0.489176	−	0.410468i
$215$	1331.83	+	7553.18i	0.422465	+	2.39592i
$216$	877.863	+	1520.50i	0.276532	+	0.478968i
$217$	8.84554	−	15.3209i	0.00276716	−	0.00479287i
$218$	562.954	+	204.899i	0.174899	+	0.0636582i
$219$	−3398.19	−	1236.84i	−1.04853	−	0.381634i
$220$	1984.09	−	3436.54i	0.608033	−	1.05314i
$221$	366.425	+	634.666i	0.111531	+	0.193178i
$222$	−1021.31	−	5792.16i	−0.308767	−	1.75110i
$223$	3353.43	+	2813.86i	1.00701	+	0.844978i	0.987939	−	0.154841i	$-0.0494864\pi$
$223$	3353.43	+	2813.86i	1.00701	+	0.844978i	0.0190656	+	0.999818i	$0.493931\pi$
$224$	−231.049	+	193.873i	−0.0689179	+	0.0578290i
$225$	2483.48	−	14084.5i	0.735847	−	4.17319i
$226$	−2885.86	+	1050.37i	−0.849401	+	0.309157i
$227$	1546.26			0.452111			0.226055	−	0.974114i	$-0.427417\pi$
$227$	1546.26			0.452111			0.226055	+	0.974114i	$0.427417\pi$
$228$	−2896.18	+	502.653i	−0.841247	+	0.146005i
$229$	−4754.72			−1.37206			−0.686028	−	0.727575i	$-0.740647\pi$
$229$	−4754.72			−1.37206			−0.686028	+	0.727575i	$0.740647\pi$
$230$	−11.6667	+	4.24634i	−0.00334470	+	0.00121737i
$231$	719.060	−	4077.99i	0.204808	−	1.16152i
$232$	257.437	−	216.015i	0.0728515	−	0.0611297i
$233$	2566.88	+	2153.87i	0.721724	+	0.605599i	0.927862	−	0.372924i	$-0.121645\pi$
$233$	2566.88	+	2153.87i	0.721724	+	0.605599i	−0.206137	+	0.978523i	$0.566089\pi$
$234$	406.815	+	2307.16i	0.113651	+	0.644547i
$235$	−1227.08	−	2125.36i	−0.340621	−	0.589972i
$236$	−1101.48	+	1907.82i	−0.303814	+	0.526222i
$237$	3377.81	+	1229.42i	0.925791	+	0.336960i
$238$	−573.332	−	208.676i	−0.156150	−	0.0568338i
$239$	−423.111	+	732.850i	−0.114514	+	0.198344i	−0.917585	−	0.397539i	$-0.869864\pi$
$239$	−423.111	+	732.850i	−0.114514	+	0.198344i	0.803072	+	0.595883i	$0.203198\pi$
$240$	−1422.28	−	2463.47i	−0.382533	−	0.662567i
$241$	932.872	+	5290.58i	0.249343	+	1.41409i	0.810187	+	0.586171i	$0.199365\pi$
$241$	932.872	+	5290.58i	0.249343	+	1.41409i	−0.560845	+	0.827921i	$0.689523\pi$
$242$	1716.68	+	1440.47i	0.456003	+	0.382632i
$243$	796.987	−	668.751i	0.210398	−	0.176545i
$244$	−366.359	+	2077.73i	−0.0961220	+	0.545135i
$245$	−4785.33	+	1741.72i	−1.24785	+	0.454181i
$246$	835.174			0.216458
$247$	−1845.86	−	330.593i	−0.475503	−	0.0851623i
$248$	15.0157			0.00384474
$249$	−6458.66	+	2350.76i	−1.64378	+	0.598286i
$250$	−1053.88	+	5976.82i	−0.266612	+	1.51203i
$251$	−1239.04	+	1039.68i	−0.311584	+	0.261450i	−0.785146	−	0.619311i	$-0.787412\pi$
$251$	−1239.04	+	1039.68i	−0.311584	+	0.261450i	0.473563	+	0.880760i	$0.342968\pi$
$252$	−1494.12	−	1253.72i	−0.373496	−	0.313400i
$253$	−2.66380	−	15.1072i	−0.000661944	−	0.00375407i
$254$	1034.89	+	1792.49i	0.255650	+	0.442799i
$255$	2877.11	−	4983.30i	0.706555	−	1.22379i
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	−1076.02	−	391.639i	−0.261168	−	0.0950574i	0.208118	−	0.978104i	$-0.433266\pi$
$257$	−1076.02	−	391.639i	−0.261168	−	0.0950574i	−0.469286	+	0.883046i	$0.655489\pi$
$258$	−3396.58	+	5883.05i	−0.819620	+	1.41962i
$259$	1561.89	+	2705.27i	0.374714	+	0.649024i
$260$	−315.116	−	1787.11i	−0.0751642	−	0.426277i
$261$	1664.76	+	1396.90i	0.394814	+	0.331288i
$262$	3783.05	−	3174.35i	0.892051	−	0.748520i
$263$	189.878	−	1076.85i	0.0445186	−	0.252477i	−0.954424	−	0.298454i	$-0.903529\pi$
$263$	189.878	−	1076.85i	0.0445186	−	0.252477i	0.998943	+	0.0459769i	$0.0146401\pi$
$264$	3302.71	−	1202.09i	0.769954	−	0.280240i
$265$	1875.03			0.434651
$266$	1354.14	−	776.967i	0.312134	−	0.179094i
$267$	7817.20			1.79178
$268$	2420.89	−	881.133i	0.551790	−	0.200835i
$269$	−22.3588	+	126.803i	−0.00506782	+	0.0287410i	−0.987237	−	0.159259i	$-0.949089\pi$
$269$	−22.3588	+	126.803i	−0.00506782	+	0.0287410i	0.982169	+	0.188000i	$0.0602006\pi$
$270$	6737.00	−	5653.02i	1.51852	−	1.27419i
$271$	−1908.33	−	1601.28i	−0.427759	−	0.358933i	0.403346	−	0.915047i	$-0.367847\pi$
$271$	−1908.33	−	1601.28i	−0.427759	−	0.358933i	−0.831106	+	0.556115i	$0.812292\pi$
$272$	−89.9250	−	509.990i	−0.0200460	−	0.113686i
$273$	−946.836	−	1639.97i	−0.209909	−	0.363573i
$274$	53.6078	−	92.8515i	0.0118196	−	0.0204721i
$275$	−12862.3	−	4681.50i	−2.82046	−	1.02656i
$276$	−10.3334	−	3.76104i	−0.00225361	−	0.000820247i
$277$	3826.59	−	6627.85i	0.830028	−	1.43765i	−0.0679880	−	0.997686i	$-0.521658\pi$
$277$	3826.59	−	6627.85i	0.830028	−	1.43765i	0.898016	−	0.439964i	$-0.145009\pi$
$278$	383.936	+	664.996i	0.0828307	+	0.143467i
$279$	16.8615	+	95.6265i	0.00361818	+	0.0205197i
$280$	1157.34	+	971.122i	0.247015	+	0.207270i
$281$	−3650.56	+	3063.18i	−0.774996	+	0.650299i	−0.941983	−	0.335660i	$-0.891041\pi$
$281$	−3650.56	+	3063.18i	−0.774996	+	0.650299i	0.166987	+	0.985959i	$0.446596\pi$
$282$	377.456	−	2140.66i	0.0797064	−	0.452037i
$283$	−644.294	+	234.504i	−0.135333	+	0.0492572i	−0.408799	−	0.912625i	$-0.634052\pi$
$283$	−644.294	+	234.504i	−0.135333	+	0.0492572i	0.273466	+	0.961882i	$0.411830\pi$
$284$	2446.89			0.511255
$285$	4998.71	+	13849.5i	1.03894	+	2.87851i
$286$	2242.17			0.463575
$287$	−416.824	+	151.712i	−0.0857294	+	0.0312030i
$288$	287.470	−	1630.32i	0.0588171	−	0.333569i
$289$	−2961.10	+	2484.65i	−0.602706	+	0.505731i
$290$	−1289.52	−	1082.03i	−0.261114	−	0.219100i
$291$	−2281.11	−	12936.8i	−0.459523	−	2.60609i
$292$	815.101	+	1411.80i	0.163357	+	0.282942i
$293$	1109.88	−	1922.37i	0.221296	−	0.383297i	−0.733905	−	0.679252i	$-0.762305\pi$
$293$	1109.88	−	1922.37i	0.221296	−	0.383297i	0.955202	+	0.295955i	$0.0956378\pi$
$294$	−4238.44	−	1542.67i	−0.840785	−	0.306021i
$295$	10369.3	+	3774.11i	2.04652	+	0.744871i
$296$	−1325.68	+	2296.15i	−0.260317	+	0.450882i
$297$	5433.14	+	9410.48i	1.06149	+	1.83856i
$298$	−720.517	−	4086.25i	−0.140062	−	0.794330i
$299$	−5.37397	−	4.50930i	−0.00103941	−	0.000872172i
$300$	−7516.44	+	6307.04i	−1.44654	+	1.21379i
$301$	626.517	−	3553.15i	0.119973	−	0.680400i
$302$	545.101	−	198.401i	0.103864	−	0.0378035i
$303$	−5407.34			−1.02523
$304$	1145.79	+	665.634i	0.216170	+	0.125581i
$305$	10568.0			1.98401
$306$	3146.87	−	1145.37i	0.587890	−	0.213975i
$307$	−1391.35	+	7890.75i	−0.258660	+	1.46693i	0.527840	+	0.849344i	$0.323002\pi$
$307$	−1391.35	+	7890.75i	−0.258660	+	1.46693i	−0.786500	+	0.617590i	$0.788109\pi$
$308$	−1429.98	+	1199.89i	−0.264547	+	0.221981i
$309$	−3747.39	−	3144.43i	−0.689907	−	0.578901i
$310$	−13.0608	−	74.0717i	−0.00239292	−	0.0135709i
$311$	−4591.42	−	7952.58i	−0.837157	−	1.45000i	−0.892262	−	0.451517i	$-0.850883\pi$
$311$	−4591.42	−	7952.58i	−0.837157	−	1.45000i	0.0551056	−	0.998481i	$-0.482450\pi$
$312$	803.645	−	1391.95i	0.145825	−	0.252577i
$313$	8755.18	+	3186.62i	1.58106	+	0.575459i	0.975434	−	0.220290i	$-0.0707005\pi$
$313$	8755.18	+	3186.62i	1.58106	+	0.575459i	0.605626	+	0.795749i	$0.292923\pi$
$314$	6123.74	+	2228.86i	1.10058	+	0.400579i
$315$	−4884.94	+	8460.96i	−0.873762	+	1.51340i
$316$	−810.214	−	1403.33i	−0.144235	−	0.249822i
$317$	−157.014	−	890.472i	−0.0278196	−	0.157773i	0.967733	−	0.251976i	$-0.0810806\pi$
$317$	−157.014	−	890.472i	−0.0278196	−	0.157773i	−0.995553	+	0.0942039i	$0.969969\pi$
$318$	1272.20	+	1067.51i	0.224345	+	0.188248i
