LMFDB - Embedded newform 74.4.f.b.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, 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("74.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.f (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:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	74.53
Dual form			74.4.f.b.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 - 0.684040i) q^{2} +(6.42413 - 2.33819i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-3.55870 + 20.1824i) q^{5} -13.6728 q^{6} +(-4.31979 + 24.4987i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(15.1191 - 12.6865i) q^{9} +O(q^{10})$	\(q+(-1.87939 - 0.684040i) q^{2} +(6.42413 - 2.33819i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-3.55870 + 20.1824i) q^{5} -13.6728 q^{6} +(-4.31979 + 24.4987i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(15.1191 - 12.6865i) q^{9} +(20.4938 - 35.4962i) q^{10} +(-11.5152 - 19.9449i) q^{11} +(25.6965 + 9.35277i) q^{12} +(11.6065 + 9.73897i) q^{13} +(24.8767 - 43.0877i) q^{14} +(24.3288 + 137.975i) q^{15} +(2.77837 + 15.7569i) q^{16} +(-22.3514 + 18.7550i) q^{17} +(-37.0927 + 13.5006i) q^{18} +(145.227 - 52.8583i) q^{19} +(-62.7965 + 52.6925i) q^{20} +(29.5319 + 167.484i) q^{21} +(7.99836 + 45.3610i) q^{22} +(91.8331 - 159.060i) q^{23} +(-41.8960 - 35.1549i) q^{24} +(-277.204 - 100.894i) q^{25} +(-15.1511 - 26.2426i) q^{26} +(-24.8277 + 43.0029i) q^{27} +(-76.2266 + 63.9617i) q^{28} +(-24.9419 - 43.2007i) q^{29} +(48.6576 - 275.951i) q^{30} +171.742 q^{31} +(5.55674 - 31.5138i) q^{32} +(-120.610 - 101.204i) q^{33} +(54.8361 - 19.9587i) q^{34} +(-479.071 - 174.368i) q^{35} +78.9465 q^{36} +(222.482 - 33.9799i) q^{37} -309.094 q^{38} +(97.3330 + 35.4263i) q^{39} +(154.063 - 56.0742i) q^{40} +(-50.7025 - 42.5445i) q^{41} +(59.0638 - 334.967i) q^{42} -22.3507 q^{43} +(15.9967 - 90.7220i) q^{44} +(202.239 + 350.288i) q^{45} +(-281.393 + 236.117i) q^{46} +(-242.360 + 419.780i) q^{47} +(54.6914 + 94.7282i) q^{48} +(-259.214 - 94.3460i) q^{49} +(451.957 + 379.237i) q^{50} +(-99.7354 + 172.747i) q^{51} +(10.5239 + 59.6839i) q^{52} +(-0.712563 - 4.04115i) q^{53} +(76.0766 - 63.8358i) q^{54} +(443.515 - 161.426i) q^{55} +(187.011 - 68.0666i) q^{56} +(809.364 - 679.137i) q^{57} +(17.3245 + 98.2520i) q^{58} +(45.6270 + 258.764i) q^{59} +(-280.208 + 485.334i) q^{60} +(137.758 + 115.593i) q^{61} +(-322.769 - 117.478i) q^{62} +(245.491 + 425.203i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-237.860 + 199.588i) q^{65} +(157.445 + 272.703i) q^{66} +(65.9225 - 373.865i) q^{67} -116.711 q^{68} +(218.036 - 1236.54i) q^{69} +(781.084 + 655.408i) q^{70} +(-896.955 + 326.465i) q^{71} +(-148.371 - 54.0026i) q^{72} +733.867 q^{73} +(-441.374 - 88.3256i) q^{74} -2016.70 q^{75} +(580.907 + 211.433i) q^{76} +(538.368 - 195.950i) q^{77} +(-158.693 - 133.159i) q^{78} +(93.2873 - 529.058i) q^{79} -327.900 q^{80} +(-151.483 + 859.101i) q^{81} +(66.1874 + 114.640i) q^{82} +(574.713 - 482.241i) q^{83} +(-340.135 + 589.131i) q^{84} +(-298.980 - 517.849i) q^{85} +(42.0056 + 15.2888i) q^{86} +(-261.242 - 219.208i) q^{87} +(-92.1215 + 159.559i) q^{88} +(-124.766 - 707.585i) q^{89} +(-140.474 - 796.665i) q^{90} +(-288.730 + 242.273i) q^{91} +(690.359 - 251.270i) q^{92} +(1103.29 - 401.566i) q^{93} +(742.634 - 623.144i) q^{94} +(549.988 + 3119.13i) q^{95} +(-37.9882 - 215.442i) q^{96} +(-189.655 + 328.493i) q^{97} +(422.626 + 354.625i) q^{98} +(-427.130 - 155.462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) $ 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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
$3$	6.42413	−	2.33819i	1.23632	−	0.449985i	0.360566	−	0.932734i	$-0.382584\pi$
$3$	6.42413	−	2.33819i	1.23632	−	0.449985i	0.875759	+	0.482748i	$0.160361\pi$
$4$	3.06418	+	2.57115i	0.383022	+	0.321394i
$5$	−3.55870	+	20.1824i	−0.318300	+	1.80517i	0.234788	+	0.972047i	$0.424560\pi$
$5$	−3.55870	+	20.1824i	−0.318300	+	1.80517i	−0.553088	+	0.833123i	$0.686551\pi$
$6$	−13.6728			−0.930319
$7$	−4.31979	+	24.4987i	−0.233247	+	1.32281i	0.613028	+	0.790061i	$0.289951\pi$
$7$	−4.31979	+	24.4987i	−0.233247	+	1.32281i	−0.846275	+	0.532747i	$0.821160\pi$
$8$	−4.00000	−	6.92820i	−0.176777	−	0.306186i
$9$	15.1191	−	12.6865i	0.559968	−	0.469869i
$10$	20.4938	−	35.4962i	0.648069	−	1.12249i
$11$	−11.5152	−	19.9449i	−0.315633	−	0.546692i	0.663939	−	0.747787i	$-0.268883\pi$
$11$	−11.5152	−	19.9449i	−0.315633	−	0.546692i	−0.979572	+	0.201095i	$0.935550\pi$
$12$	25.6965	+	9.35277i	0.618162	+	0.224993i
$13$	11.6065	+	9.73897i	0.247619	+	0.207777i	0.758146	−	0.652084i	$-0.226105\pi$
$13$	11.6065	