$319$	1593.29	−	1336.93i	0.279646	−	0.234651i
$320$	−222.672	+	1262.84i	−0.0388993	+	0.220609i
$321$	−8334.27	+	3033.43i	−1.44914	+	0.527444i
$322$	5.84046			0.00101080
$323$	−7.20391	+	2680.52i	−0.00124098	+	0.461759i
$324$	2202.22			0.377610
$325$	−5882.05	+	2140.89i	−1.00393	+	0.365401i
$326$	93.0755	−	527.858i	0.0158128	−	0.0896789i
$327$	2036.06	−	1708.46i	0.344326	−	0.288924i
$328$	−288.410	−	242.005i	−0.0485512	−	0.0407393i
$329$	200.473	+	1136.94i	0.0335941	+	0.190522i
$330$	−8802.60	−	15246.6i	−1.46839	−	2.54332i
$331$	1481.76	−	2566.48i	0.246057	−	0.426183i	−0.716371	−	0.697719i	$-0.754198\pi$
$331$	1481.76	−	2566.48i	0.246057	−	0.426183i	0.962428	+	0.271536i	$0.0875316\pi$
$332$	2911.54	+	1059.71i	0.481299	+	0.175179i
$333$	−16111.6	−	5864.13i	−2.65138	−	0.965022i
$334$	1517.57	−	2628.51i	0.248616	−	0.430615i
$335$	−6452.33	−	11175.8i	−1.05232	−	1.82268i
$336$	232.365	+	1317.81i	0.0377278	+	0.213965i
$337$	1394.43	+	1170.07i	0.225399	+	0.189132i	0.748493	−	0.663143i	$-0.230778\pi$
$337$	1394.43	+	1170.07i	0.225399	+	0.189132i	−0.523094	+	0.852275i	$0.675222\pi$
$338$	−2580.52	+	2165.32i	−0.415272	+	0.348455i
$339$	−2365.97	+	13418.1i	−0.379062	+	2.14977i
$340$	−2437.54	+	887.193i	−0.388807	+	0.141514i
$341$	92.9328			0.0147583
$342$	−2952.42	+	8044.37i	−0.466808	+	1.27190i
$343$	5628.49			0.886035
$344$	2877.65	−	1047.38i	0.451025	−	0.164160i
$345$	−9.56496	+	54.2456i	−0.00149264	+	0.00846517i
$346$	−6810.15	+	5714.39i	−1.05814	+	0.887883i
$347$	−5948.14	−	4991.09i	−0.920211	−	0.772148i	0.0538232	−	0.998550i	$-0.482859\pi$
$347$	−5948.14	−	4991.09i	−0.920211	−	0.772148i	−0.974034	+	0.226402i	$0.927304\pi$
$348$	−258.903	−	1468.31i	−0.0398812	−	0.226177i
$349$	−3254.54	−	5637.03i	−0.499173	−	0.864594i	0.500826	−	0.865548i	$-0.333030\pi$
$349$	−3254.54	−	5637.03i	−0.499173	−	0.864594i	−1.00000		0.000954101i	$0.999696\pi$
$350$	2605.66	−	4513.14i	0.397939	−	0.689251i
$351$	4669.57	+	1699.58i	0.710095	+	0.258453i
$352$	−1488.85	−	541.897i	−0.225443	−	0.0820545i
$353$	3799.48	−	6580.90i	0.572878	−	0.992255i	−0.423390	−	0.905947i	$-0.639160\pi$
$353$	3799.48	−	6580.90i	0.572878	−	0.992255i	0.996269	−	0.0863071i	$-0.0275066\pi$
$354$	4886.82	+	8464.22i	0.733705	+	1.27081i
$355$	−2128.34	−	12070.4i	−0.318199	−	1.80460i
$356$	−2699.51	−	2265.16i	−0.401893	−	0.337228i
$357$	−2073.60	+	1739.95i	−0.307413	+	0.257950i
$358$	−295.725	+	1677.14i	−0.0436580	+	0.247597i
$359$	2017.65	−	734.365i	0.296623	−	0.107962i	−0.189422	−	0.981896i	$-0.560661\pi$
$359$	2017.65	−	734.365i	0.296623	−	0.107962i	0.486045	+	0.873934i	$0.338439\pi$
$360$	−8292.37			−1.21402
$361$	−5230.53	−	4437.06i	−0.762578	−	0.646896i
$362$	−3042.32			−0.441715
$363$	9342.70	−	3400.46i	1.35087	−	0.491675i
$364$	−148.236	+	840.690i	−0.0213453	+	0.121055i
$365$	6255.36	−	5248.87i	0.897042	−	0.752708i
$366$	7170.36	+	6016.65i	1.02405	+	0.859276i
$367$	536.219	+	3041.05i	0.0762681	+	0.432538i	0.998901	+	0.0468596i	$0.0149214\pi$
$367$	536.219	+	3041.05i	0.0762681	+	0.432538i	−0.922633	+	0.385678i	$0.873968\pi$
$368$	2.47860	+	4.29306i	0.000351103	+	0.000608129i
$369$	1217.33	−	2108.48i	0.171739	−	0.297461i
$370$	12479.9	+	4542.32i	1.75351	+	0.638227i
$371$	−828.855	−	301.679i	−0.115989	−	0.0422166i
$372$	33.3092	−	57.6932i	0.00464248	−	0.00804101i
$373$	4334.36	+	7507.33i	0.601675	+	1.04213i	0.992568	+	0.121695i	$0.0388330\pi$
$373$	4334.36	+	7507.33i	0.601675	+	1.04213i	−0.390893	+	0.920436i	$0.627834\pi$
$374$	−556.551	−	3156.36i	−0.0769481	−	0.436394i
$375$	20626.4	+	17307.6i	2.84038	+	2.38336i
$376$	−750.638	+	629.860i	−0.102955	+	0.0863897i
$377$	165.166	−	936.704i	0.0225636	−	0.127965i
$378$	−3887.61	+	1414.97i	−0.528987	+	0.192535i
$379$	−1288.19			−0.174591			−0.0872956	−	0.996182i	$-0.527822\pi$
$379$	−1288.19			−0.174591			−0.0872956	+	0.996182i	$0.527822\pi$
$380$	2286.92	−	6231.12i	0.308728	−	0.841183i
$381$	9182.82			1.23478
$382$	−7965.77	+	2899.30i	−1.06692	+	0.388328i
$383$	−2141.84	+	12147.0i	−0.285752	+	1.62058i	0.416833	+	0.908983i	$0.363140\pi$
$383$	−2141.84	+	12147.0i	−0.285752	+	1.62058i	−0.702586	+	0.711599i	$0.747971\pi$
$384$	−870.049	+	730.058i	−0.115624	+	0.0970198i
$385$	7162.84	+	6010.34i	0.948187	+	0.795624i
$386$	314.908	+	1785.93i	0.0415244	+	0.235496i
$387$	9901.58	+	17150.0i	1.30058	+	2.25268i
$388$	−2960.92	+	5128.46i	−0.387417	+	0.671027i
$389$	−4552.89	−	1657.11i	−0.593420	−	0.215987i	0.0278129	−	0.999613i	$-0.491146\pi$
$389$	−4552.89	−	1657.11i	−0.593420	−	0.215987i	−0.621233	+	0.783626i	$0.713368\pi$
$390$	−7565.48	−	2753.61i	−0.982290	−	0.357524i
$391$	−5.01392	+	8.68436i	−0.000648503	+	0.00112324i
$392$	1016.65	+	1760.88i	0.130991	+	0.226883i
$393$	−3804.59	−	21576.9i	−0.488336	−	2.76949i
$394$	−6597.96	−	5536.35i	−0.843656	−	0.707911i
$395$	−6217.85	+	5217.39i	−0.792035	+	0.664597i
$396$	1779.17	−	10090.2i	0.225774	−	1.28043i
$397$	6469.47	−	2354.69i	0.817867	−	0.297679i	0.100998	−	0.994887i	$-0.467797\pi$
$397$	6469.47	−	2354.69i	0.817867	−	0.297679i	0.716870	+	0.697207i	$0.245574\pi$
$398$	4810.86			0.605895
$399$	18.6148	−	6926.42i	0.00233560	−	0.869060i
$400$	4423.22			0.552902
$401$	−4592.90	+	1671.68i	−0.571967	+	0.208179i	−0.611780	−	0.791028i	$-0.709546\pi$
$401$	−4592.90	+	1671.68i	−0.571967	+	0.208179i	0.0398128	+	0.999207i	$0.487324\pi$
$402$	1984.77	−	11256.2i	0.246247	−	1.39654i
$403$	32.5561	−	27.3178i	0.00402416	−	0.00337667i
$404$	1867.32	+	1566.86i	0.229956	+	0.192956i
$405$	−1915.52	−	10863.5i	−0.235020	−	1.33286i
$406$	395.937	+	685.784i	0.0483991	+	0.0838297i
$407$	−8204.73	+	14211.0i	−0.999246	+	1.73075i
$408$	−2158.97	−	785.800i	−0.261972	−	0.0953502i
$409$	5640.45	+	2052.96i	0.681913	+	0.248196i	0.659669	−	0.751556i	$-0.270697\pi$
$409$	5640.45	+	2052.96i	0.681913	+	0.248196i	0.0222444	+	0.999753i	$0.492919\pi$
$410$	−942.938	+	1633.22i	−0.113581	+	0.196729i
$411$	−237.836	−	411.945i	−0.0285440	−	0.0494397i
$412$	382.935	+	2171.73i	0.0457909	+	0.259693i
$413$	−3976.49	−	3336.67i	−0.473778	−	0.397547i
$414$	−24.5569	+	20.6057i	−0.00291523	+	0.00244617i
$415$	2695.03	−	15284.3i	0.318780	−	1.80789i
$416$	−680.864	+	247.814i	−0.0802454	+	0.0292069i
$417$	3406.73			0.400068
$418$	7091.36	+	4119.65i	0.829785	+	0.482054i
$419$	2289.90			0.266990			0.133495	−	0.991049i	$-0.457380\pi$
$419$	2289.90			0.266990			0.133495	+	0.991049i	$0.457380\pi$
$420$	6298.57	−	2292.49i	0.731759	−	0.266339i
$421$	563.715	−	3196.99i	0.0652584	−	0.370099i	−0.934637	−	0.355604i	$-0.884275\pi$
$421$	563.715	−	3196.99i	0.0652584	−	0.370099i	0.999895	−	0.0144944i	$-0.00461386\pi$
$422$	−8751.48	+	7343.36i	−1.00951	+	0.847083i
$423$	−4854.15	−	4073.11i	−0.557959	−	0.468183i
$424$	−130.003	−	737.283i	−0.0148903	−	0.0844472i
$425$	4473.82	+	7748.89i	0.510617	+	0.884414i
$426$	5427.94	−	9401.47i	0.617335	−	1.06926i
$427$	−4671.57	−	1700.31i	−0.529445	−	0.192702i
$428$	3757.06	+	1367.46i	0.424309	+	0.154436i
$429$	4973.81	−	8614.89i	0.559762	−	0.969536i
$430$	−7669.70	−	13284.3i	−0.860154	−	1.48983i
$431$	1501.14	+	8513.41i	0.167767	+	0.951454i	0.946165	+	0.323683i	$0.104921\pi$
$431$	1501.14	+	8513.41i	0.167767	+	0.951454i	−0.778398	+	0.627771i	$0.783968\pi$
$432$	−2689.93	−	2257.12i	−0.299581	−	0.251379i
$433$	−9085.03	+	7623.25i	−1.00831	+	0.846073i	−0.988114	−	0.153723i	$-0.950874\pi$
$433$	−9085.03	+	7623.25i	−1.00831	+	0.846073i	−0.0201970	+	0.999796i	$0.506429\pi$
$434$	−6.14405	+	34.8446i	−0.000679548	+	0.00385391i
$435$	−7017.92	+	2554.32i	−0.773526	+	0.281540i
$436$	−1198.17			−0.131610
$437$	−8.71121	−	24.1355i	−0.000953579	−	0.00264201i
$438$	7232.55			0.789006
$439$	3527.14	−	1283.77i	0.383465	−	0.139570i	−0.143093	−	0.989709i	$-0.545705\pi$
$439$	3527.14	−	1283.77i	0.383465	−	0.139570i	0.526558	+	0.850139i	$0.323482\pi$
$440$	−1378.13	+	7815.78i	−0.149318	+	0.846825i
$441$	−10072.5	+	8451.81i	−1.08762	+	0.912624i
$442$	−1122.79	−	942.133i	−0.120827	−	0.101386i
$443$	−940.654	−	5334.71i	−0.100884	−	0.572144i	−0.992785	−	0.119912i	$-0.961739\pi$
$443$	−940.654	−	5334.71i	−0.100884	−	0.572144i	0.891900	−	0.452232i	$-0.149372\pi$
$444$	5881.52	+	10187.1i	0.628659	+	1.08887i
$445$	−8825.88	+	15286.9i	−0.940195	+	1.62847i
$446$	−8227.18	−	2994.45i	−0.873471	−	0.317917i
$447$	−17298.5	−	6296.16i	−1.83041	−	0.666215i
$448$	301.613	−	522.409i	0.0318078	−	0.0550927i
$449$	−137.961	−	238.955i	−0.0145006	−	0.0251158i	0.858684	−	0.512505i	$-0.171283\pi$
$449$	−137.961	−	238.955i	−0.0145006	−	0.0251158i	−0.873185	+	0.487390i	$0.837949\pi$
$450$	4966.96	+	28169.1i	0.520322	+	2.95089i
$451$	−1784.99	−	1497.78i	−0.186368	−	0.156381i
$452$	4705.15	−	3948.09i	0.489628	−	0.410846i
$453$	446.901	−	2534.50i	0.0463515	−	0.262873i
$454$	−2906.03	+	1057.71i	−0.300411	+	0.109341i
$455$	4276.03			0.440579
$456$	5099.21	−	2925.79i	0.523667	−	0.300466i
$457$	−14563.9			−1.49075			−0.745374	−	0.666646i	$-0.767729\pi$
$457$	−14563.9			−1.49075			−0.745374	+	0.666646i	$0.767729\pi$
$458$	8935.95	−	3252.42i	0.911680	−	0.331824i
$459$	1233.47	−	6995.33i	0.125432	−	0.711359i
$460$	19.0216	−	15.9610i	0.00192801	−	0.00161780i
$461$	−2390.64	−	2005.98i	−0.241525	−	0.202664i	0.513988	−	0.857798i	$-0.328168\pi$
$461$	−2390.64	−	2005.98i	−0.241525	−	0.202664i	−0.755513	+	0.655134i	$0.772612\pi$
$462$	1438.12	+	8155.98i	0.144821	+	0.821322i
$463$	−4037.27	−	6992.76i	−0.405244	−	0.701903i	0.589106	−	0.808056i	$-0.299480\pi$
$463$	−4037.27	−	6992.76i	−0.405244	−	0.701903i	−0.994350	+	0.106153i	$0.966147\pi$
$464$	−336.060	+	582.073i	−0.0336232	+	0.0582372i
$465$	−313.571	−	114.131i	−0.0312721	−	0.0113821i
$466$	−6297.48	−	2292.10i	−0.626020	−	0.227853i
$467$	−9125.29	+	15805.5i	−0.904214	+	1.56614i	−0.0822446	+	0.996612i	$0.526209\pi$
$467$	−9125.29	+	15805.5i	−0.904214	+	1.56614i	−0.821969	+	0.569532i	$0.807124\pi$
$468$	−2342.76	−	4057.77i	−0.231397	−	0.400792i
$469$	1054.14	+	5978.35i	0.103787	+	0.588603i
$470$	3759.99	+	3155.01i	0.369012	+	0.309637i
$471$	22148.0	−	18584.4i	2.16672	−	1.81810i
$472$	765.079	−	4338.98i	0.0746094	−	0.423131i
$473$	17810.0	−	6482.29i	1.73130	−	0.630140i
$474$	−7189.19			−0.696646
$475$	−22536.8	−	4036.33i	−2.17697	−	0.389894i
$476$	1220.25			0.117501
$477$	4549.37	−	1655.83i	0.436690	−	0.158942i
$478$	293.890	−	1666.73i	0.0281218	−	0.159487i
$479$	301.846	−	253.279i	0.0287927	−	0.0241600i	−0.628278	−	0.777989i	$-0.716240\pi$
$479$	301.846	−	253.279i	0.0287927	−	0.0241600i	0.657070	+	0.753829i	$0.271795\pi$
$480$	4358.13	+	3656.91i	0.414418	+	0.347738i
$481$	1303.09	+	7390.19i	0.123526	+	0.700548i
$482$	−5372.20	−	9304.92i	−0.507670	−	0.879310i
$483$	12.9559	−	22.4402i	0.00122052	−	0.00211401i
$484$	−4211.65	−	1532.92i	−0.395534	−	0.143963i
$485$	27874.0	+	10145.3i	2.60967	+	0.949844i
$486$	−1040.39	+	1802.01i	−0.0971052	+	0.168191i
$487$	5345.83	+	9259.25i	0.497418	+	0.861553i	0.999996	−	0.00297872i	$-0.000948157\pi$
$487$	5345.83	+	9259.25i	0.497418	+	0.861553i	−0.502577	+	0.864532i	$0.667615\pi$
$488$	−732.719	−	4155.45i	−0.0679685	−	0.385468i
$489$	−1821.67	−	1528.56i	−0.168464	−	0.141358i
$490$	7802.08	−	6546.72i	0.719310	−	0.603573i
$491$	493.287	−	2797.57i	0.0453396	−	0.257134i	−0.953710	−	0.300729i	$-0.902770\pi$
$491$	493.287	−	2797.57i	0.0453396	−	0.257134i	0.999049	+	0.0435952i	$0.0138812\pi$
$492$	−1569.61	+	571.292i	−0.143829	+	0.0523493i
$493$	−1359.62			−0.124207
$494$	3695.22	−	641.333i	0.336550	−	0.0584108i
$495$	−51322.0			−4.66010
$496$	−28.2202	+	10.2713i	−0.00255469	+	0.000929830i
$497$	−1001.21	+	5678.15i	−0.0903631	+	0.512474i
$498$	10530.3	−	8835.97i	0.947538	−	0.795078i
$499$	1340.63	+	1124.92i	0.120270	+	0.100919i	0.700939	−	0.713221i	$-0.252765\pi$
$499$	1340.63	+	1124.92i	0.120270	+	0.100919i	−0.580669	+	0.814140i	$0.697209\pi$
$500$	−2107.75	−	11953.6i	−0.188523	−	1.06917i
$501$	−6732.84	−	11661.6i	−0.600402	−	1.03993i
$502$	1617.45	−	2801.51i	0.143806	−	0.249078i
$503$	7672.22	+	2792.46i	0.680094	+	0.247534i	0.658888	−	0.752241i	$-0.271027\pi$
$503$	7672.22	+	2792.46i	0.680094	+	0.247534i	0.0212063	+	0.999775i	$0.493249\pi$
$504$	3665.63	+	1334.18i	0.323968	+	0.117915i
$505$	6105.06	−	10574.3i	0.537964	−	0.931781i
$506$	15.3402	+	26.5700i	0.00134774	+	0.00233435i
$507$	2595.22	+	14718.2i	0.227333	+	1.28927i
$508$	−3171.10	−	2660.87i	−0.276958	−	0.232396i
$509$	15546.6	−	13045.1i	1.35381	−	1.13598i	0.375969	−	0.926632i	$-0.377310\pi$
$509$	15546.6	−	13045.1i	1.35381	−	1.13598i	0.977841	−	0.209349i	$-0.0671345\pi$
$510$	−1998.42	+	11333.6i	−0.173513	+	0.984040i
$511$	−3609.67	+	1313.81i	−0.312490	+	0.113737i
$512$	512.000			0.0441942
$513$	11645.8	+	13954.9i	1.00229	+	1.20102i
$514$	2290.15			0.196526
$515$	10380.0	−	3778.01i	0.888149	−	0.323260i
$516$	2359.24	−	13379.9i	0.201279	−	1.14151i
$517$	−4645.74	+	3898.24i	−0.395202	+	0.331614i
$518$	−4785.90	−	4015.85i	−0.405947	−	0.340630i
$519$	6848.93	+	38842.2i	0.579257	+	3.28513i
$520$	1814.68	+	3143.12i	0.153037	+	0.265068i
$521$	6316.12	−	10939.8i	0.531121	−	0.919929i	−0.468219	−	0.883612i	$-0.655104\pi$
$521$	6316.12	−	10939.8i	0.531121	−	0.919929i	0.999340	−	0.0363166i	$-0.0115625\pi$
$522$	−4084.27	−	1486.55i	−0.342459	−	0.124645i
$523$	−8670.46	−	3155.79i	−0.724919	−	0.263849i	−0.0469064	−	0.998899i	$-0.514936\pi$
$523$	−8670.46	−	3155.79i	−0.724919	−	0.263849i	−0.678012	+	0.735050i	$0.737158\pi$
$524$	−4938.42	+	8553.59i	−0.411709	+	0.713101i
$525$	−11560.3	−	20023.0i	−0.961014	−	1.66452i
$526$	379.756	+	2153.71i	0.0314794	+	0.178529i
$527$	−46.5370	−	39.0492i	−0.00384665	−	0.00322772i
$528$	−5384.79	+	4518.37i	−0.443831	+	0.372419i
$529$	−2112.76	+	11982.1i	−0.173647	+	0.984800i
$530$	−3523.91	+	1282.60i	−0.288809	+	0.105118i
$531$	28491.7			2.32850
$532$	−2013.47	+	2386.51i	−0.164088	+	0.194489i
$533$	−1065.59			−0.0865966
$534$	−14691.5	+	5347.28i	−1.19057	+	0.433333i
$535$	3477.67	−	19722.9i	0.281033	−	1.59382i
$536$	−3947.06	+	3311.98i	−0.318073	+	0.266895i
$537$	5787.91	+	4856.63i	0.465115	+	0.390278i
$538$	−44.7177	−	253.607i	−0.00358349	−	0.0203230i
$539$	6292.09	+	10898.2i	0.502819	+	0.870908i
$540$	−8794.54	+	15232.6i	−0.700845	+	1.21390i
$541$	−10079.7	−	3668.70i	−0.801032	−	0.291552i	−0.0911182	−	0.995840i	$-0.529044\pi$
$541$	−10079.7	−	3668.70i	−0.801032	−	0.291552i	−0.709914	+	0.704288i	$0.751266\pi$
$542$	4681.83	+	1704.05i	0.371036	+	0.135046i
$543$	−6748.77	+	11689.2i	−0.533366	+	0.923817i
$544$	517.857	+	896.955i	0.0408142	+	0.0706924i
$545$	1042.18	+	5910.51i	0.0819123	+	0.464548i
$546$	2901.27	+	2434.46i	0.227405	+	0.190815i
$547$	−7114.42	+	5969.71i	−0.556107	+	0.466630i	−0.877003	−	0.480485i	$-0.840461\pi$
$547$	−7114.42	+	5969.71i	−0.556107	+	0.466630i	0.320895	+	0.947115i	$0.396016\pi$
$548$	−37.2356	+	211.174i	−0.00290260	+	0.0164615i
$549$	25641.0	−	9332.57i	1.99332	−	0.725509i
$550$	27375.6			2.12236
$551$	2243.43	−	2659.06i	0.173454	−	0.205590i
$552$	21.9931			0.00169581
$553$	3588.03	−	1305.94i	0.275910	−	0.100423i
$554$	−2657.92	+	15073.8i	−0.203835	+	1.15600i
$555$	45136.7	−	37874.2i	3.45216	−	2.89670i
$556$	−1176.45	−	987.156i	−0.0897346	−	0.0752963i
$557$	−2869.60	−	16274.3i	−0.218292	−	1.23800i	−0.875101	−	0.483940i	$-0.839205\pi$
$557$	−2869.60	−	16274.3i	−0.218292	−	1.23800i	0.656809	−	0.754057i	$-0.271906\pi$
$558$	−97.1017	−	168.185i	−0.00736674	−	0.0127596i
$559$	4333.68	−	7506.15i	0.327898	−	0.567936i
$560$	−2839.37	−	1033.45i	−0.214260	−	0.0779841i
$561$	−13362.0	−	4863.36i	−1.00560	−	0.366009i
$562$	4765.46	−	8254.03i	0.357685	−	0.619529i
$563$	−3080.14	−	5334.97i	−0.230573	−	0.399364i	0.727404	−	0.686210i	$-0.240727\pi$
$563$	−3080.14	−	5334.97i	−0.230573	−	0.399364i	−0.957977	+	0.286845i	$0.907393\pi$
$564$	754.913	+	4281.32i	0.0563609	+	0.319639i
$565$	−23568.4	−	19776.2i	−1.75492	−	1.47255i
$566$	1050.47	−	881.446i	0.0780113	−	0.0654592i
$567$	−901.096	+	5110.37i	−0.0667416	+	0.378510i
$568$	−4598.66	+	1673.77i	−0.339710	+	0.123644i
$569$	−16846.5			−1.24120			−0.620599	−	0.784128i	$-0.713110\pi$
$569$	−16846.5			−1.24120			−0.620599	+	0.784128i	$0.713110\pi$
$570$	−18868.2	−	22609.3i	−1.38649	−	1.66140i
$571$	4447.37			0.325948			0.162974	−	0.986630i	$-0.447891\pi$
$571$	4447.37			0.325948			0.162974	+	0.986630i	$0.447891\pi$
$572$	−4213.91	+	1533.74i	−0.308029	+	0.112113i
$573$	−6530.74	+	37037.7i	−0.476135	+	2.70030i
$574$	679.596	−	570.249i	0.0494178	−	0.0414664i
$575$	−65.6129	−	55.0558i	−0.00475869	−	0.00399302i
$576$	574.940	+	3260.65i	0.0415900	+	0.235869i
$577$	−456.989	−	791.529i	−0.0329718	−	0.0571088i	0.849069	−	0.528283i	$-0.177164\pi$
$577$	−456.989	−	791.529i	−0.0329718	−	0.0571088i	−0.882040	+	0.471174i	$0.843830\pi$
$578$	3865.44	−	6695.13i	0.278168	−	0.481801i
$579$	7560.49	+	2751.79i	0.542665	+	0.197514i
$580$	3163.65	+	1151.48i	0.226489	+	0.0824352i
$581$	−3650.45	+	6322.77i	−0.260665	+	0.451485i
$582$	13136.4	+	22752.9i	0.935604	+	1.62051i
$583$	−804.596	−	4563.09i	−0.0571577	−	0.324158i
$584$	−2497.62	−	2095.75i	−0.176973	−	0.148498i
$585$	−17979.1	+	15086.2i	−1.27067	+	1.06622i
$586$	−770.914	+	4372.07i	−0.0543450	+	0.308206i
$587$	8478.22	−	3085.82i	0.596139	−	0.216977i	−0.0262884	−	0.999654i	$-0.508369\pi$
$587$	8478.22	−	3085.82i	0.596139	−	0.216977i	0.622427	+	0.782678i	$0.286147\pi$
$588$	9020.90			0.632680
$589$	153.158	−	26.5817i	0.0107144	−	0.00185956i
$590$	−22069.5			−1.53998
$591$	−35908.0	+	13069.5i	−2.49925	+	0.909654i
$592$	920.809	−	5222.17i	0.0639274	−	0.362550i
$593$	5322.15	−	4465.81i	0.368557	−	0.309256i	−0.439633	−	0.898177i	$-0.644892\pi$
$593$	5322.15	−	4465.81i	0.368557	−	0.309256i	0.808191	+	0.588921i	$0.200447\pi$
$594$	−16648.1	−	13969.4i	−1.14997	−	0.964937i
$595$	−1061.39	−	6019.47i	−0.0731310	−	0.414746i
$596$	4149.29	+	7186.78i	0.285170	+	0.493930i
$597$	10671.9	−	18484.3i	0.731612	−	1.26719i
$598$	13.1843	+	4.79869i	0.000901582	+	0.000328149i
$599$	−13743.2	−	5002.13i	−0.937451	−	0.341204i	−0.172292	−	0.985046i	$-0.555117\pi$
$599$	−13743.2	−	5002.13i	−0.937451	−	0.341204i	−0.765159	+	0.643842i	$0.777340\pi$
$600$	9812.02	−	16994.9i	0.667623	−	1.15636i
$601$	9988.09	+	17299.9i	0.677908	+	1.17417i	0.975610	+	0.219513i	$0.0704467\pi$
$601$	9988.09	+	17299.9i	0.677908	+	1.17417i	−0.297701	+	0.954659i	$0.596220\pi$
$602$	1253.03	+	7106.31i	0.0848336	+	0.481115i
$603$	−25524.4	−	21417.5i	−1.72377	−	1.44642i
$604$	−888.741	+	745.742i	−0.0598715	+	0.0502381i
$605$	−3898.46	+	22109.3i	−0.261975	+	1.48573i
$606$	10162.5	−	3698.84i	0.681225	−	0.247946i
$607$	17106.1			1.14385			0.571923	−	0.820307i	$-0.306198\pi$
$607$	17106.1			1.14385			0.571923	+	0.820307i	$0.306198\pi$
$608$	−2608.70	−	467.217i	−0.174008	−	0.0311647i
$609$	3513.23			0.233766
$610$	−19861.4	+	7228.95i	−1.31830	+	0.479822i
$611$	−481.594	+	2731.26i	−0.0318874	+	0.180843i
$612$	−5130.70	+	4305.17i	−0.338883	+	0.284356i
$613$	19079.8	+	16009.8i	1.25714	+	1.05486i	0.995981	+	0.0895677i	$0.0285486\pi$
$613$	19079.8	+	16009.8i	1.25714	+	1.05486i	0.261157	+	0.965296i	$0.415896\pi$
$614$	−2782.70	−	15781.5i	−0.182900	−	1.03728i
$615$	4183.44	+	7245.92i	0.274297	+	0.475096i
$616$	1866.70	−	3233.22i	0.122097	−	0.211478i
$617$	−14657.1	−	5334.75i	−0.956358	−	0.348086i	−0.183753	−	0.982972i	$-0.558825\pi$
$617$	−14657.1	−	5334.75i	−0.956358	−	0.348086i	−0.772605	+	0.634887i	$0.781047\pi$
$618$	9193.70	+	3346.23i	0.598422	+	0.217808i
$619$	7588.12	−	13143.0i	0.492718	−	0.853412i	−0.507247	−	0.861801i	$-0.669337\pi$
$619$	7588.12	−	13143.0i	0.492718	−	0.853412i	0.999965	+	0.00838852i	$0.00267018\pi$
$620$	75.2144	+	130.275i	0.00487207	+	0.00843867i
$621$	11.8074	+	66.9630i	0.000762985	+	0.00432710i
$622$	14068.9	+	11805.2i	0.906934	+	0.761008i
$623$	6361.00	−	5337.52i	0.409066	−	0.343247i
$624$	−558.206	+	3165.74i	−0.0358111	+	0.203095i
$625$	−24661.2	+	8975.93i	−1.57831	+	0.574459i
$626$	−18634.1			−1.18973
$627$	31559.3	−	18107.9i	2.01014	−	1.15336i
$628$	−13033.5			−0.828174
$629$	10079.9	−	3668.78i	0.638969	−	0.232566i
$630$	3393.04	−	19242.9i	0.214575	−	1.21691i
$631$	−13569.0	+	11385.7i	−0.856058	+	0.718318i	−0.961115	−	0.276148i	$-0.910942\pi$
$631$	−13569.0	+	11385.7i	−0.856058	+	0.718318i	0.105057	+	0.994466i	$0.466497\pi$
$632$	2482.64	+	2083.18i	0.156257	+	0.131115i
$633$	8801.31	+	49914.7i	0.552640	+	3.13417i
$634$	904.209	+	1566.14i	0.0566415	+	0.0981060i
$635$	−10367.7	+	17957.4i	−0.647921	+	1.12223i
$636$	−3121.18	−	1136.02i	−0.194596	−	0.0708270i
$637$	5407.80	+	1968.28i	0.336365	+	0.122427i
$638$	−2079.89	+	3602.48i	−0.129066	+	0.223548i
$639$	−15823.3	−	27406.8i	−0.979594	−	1.69671i
$640$	−445.345	−	2525.68i	−0.0275059	−	0.155994i
$641$	−5020.83	−	4212.98i	−0.309377	−	0.259598i	0.474857	−	0.880063i	$-0.342500\pi$
$641$	−5020.83	−	4212.98i	−0.309377	−	0.259598i	−0.784235	+	0.620464i	$0.786944\pi$
$642$	13588.3	−	11402.0i	0.835340	−	0.700934i
$643$	−1042.67	+	5913.29i	−0.0639486	+	0.362671i	0.935995	+	0.352014i	$0.114503\pi$
$643$	−1042.67	+	5913.29i	−0.0639486	+	0.362671i	−0.999943	+	0.0106563i	$0.996608\pi$
$644$	−10.9765	+	3.99511i	−0.000671636	+	0.000244455i
$645$	−68054.8			−4.15450
$646$	−1820.04	−	5042.66i	−0.110849	−	0.307122i
$647$	17229.0			1.04690			0.523448	−	0.852058i	$-0.324646\pi$
$647$	17229.0			1.04690			0.523448	+	0.852058i	$0.324646\pi$
$648$	−4138.82	+	1506.41i	−0.250908	+	0.0913229i
$649$	4735.12	−	26854.2i	0.286394	−	1.62422i
$650$	9590.18	−	8047.12i	0.578705	−	0.485591i
$651$	120.251	+	100.903i	0.00723964	+	0.00607478i
$652$	186.151	+	1055.72i	0.0111813	+	0.0634126i
$653$	−8926.03	−	15460.3i	−0.534920	−	0.926508i	−0.999167	−	0.0408027i	$-0.987008\pi$
$653$	−8926.03	−	15460.3i	−0.534920	−	0.926508i	0.464247	−	0.885706i	$-0.346325\pi$
$654$	−2657.89	+	4603.60i	−0.158917	+	0.275252i
$655$	46490.0	+	16921.0i	2.77331	+	1.00940i
$656$	707.575	+	257.536i	0.0421131	+	0.0153279i
$657$	10542.0	−	18259.3i	0.626002	−	1.08427i
$658$	−1154.48	−	1999.62i	−0.0683987	−	0.118470i
$659$	−325.099	−	1843.73i	−0.0192171	−	0.108985i	0.973690	−	0.227875i	$-0.0731777\pi$
$659$	−325.099	−	1843.73i	−0.0192171	−	0.108985i	−0.992907	+	0.118889i	$0.962067\pi$
$660$	26972.7	+	22632.8i	1.59078	+	1.33482i
$661$	12577.8	−	10554.1i	0.740123	−	0.621037i	−0.192748	−	0.981248i	$-0.561740\pi$
$661$	12577.8	−	10554.1i	0.740123	−	0.621037i	0.932871	+	0.360211i	$0.117295\pi$
$662$	−1029.22	+	5836.99i	−0.0604256	+	0.342691i
$663$	−6110.55	+	2224.06i	−0.357940	+	0.130279i
$664$	−6196.79			−0.362172
$665$	13523.9	+	7856.56i	0.788622	+	0.458142i
$666$	34291.1			1.99513
$667$	12.2301	−	4.45138i	0.000709971	−	0.000258408i
$668$	−1054.09	+	5978.06i	−0.0610540	+	0.346254i
$669$	−29755.6	+	24967.9i	−1.71961	+	1.44292i
$670$	19771.1	+	16589.9i	1.14003	+	0.956603i
$671$	−4534.84	−	25718.4i	−0.260903	−	1.47965i
$672$	−1338.14	−	2317.72i	−0.0768150	−	0.133048i
$673$	299.310	−	518.421i	0.0171435	−	0.0296934i	−0.857326	−	0.514773i	$-0.827876\pi$
$673$	299.310	−	518.421i	0.0171435	−	0.0296934i	0.874470	+	0.485080i	$0.161209\pi$
$674$	−3421.04	−	1245.16i	−0.195510	−	0.0711598i
$675$	57012.6	+	20750.9i	3.25099	+	1.18326i
$676$	3368.63	−	5834.64i	0.191661	−	0.331967i
$677$	−5081.46	−	8801.35i	−0.288473	−	0.499651i	0.684972	−	0.728569i	$-0.259814\pi$
$677$	−5081.46	−	8801.35i	−0.288473	−	0.499651i	−0.973446	+	0.228919i	$0.926481\pi$
$678$	−4731.95	−	26836.2i	−0.268037	−	1.52011i
$679$	−10689.3	−	8969.42i	−0.604152	−	0.506944i
$680$	3974.21	−	3334.76i	0.224123	−	0.188062i
$681$	−2382.51	+	13511.9i	−0.134064	+	0.760317i
$682$	−174.657	+	63.5698i	−0.00980637	+	0.00356923i
$683$	−18327.0			−1.02674			−0.513371	−	0.858167i	$-0.671603\pi$
$683$	−18327.0			−1.02674			−0.513371	+	0.858167i	$0.671603\pi$
$684$	46.0586	−	17138.0i	0.00257470	−	0.958025i
$685$	1074.10			0.0599113
$686$	−10578.1	+	3850.12i	−0.588737	+	0.214283i
$687$	7326.14	−	41548.6i	0.406855	−	2.30739i
$688$	−4691.76	+	3936.86i	−0.259988	+	0.218156i
$689$	−1623.20	−	1362.02i	−0.0897516	−	0.0753106i
$690$	−19.1299	−	108.491i	−0.00105545	−	0.00598578i
$691$	54.8896	+	95.0716i	0.00302185	+	0.00523400i	0.867532	−	0.497381i	$-0.165705\pi$
$691$	54.8896	+	95.0716i	0.00302185	+	0.00523400i	−0.864511	+	0.502615i	$0.832371\pi$
$692$	8890.01	−	15398.0i	0.488364	−	0.845871i
$693$	22686.8	+	8257.32i	1.24358	+	0.452625i
$694$	14593.0	+	5311.40i	0.798186	+	0.290516i
$695$	−3846.31	+	6662.01i	−0.209927	+	0.363604i
$696$	1490.96	+	2582.42i	0.0811993	+	0.140641i
$697$	264.501	+	1500.06i	0.0143740	+	0.0815191i
$698$	9972.49	+	8367.91i	0.540780	+	0.453768i
$699$	−22776.4	+	19111.7i	−1.23245	+	1.03415i
$700$	−1809.88	+	10264.3i	−0.0977241	+	0.554221i
$701$	21318.7	−	7759.36i	1.14864	−	0.418070i	0.303612	−	0.952796i	$-0.401807\pi$
$701$	21318.7	−	7759.36i	1.14864	−	0.418070i	0.845026	+	0.534726i	$0.179585\pi$
$702$	−9938.50			−0.534337
$703$	−9457.04	+	25767.3i	−0.507367	+	1.38241i
$704$	3168.80			0.169643
$705$	20463.0	−	7447.91i	1.09316	−	0.397879i
$706$	−2639.09	+	14967.0i	−0.140685	+	0.797864i
$707$	−4400.05	+	3692.08i	−0.234061	+	0.196400i
$708$	−14974.1	−	12564.7i	−0.794859	−	0.666966i
$709$	−1633.44	−	9263.71i	−0.0865235	−	0.490699i	−0.997017	−	0.0771768i	$-0.975409\pi$
$709$	−1633.44	−	9263.71i	−0.0865235	−	0.490699i	0.910494	−	0.413522i	$-0.135702\pi$
$710$	12256.6	+	21229.1i	0.647864	+	1.12213i
$711$	−10478.8	+	18149.8i	−0.552723	+	0.957345i
$712$	6622.89	+	2410.53i	0.348600	+	0.126880i
$713$	0.546458	+	0.198895i	2.87027e−5	+	1.04469e-5i
$714$	2706.89	−	4688.47i	0.141881	−	0.245744i
$715$	11231.2	+	19453.0i	0.587444	+	1.01748i
$716$	−591.450	−	3354.28i	−0.0308708	−	0.175077i
$717$	−5751.99	−	4826.50i	−0.299599	−	0.251393i
$718$	−3289.61	+	2760.31i	−0.170985	+	0.143473i
$719$	−3550.99	+	20138.6i	−0.184186	+	1.04457i	0.742812	+	0.669500i	$0.233492\pi$
$719$	−3550.99	+	20138.6i	−0.184186	+	1.04457i	−0.926997	+	0.375068i	$0.877619\pi$
$720$	15584.6	−	5672.32i	0.806670	−	0.293604i
$721$	−5196.31			−0.268406
$722$	12865.3	+	4761.05i	0.663154	+	0.245413i
$723$	−47668.5			−2.45202
$724$	5717.69	−	2081.07i	0.293503	−	0.106826i
$725$	2016.58	−	11436.6i	0.103302	−	0.585854i
$726$	−15232.5	+	12781.6i	−0.778692	+	0.653400i
$727$	−11246.2	−	9436.70i	−0.573727	−	0.481414i	0.309154	−	0.951012i	$-0.399954\pi$
$727$	−11246.2	−	9436.70i	−0.573727	−	0.481414i	−0.882880	+	0.469598i	$0.844399\pi$
$728$	−296.473	−	1681.38i	−0.0150934	−	0.0855991i
$729$	12048.3	+	20868.3i	0.612117	+	1.06022i
$730$	−8165.79	+	14143.6i	−0.414013	+	0.717091i
$731$	−11642.3	−	4237.45i	−0.589064	−	0.214402i
$732$	−17591.5	−	6402.78i	−0.888252	−	0.323297i
$733$	−8525.63	+	14766.8i	−0.429606	+	0.744099i	−0.996838	−	0.0794585i	$-0.974681\pi$
$733$	−8525.63	+	14766.8i	−0.429606	+	0.744099i	0.567232	+	0.823558i	$0.308014\pi$
$734$	−3087.96	−	5348.50i	−0.155284	−	0.268960i
$735$	−7846.51	−	44499.8i	−0.393773	−	2.23320i
$736$	−7.59488	−	6.37286i	−0.000380368	−	0.000319167i
$737$	−24428.6	+	20498.0i	−1.22095	+	1.02450i
$738$	−845.550	+	4795.35i	−0.0421750	+	0.239186i
$739$	−18432.0	+	6708.68i	−0.917497	+	0.333942i	−0.757242	−	0.653134i	$-0.773454\pi$
$739$	−18432.0	+	6708.68i	−0.917497	+	0.333942i	−0.160255	+	0.987076i	$0.551232\pi$
$740$	−26561.7			−1.31950
$741$	5732.97	−	15620.5i	0.284219	−	0.774403i
$742$	1764.10			0.0872804
$743$	29984.0	−	10913.3i	1.48049	−	0.538856i	0.529566	−	0.848269i	$-0.322355\pi$
$743$	29984.0	−	10913.3i	1.48049	−	0.538856i	0.950928	+	0.309413i	$0.100133\pi$
$744$	−23.1363	+	131.213i	−0.00114008	+	0.00646571i
$745$	31843.0	−	26719.5i	1.56596	−	1.31399i
$746$	−13281.3	−	11144.3i	−0.651825	−	0.546946i
$747$	−6958.56	−	39463.9i	−0.340830	−	1.93294i
$748$	3205.05	+	5551.31i	0.156669	+	0.271358i
$749$	−4710.56	+	8158.92i	−0.229800	+	0.398025i
$750$	−50604.0	−	18418.3i	−2.46373	−	0.896724i
$751$	30660.9	+	11159.6i	1.48979	+	0.542239i	0.953394	−	0.301728i	$-0.0975636\pi$
$751$	30660.9	+	11159.6i	1.48979	+	0.542239i	0.536395	+	0.843967i	$0.319786\pi$
$752$	979.888	−	1697.22i	0.0475171	−	0.0823020i
$753$	−7175.98	−	12429.2i	−0.347287	−	0.601519i
$754$	330.332	+	1873.41i	0.0159549	+	0.0904848i
$755$	4451.76	+	3735.47i	0.214591	+	0.180063i
$756$	6338.41	−	5318.56i	0.304928	−	0.255865i
$757$	4285.83	−	24306.1i	0.205774	−	1.16700i	−0.690443	−	0.723387i	$-0.742584\pi$
$757$	4285.83	−	24306.1i	0.205774	−	1.16700i	0.896217	−	0.443616i	$-0.146305\pi$
$758$	2421.01	−	881.177i	0.116009	−	0.0422240i
$759$	136.117			0.00650952
$760$	−35.6767	+	13275.0i	−0.00170280	+	0.633599i
$761$	12530.3			0.596876			0.298438	−	0.954429i	$-0.403534\pi$
$761$	12530.3			0.596876			0.298438	+	0.954429i	$0.403534\pi$
$762$	−17258.1	+	6281.42i	−0.820464	+	0.298624i
$763$	490.261	−	2780.41i	0.0232617	−	0.131923i
$764$	12987.5	−	10897.8i	0.615016	−	0.516059i
$765$	25700.0	+	21564.8i	1.21462	+	1.01919i
$766$	−4283.69	−	24294.0i	−0.202057	−	1.14592i
$767$	−6235.06	−	10799.4i	−0.293527	−	0.508403i
$768$	1135.77	−	1967.21i	0.0533640	−	0.0924291i
$769$	19987.7	+	7274.94i	0.937290	+	0.341145i	0.765095	−	0.643917i	$-0.222692\pi$
$769$	19987.7	+	7274.94i	0.937290	+	0.341145i	0.172195	+	0.985063i	$0.444914\pi$
$770$	−17573.0	−	6396.07i	−0.822453	−	0.299348i
$771$	5080.24	−	8799.23i	0.237303	−	0.411020i
$772$	−1813.48	−	3141.05i	−0.0845450	−	0.146436i
$773$	−6129.74	−	34763.5i	−0.285216	−	1.61754i	−0.704515	−	0.709689i	$-0.748835\pi$
$773$	−6129.74	−	34763.5i	−0.285216	−	1.61754i	0.419299	−	0.907848i	$-0.362276\pi$
$774$	−30340.2	−	25458.5i	−1.40899	−	1.18228i
$775$	397.491	−	333.534i	0.0184236	−	0.0154592i
$776$	2056.63	−	11663.7i	0.0951403	−	0.539567i
$777$	−26046.3	+	9480.06i	−1.20258	+	0.437703i
$778$	9690.16			0.446541
$779$	−3370.17	−	1957.86i	−0.155005	−	0.0900485i
$780$	16102.0			0.739161
$781$	−28461.4	+	10359.1i	−1.30400	+	0.474619i
$782$	3.48263	−	19.7510i	0.000159256	−	0.000903188i
$783$	−7062.31	+	5925.98i	−0.322333	+	0.270469i
$784$	−3115.19	−	2613.95i	−0.141909	−	0.119076i
$785$	11336.7	+	64293.8i	0.515446	+	2.92324i
$786$	21909.8	+	37948.8i	0.994269	+	1.72212i
$787$	−15848.1	+	27449.7i	−0.717818	+	1.24330i	0.244044	+	0.969764i	$0.421526\pi$
$787$	−15848.1	+	27449.7i	−0.717818	+	1.24330i	−0.961863	+	0.273533i	$0.911808\pi$
$788$	16187.2	+	5891.66i	0.731783	+	0.266347i
$789$	9117.39	+	3318.46i	0.411391	+	0.149734i
$790$	8116.83	−	14058.8i	0.365549	−	0.633149i
$791$	7236.52	+	12534.0i	0.325286	+	0.563411i
$792$	3558.34	+	20180.3i	0.159647	+	0.905401i
$793$	−9148.62	−	7676.60i	−0.409681	−	0.343763i
$794$	−10547.9	+	8850.75i	−0.471450	+	0.395594i
$795$	−2889.08	+	16384.8i	−0.128887	+	0.730954i
$796$	−9041.45	+	3290.82i	−0.402595	+	0.146533i
$797$	−15320.9			−0.680922			−0.340461	−	0.940259i	$-0.610583\pi$
$797$	−15320.9			−0.680922			−0.340461	+	0.940259i	$0.610583\pi$
$798$	4702.97	+	13030.1i	0.208626	+	0.578023i
$799$	3964.39			0.175532
$800$	−8312.93	+	3025.66i	−0.367383	+	0.133717i
$801$	−7914.33	+	44884.4i	−0.349112	+	1.97992i
$802$	7488.34	−	6283.46i	0.329704	−	0.276654i
$803$	−15457.9	−	12970.7i	−0.679324	−	0.570021i
$804$	3969.54	+	22512.4i	0.174123	+	0.987500i
$805$	29.2552	+	50.6715i	0.00128088	+	0.00221855i
$806$	−42.4990	+	73.6105i	−0.00185728	+	0.00321690i
$807$	−1073.61	−	390.760i	−0.0468311	−	0.0170451i
$808$	−4581.20	−	1667.42i	−0.199463	−	0.0725986i
$809$	−6645.39	+	11510.1i	−0.288800	+	0.500217i	−0.973524	−	0.228586i	$-0.926590\pi$
$809$	−6645.39	+	11510.1i	−0.288800	+	0.500217i	0.684723	+	0.728803i	$0.259923\pi$
$810$	11031.1	+	19106.3i	0.478508	+	0.828801i
$811$	935.936	+	5307.95i	0.0405242	+	0.229824i	0.998343	−	0.0575498i	$-0.0183288\pi$
$811$	935.936	+	5307.95i	0.0405242	+	0.229824i	−0.957818	+	0.287374i	$0.907218\pi$
$812$	−1213.22	−	1018.01i	−0.0524332	−	0.0439967i
$813$	16933.0	−	14208.5i	0.730462	−	0.612930i
$814$	5698.94	−	32320.3i	0.245391	−	1.39168i
$815$	5045.89	−	1836.55i	0.216871	−	0.0789345i
$816$	4595.05			0.197131
$817$	27497.6	−	15777.4i	1.17750	−	0.675619i
$818$	−12004.9			−0.513131
$819$	10374.9	−	3776.15i	0.442646	−	0.161110i
$820$	654.958	−	3714.45i	0.0278928	−	0.158188i
$821$	19271.3	−	16170.6i	0.819213	−	0.687401i	−0.133575	−	0.991039i	$-0.542646\pi$
$821$	19271.3	−	16170.6i	0.819213	−	0.687401i	0.952788	+	0.303637i	$0.0982011\pi$
$822$	728.773	+	611.513i	0.0309232	+	0.0259476i
$823$	3839.33	+	21773.9i	0.162613	+	0.922224i	0.951491	+	0.307675i	$0.0995510\pi$
$823$	3839.33	+	21773.9i	0.162613	+	0.922224i	−0.788878	+	0.614549i	$0.789338\pi$
$824$	−2205.23	−	3819.58i	−0.0932317	−	0.161482i
$825$	60727.2	−	105183.i	2.56273	−	4.43877i
$826$	9755.78	+	3550.82i	0.410953	+	0.149575i
$827$	−2213.91	−	805.796i	−0.0930895	−	0.0338818i	0.295056	−	0.955480i	$-0.404662\pi$
$827$	−2213.91	−	805.796i	−0.0930895	−	0.0338818i	−0.388145	+	0.921598i	$0.626884\pi$
$828$	32.0567	−	55.5239i	0.00134547	−	0.00233042i
$829$	8179.42	+	14167.2i	0.342682	+	0.593542i	0.984930	−	0.172955i	$-0.0553314\pi$
$829$	8179.42	+	14167.2i	0.342682	+	0.593542i	−0.642248	+	0.766497i	$0.721998\pi$
$830$	5390.05	+	30568.5i	0.225411	+	1.27837i
$831$	52020.7	+	43650.5i	2.17157	+	1.82217i
$832$	1110.09	−	931.477i	0.0462566	−	0.0388139i
$833$	1428.47	−	8101.24i	0.0594159	−	0.336965i
$834$	−6402.57	+	2330.34i	−0.265831	+	0.0967544i
$835$	30406.4			1.26019
$836$	−16145.4	−	2891.63i	−0.667944	−	0.119628i
$837$	−411.928			−0.0170111
$838$	−4303.60	+	1566.38i	−0.177405	+	0.0645701i
$839$	6989.04	−	39636.8i	0.287590	−	1.63101i	−0.408292	−	0.912851i	$-0.633876\pi$
$839$	6989.04	−	39636.8i	0.287590	−	1.63101i	0.695883	−	0.718155i	$-0.255013\pi$
$840$	−10269.3	+	8616.96i	−0.421814	+	0.353944i
$841$	−17331.3	−	14542.7i	−0.710619	−	0.596280i
$842$	1127.43	+	6393.97i	0.0461447	+	0.261699i
$843$	−21142.4	−	36619.8i	−0.863801	−	1.49615i
$844$	11424.2	−	19787.4i	0.465922	−	0.807001i
$845$	−31712.2	−	11542.3i	−1.29104	−	0.469901i
$846$	11909.0	+	4334.51i	0.483971	+	0.176151i
$847$	5280.52	−	9146.13i	0.214216	−	0.371033i
$848$	748.657	+	1296.71i	0.0303172	+	0.0525109i
$849$	−1056.45	−	5991.42i	−0.0427058	−	0.242197i
$850$	−13708.6	−	11502.9i	−0.553177	−	0.464171i
$851$	−78.6593	+	66.0030i	−0.00316852	+	0.00265870i
$852$	−3770.21	+	21381.9i	−0.151602	+	0.859780i
$853$	25835.8	−	9403.47i	1.03705	−	0.377454i	0.233287	−	0.972408i	$-0.425052\pi$
$853$	25835.8	−	9403.47i	1.03705	−	0.377454i	0.803760	+	0.594954i	$0.202830\pi$
$854$	9942.77			0.398401
$855$	−84581.4	+	14679.7i	−3.38318	+	0.587176i
$856$	−7996.35			−0.319287
$857$	−25711.9	+	9358.37i	−1.02486	+	0.373017i	−0.799120	−	0.601171i	$-0.794701\pi$
$857$	−25711.9	+	9358.37i	−1.02486	+	0.373017i	−0.225736	+	0.974188i	$0.572479\pi$
$858$	−3454.77	+	19593.0i	−0.137464	+	0.779596i
$859$	−5285.59	+	4435.14i	−0.209944	+	0.176164i	−0.741696	−	0.670736i	$-0.765978\pi$
$859$	−5285.59	+	4435.14i	−0.209944	+	0.176164i	0.531752	+	0.846900i	$0.321534\pi$
$860$	23501.3	+	19720.0i	0.931848	+	0.781913i
$861$	−683.466	−	3876.13i	−0.0270528	−	0.153424i
$862$	−8644.75	−	14973.1i	−0.341579	−	0.591632i
$863$	−1702.63	+	2949.03i	−0.0671588	+	0.116323i	−0.897650	−	0.440710i	$-0.854727\pi$
$863$	−1702.63	+	2949.03i	−0.0671588	+	0.116323i	0.830491	+	0.557032i	$0.188060\pi$
$864$	6599.37	+	2401.97i	0.259855	+	0.0945796i
$865$	−83690.2	−	30460.7i	−3.28966	−	1.19734i
$866$	11859.7	−	20541.5i	0.465367	−	0.806039i
$867$	−17149.4	−	29703.6i	−0.671769	−	1.16354i
$868$	−12.2881	−	69.6893i	−0.000480513	−	0.00272512i
$869$	15365.2	+	12892.9i	0.599803	+	0.503295i
$870$	11442.1	−	9601.08i	0.445890	−	0.374146i
$871$	−2532.36	+	14361.7i	−0.0985139	+	0.558700i
$872$	2251.82	−	819.594i	0.0874497	−	0.0318291i
$873$	76589.5			2.96926
$874$	32.8814	+	39.4011i	0.00127257	+	0.00152490i
$875$	28601.5			1.10504
$876$	−13592.8	+	4947.36i	−0.524265	+	0.190817i
$877$	1525.08	−	8649.17i	0.0587211	−	0.333024i	−0.941268	−	0.337660i	$-0.890365\pi$
$877$	1525.08	−	8649.17i	0.0587211	−	0.333024i	0.999989	+	0.00463620i	$0.00147575\pi$
$878$	−5750.70	+	4825.41i	−0.221044	+	0.185478i
$879$	15088.3	+	12660.6i	0.578970	+	0.485814i
$880$	−2756.27	−	15631.6i	−0.105584	−	0.598795i
$881$	16321.1	+	28268.9i	0.624144	+	1.08105i	0.988706	+	0.149870i	$0.0478856\pi$
$881$	16321.1	+	28268.9i	0.624144	+	1.08105i	−0.364561	+	0.931179i	$0.618781\pi$
$882$	13148.7	−	22774.2i	0.501972	−	0.869441i
$883$	34623.6	+	12602.0i	1.31957	+	0.480282i	0.903319	−	0.428969i	$-0.141123\pi$
$883$	34623.6	+	12602.0i	1.31957	+	0.480282i	0.416246	+	0.909252i	$0.363345\pi$
$884$	2754.61	+	1002.60i	0.104805	+	0.0381459i
$885$	−48956.8	+	84795.6i	−1.85951	+	3.22076i
$886$	5417.01	+	9382.53i	0.205404	+	0.355770i
$887$	7207.23	+	40874.2i	0.272824	+	1.54726i	0.745789	+	0.666182i	$0.232073\pi$
$887$	7207.23	+	40874.2i	0.272824	+	1.54726i	−0.472965	+	0.881081i	$0.656816\pi$
$888$	−18022.0	−	15122.3i	−0.681058	−	0.571475i
$889$	7472.23	−	6269.95i	0.281902	−	0.236544i
$890$	6130.39	−	34767.2i	0.230889	−	1.30944i
$891$	−25615.4	+	9323.24i	−0.963129	+	0.350550i
$892$	17510.4			0.657276
$893$	−6541.41	+	7753.34i	−0.245129	+	0.290544i
$894$	36817.5			1.37736
$895$	−16032.1	+	5835.20i	−0.598764	+	0.217932i
$896$	−209.498	+	1188.12i	−0.00781121	+	0.0442996i
$897$	47.6843	−	40.0119i	0.00177495	−	0.00148936i
$898$	422.736	+	354.717i	0.0157092	+	0.0131816i
$899$	13.6915	+	77.6484i	0.000507939	+	0.00288067i
$900$	−28603.6	−	49542.9i	−1.05939	−	1.83492i
$901$	−1514.44	+	2623.09i	−0.0559971	+	0.0969899i
$902$	4379.23	+	1593.91i	0.161654	+	0.0588374i
$903$	30083.5	+	10949.5i	1.10866	+	0.403518i
$904$	−6142.14	+	10638.5i	−0.225978	+	0.391406i
$905$	−15239.2	−	26395.0i	−0.559743	−	0.969503i
$906$	893.802	+	5069.00i	0.0327755	+	0.185879i
$907$	−14285.1	−	11986.6i	−0.522966	−	0.438820i	0.342698	−	0.939445i	$-0.388659\pi$
$907$	−14285.1	−	11986.6i	−0.522966	−	0.438820i	−0.865664	+	0.500625i	$0.833104\pi$
$908$	4738.03	−	3975.68i	0.173169	−	0.145306i
$909$	5474.52	−	31047.6i	0.199756	−	1.13287i
$910$	−8036.31	+	2924.98i	−0.292749	+	0.106552i
$911$	45819.5			1.66637			0.833187	−	0.552991i	$-0.186514\pi$
$911$	45819.5			1.66637			0.833187	+	0.552991i	$0.186514\pi$
$912$	−7582.02	+	8986.74i	−0.275291	+	0.326295i
$913$	−38352.3			−1.39023
$914$	27371.2	−	9962.32i	0.990547	−	0.360530i
$915$	−16283.3	+	92347.4i	−0.588318	+	3.33652i
$916$	−14569.3	+	12225.1i	−0.525528	+	0.440970i
$917$	−17828.4	−	14959.8i	−0.642034	−	0.538730i
$918$	2466.93	+	13990.7i	0.0886937	+	0.503007i
$919$	−18660.9	−	32321.6i	−0.669821	−	1.16016i	−0.977954	−	0.208821i	$-0.933037\pi$
$919$	−18660.9	−	32321.6i	−0.669821	−	1.16016i	0.308133	−	0.951343i	$-0.400296\pi$
$920$	−24.8309	+	43.0085i	−0.000889839	+	0.00154125i
$921$	−66808.6	−	24316.3i	−2.39025	−	0.869979i
$922$	5865.10	+	2134.72i	0.209498	+	0.0762509i
$923$	−6925.48	+	11995.3i	−0.246972	+	0.427768i
$924$	−8281.80	−	14344.5i	−0.294861	−	0.510714i
$925$	15909.9	+	90229.7i	0.565530	+	3.20728i
$926$	12370.9	+	10380.4i	0.439021	+	0.368383i
$927$	21848.5	−	18333.0i	0.774107	−	0.649553i
$928$	233.425	−	1323.82i	0.00825705	−	0.0468280i
$929$	12064.1	−	4390.97i	0.426060	−	0.155073i	−0.120085	−	0.992764i	$-0.538317\pi$
$929$	12064.1	−	4390.97i	0.426060	−	0.155073i	0.546145	+	0.837690i	$0.316095\pi$
$930$	667.392			0.0235319
$931$	13486.9	+	16161.1i	0.474776	+	0.568914i
$932$	13403.3			0.471072
$933$	76567.3	−	27868.2i	2.68671	−	0.977882i
$934$	6338.36	−	35946.6i	0.222053	−	1.25932i
$935$	24596.6	−	20639.0i	0.860316	−	0.721891i
$936$	7178.62	+	6023.58i	0.250684	+	0.210349i
$937$	−5661.39	−	32107.3i	−0.197385	−	1.11942i	−0.908981	−	0.416836i	$-0.863139\pi$
$937$	−5661.39	−	32107.3i	−0.197385	−	1.11942i	0.711597	−	0.702588i	$-0.247972\pi$
$938$	−6070.58	−	10514.5i	−0.211313	−	0.366004i
$939$	−41336.1	+	71596.2i	−1.43658	+	2.48823i
$940$	−9224.62	−	3357.49i	−0.320079	−	0.116499i
$941$	−23090.3	−	8404.18i	−0.799917	−	0.291146i	−0.0904648	−	0.995900i	$-0.528835\pi$
$941$	−23090.3	−	8404.18i	−0.799917	−	0.291146i	−0.709452	+	0.704754i	$0.751057\pi$
$942$	−28912.2	+	50077.4i	−1.00001	+	1.73207i
$943$	−7.29044	−	12.6274i	−0.000251760	−	0.000436061i
$944$	1530.16	+	8677.96i	0.0527568	+	0.299199i
$945$	−31749.5	−	26641.0i	−1.09292	−	0.917071i
$946$	−29037.6	+	24365.5i	−0.997986	+	0.837409i
$947$	2906.74	−	16484.9i	0.0997428	−	0.565669i	−0.893448	−	0.449167i	$-0.851721\pi$
$947$	2906.74	−	16484.9i	0.0997428	−	0.565669i	0.993190	−	0.116502i	$-0.0371682\pi$
$948$	13511.3	−	4917.69i	0.462896	−	0.168480i
$949$	−9227.97			−0.315651
$950$	45116.4	−	7830.28i	1.54081	−	0.267419i
$951$	8023.22			0.273576
$952$	−2293.33	+	834.703i	−0.0780748	+	0.0284169i
$953$	3171.20	−	17984.8i	0.107791	−	0.611316i	−0.882277	−	0.470730i	$-0.843990\pi$
$953$	3171.20	−	17984.8i	0.107791	−	0.611316i	0.990069	−	0.140585i	$-0.0448984\pi$
$954$	−7417.35	+	6223.90i	−0.251725	+	0.211222i
$955$	−65055.3	−	54587.9i	−2.20433	−	1.84966i
$956$	587.780	+	3333.47i	0.0198851	+	0.112774i
$957$	9227.65	+	15982.8i	0.311690	+	0.539863i
$958$	−394.032	+	682.484i	−0.0132887	+	0.0230168i
$959$	−474.804	−	172.814i	−0.0159877	−	0.00581905i
$960$	−10692.1	−	3891.60i	−0.359464	−	0.130834i
$961$	14893.7	−	25796.7i	0.499941	−	0.865923i
$962$	−7504.19	−	12997.6i	−0.251502	−	0.435614i
$963$	−8979.34	−	50924.4i	−0.300473	−	1.70407i
$964$	16461.4	+	13812.7i	0.549984	+	0.461492i
$965$	−13917.3	+	11678.0i	−0.464262	+	0.389562i
$966$	−8.99906	+	51.0362i	−0.000299731	+	0.00169986i
$967$	−34470.4	+	12546.2i	−1.14632	+	0.417227i	−0.844193	−	0.536040i	$-0.819920\pi$
$967$	−34470.4	+	12546.2i	−1.14632	+	0.417227i	−0.302129	+	0.953267i	$0.597697\pi$
$968$	8963.89			0.297635
$969$	−23412.3	−	4193.13i	−0.776174	−	0.139012i
$970$	−59325.7			−1.96375
$971$	−51355.9	+	18692.0i	−1.69731	+	0.617771i	−0.995515	−	0.0946055i	$-0.969841\pi$
$971$	−51355.9	+	18692.0i	−1.69731	+	0.617771i	−0.701797	+	0.712377i	$0.747619\pi$
$972$	722.649	−	4098.34i	0.0238467	−	0.135241i
$973$	2772.12	−	2326.09i	0.0913362	−	0.0766402i
$974$	−16380.6	−	13744.9i	−0.538878	−	0.452172i
$975$	−9644.80	−	54698.4i	−0.316801	−	1.79667i
$976$	4219.56	+	7308.49i	0.138386	+	0.239692i
$977$	−19122.3	+	33120.8i	−0.626178	+	1.08457i	0.362134	+	0.932126i	$0.382048\pi$
$977$	−19122.3	+	33120.8i	−0.626178	+	1.08457i	−0.988312	+	0.152446i	$0.951285\pi$
$978$	4469.21	+	1626.66i	0.146124	+	0.0531849i
$979$	40989.5	+	14918.9i	1.33813	+	0.487039i
$980$	−10184.9	+	17640.8i	−0.331984	+	0.575013i
$981$	7748.18	+	13420.2i	0.252172	+	0.436774i
$982$	986.575	+	5595.14i	0.0320599	+	0.181821i
$983$	1737.09	+	1457.60i	0.0563629	+	0.0472941i	0.670534	−	0.741879i	$-0.266065\pi$
$983$	1737.09	+	1457.60i	0.0563629	+	0.0472941i	−0.614171	+	0.789173i	$0.710510\pi$
$984$	2559.12	−	2147.36i	0.0829083	−	0.0695683i
$985$	14983.5	−	84975.5i	0.484683	−	2.74878i
$986$	2555.24	−	930.033i	0.0825310	−	0.0300388i
$987$	−10243.9			−0.330363
$988$	−6506.05	+	3732.99i	−0.209499	+	0.120205i
$989$	118.598			0.00381316
$990$	96453.8	−	35106.3i	3.09647	−	1.12702i
$991$	−8013.62	+	45447.5i	−0.256873	+	1.45680i	0.534346	+	0.845266i	$0.320558\pi$
$991$	−8013.62	+	45447.5i	−0.256873	+	1.45680i	−0.791219	+	0.611533i	$0.790553\pi$
$992$	46.0107	−	38.6075i	0.00147262	−	0.00123568i
$993$	20143.8	+	16902.7i	0.643751	+	0.540171i
$994$	−2002.42	−	11356.3i	−0.0638963	−	0.362374i
$995$	24097.9	+	41738.7i	0.767793	+	1.32986i
$996$	−13746.3	+	23809.3i	−0.437318	+	0.757457i
$997$	28646.2	+	10426.3i	0.909963	+	0.331199i	0.754238	−	0.656601i	$-0.228006\pi$
$997$	28646.2	+	10426.3i	0.909963	+	0.331199i	0.155725	+	0.987800i	$0.450229\pi$
$998$	−3289.05	−	1197.11i	−0.104322	−	0.0379699i
$999$	36367.7	−	62990.7i	1.15178	−	1.99493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.e.a.5.1	✓	12
19.2	odd	18		722.4.a.o.1.6		6
19.4	even	9	inner	38.4.e.a.23.1	yes	12
19.17	even	9		722.4.a.p.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.a.5.1	✓	12	1.1	even	1	trivial
38.4.e.a.23.1	yes	12	19.4	even	9	inner
722.4.a.o.1.6		6	19.2	odd	18
722.4.a.p.1.1		6	19.17	even	9

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87939 + 0.684040i) q^{2} +(-1.54081 + 8.73839i) q^{3} +(3.06418 - 2.57115i) q^{4} +(-15.3487 - 12.8791i) q^{5} +(-3.08163 - 17.4768i) q^{6} +(4.71270 + 8.16264i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-48.6136 - 17.6939i) q^{9} +O(q^{10})\)	\(q+(-1.87939 + 0.684040i) q^{2} +(-1.54081 + 8.73839i) q^{3} +(3.06418 - 2.57115i) q^{4} +(-15.3487 - 12.8791i) q^{5} +(-3.08163 - 17.4768i) q^{6} +(4.71270 + 8.16264i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-48.6136 - 17.6939i) q^{9} +(37.6558 + 13.7056i) q^{10} +(-24.7562 + 42.8791i) q^{11} +(17.7464 + 30.7376i) q^{12} +(3.93183 + 22.2985i) q^{13} +(-14.4406 - 12.1171i) q^{14} +(136.192 - 114.278i) q^{15} +(2.77837 - 15.7569i) q^{16} +(30.4142 - 11.0699i) q^{17} +103.467 q^{18} +(-28.5348 + 77.7481i) q^{19} -80.1450 q^{20} +(-78.5897 + 28.6043i) q^{21} +(17.1955 - 97.5206i) q^{22} +(-0.237340 + 0.199152i) q^{23} +(-54.3781 - 45.6286i) q^{24} +(48.0052 + 272.251i) q^{25} +(-22.6425 - 39.2180i) q^{26} +(109.733 - 190.063i) q^{27} +(35.4279 + 12.8947i) q^{28} +(-39.4741 - 14.3674i) q^{29} +(-177.785 + 307.933i) q^{30} +(-0.938479 - 1.62549i) q^{31} +(5.55674 + 31.5138i) q^{32} +(-336.549 - 282.398i) q^{33} +(-49.5877 + 41.6090i) q^{34} +(32.7934 - 185.981i) q^{35} +(-194.455 + 70.7757i) q^{36} +331.421 q^{37} +(0.445152 - 165.638i) q^{38} -200.911 q^{39} +(150.623 - 54.8224i) q^{40} +(-8.17216 + 46.3466i) q^{41} +(128.134 - 107.517i) q^{42} +(-293.235 - 246.054i) q^{43} +(34.3910 + 195.041i) q^{44} +(518.273 + 897.675i) q^{45} +(0.309825 - 0.536633i) q^{46} +(115.099 + 41.8927i) q^{47} +(133.409 + 48.5570i) q^{48} +(127.081 - 220.110i) q^{49} +(-276.451 - 478.827i) q^{50} +(49.8701 + 282.827i) q^{51} +(69.3807 + 58.2173i) q^{52} +(-71.6880 + 60.1534i) q^{53} +(-76.2196 + 432.263i) q^{54} +(932.217 - 339.299i) q^{55} -75.4033 q^{56} +(-635.426 - 369.144i) q^{57} +84.0149 q^{58} +(-517.526 + 188.364i) q^{59} +(123.489 - 700.338i) q^{60} +(-404.046 + 339.035i) q^{61} +(2.87567 + 2.41297i) q^{62} +(-84.6726 - 480.202i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(226.835 - 392.891i) q^{65} +(825.678 + 300.522i) q^{66} +(605.223 + 220.283i) q^{67} +(64.7322 - 112.119i) q^{68} +(-1.37457 - 2.38082i) q^{69} +(65.5868 + 371.961i) q^{70} +(468.607 + 393.208i) q^{71} +(317.042 - 266.030i) q^{72} +(-70.7704 + 401.359i) q^{73} +(-622.867 + 226.705i) q^{74} -2453.00 q^{75} +(112.466 + 311.601i) q^{76} -466.675 q^{77} +(377.590 - 137.431i) q^{78} +(70.3461 - 398.953i) q^{79} +(-245.578 + 206.065i) q^{80} +(421.750 + 353.890i) q^{81} +(-16.3443 - 92.6933i) q^{82} +(387.299 + 670.822i) q^{83} +(-167.267 + 289.715i) q^{84} +(-609.386 - 221.798i) q^{85} +(719.413 + 261.845i) q^{86} +(186.370 - 322.803i) q^{87} +(-198.050 - 343.033i) q^{88} +(-152.983 - 867.607i) q^{89} +(-1588.08 - 1332.56i) q^{90} +(-163.485 + 137.180i) q^{91} +(-0.215202 + 1.22047i) q^{92} +(15.6502 - 5.69621i) q^{93} -244.972 q^{94} +(1439.29 - 825.827i) q^{95} -283.942 q^{96} +(-1391.18 + 506.347i) q^{97} +(-88.2694 + 500.601i) q^{98} +(1962.19 - 1646.47i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9	\( 12 q - 9 q^{3} - 18 q^{6} + 21 q^{7} - 48 q^{8} - 27 q^{9} - 9 q^{11} + 36 q^{12} + 39 q^{13} - 138 q^{14} + 423 q^{15} + 69 q^{17} + 132 q^{18} - 462 q^{19} - 216 q^{20} - 279 q^{21} + 204 q^{22} - 66 q^{23} - 72 q^{24} + 342 q^{25} + 48 q^{26} + 189 q^{27} + 192 q^{28} + 159 q^{29} + 72 q^{31} - 1560 q^{33} + 408 q^{34} - 135 q^{35} - 108 q^{36} + 1116 q^{37} - 294 q^{38} - 1248 q^{39} + 147 q^{41} + 414 q^{42} - 117 q^{43} + 408 q^{44} + 1296 q^{45} + 528 q^{46} + 783 q^{47} + 288 q^{48} + 1413 q^{49} - 354 q^{50} - 2301 q^{51} - 348 q^{52} - 249 q^{53} - 540 q^{54} + 2187 q^{55} - 336 q^{56} - 2670 q^{57} - 1932 q^{58} - 4248 q^{59} + 324 q^{60} + 3114 q^{61} - 438 q^{62} + 363 q^{63} - 384 q^{64} + 495 q^{65} + 822 q^{66} + 3060 q^{67} + 408 q^{68} - 237 q^{69} - 270 q^{70} + 1686 q^{71} + 432 q^{72} + 1626 q^{73} + 90 q^{74} - 1854 q^{75} - 1416 q^{77} - 108 q^{78} - 327 q^{79} + 3483 q^{81} + 294 q^{82} + 927 q^{83} + 204 q^{84} - 3294 q^{85} + 1188 q^{86} + 2892 q^{87} - 72 q^{88} - 6366 q^{89} - 5076 q^{90} + 840 q^{91} - 156 q^{92} + 870 q^{93} + 3432 q^{94} + 513 q^{95} - 576 q^{96} - 8052 q^{97} + 378 q^{98} + 4494 q^{99}+O(q^{100}) \) 12 * q - 9 * q^3 - 18 * q^6 + 21 * q^7 - 48 * q^8 - 27 * q^9 - 9 * q^11 + 36 * q^12 + 39 * q^13 - 138 * q^14 + 423 * q^15 + 69 * q^17 + 132 * q^18 - 462 * q^19 - 216 * q^20 - 279 * q^21 + 204 * q^22 - 66 * q^23 - 72 * q^24 + 342 * q^25 + 48 * q^26 + 189 * q^27 + 192 * q^28 + 159 * q^29 + 72 * q^31 - 1560 * q^33 + 408 * q^34 - 135 * q^35 - 108 * q^36 + 1116 * q^37 - 294 * q^38 - 1248 * q^39 + 147 * q^41 + 414 * q^42 - 117 * q^43 + 408 * q^44 + 1296 * q^45 + 528 * q^46 + 783 * q^47 + 288 * q^48 + 1413 * q^49 - 354 * q^50 - 2301 * q^51 - 348 * q^52 - 249 * q^53 - 540 * q^54 + 2187 * q^55 - 336 * q^56 - 2670 * q^57 - 1932 * q^58 - 4248 * q^59 + 324 * q^60 + 3114 * q^61 - 438 * q^62 + 363 * q^63 - 384 * q^64 + 495 * q^65 + 822 * q^66 + 3060 * q^67 + 408 * q^68 - 237 * q^69 - 270 * q^70 + 1686 * q^71 + 432 * q^72 + 1626 * q^73 + 90 * q^74 - 1854 * q^75 - 1416 * q^77 - 108 * q^78 - 327 * q^79 + 3483 * q^81 + 294 * q^82 + 927 * q^83 + 204 * q^84 - 3294 * q^85 + 1188 * q^86 + 2892 * q^87 - 72 * q^88 - 6366 * q^89 - 5076 * q^90 + 840 * q^91 - 156 * q^92 + 870 * q^93 + 3432 * q^94 + 513 * q^95 - 576 * q^96 - 8052 * q^97 + 378 * q^98 + 4494 * q^99

Introduction

L-functions

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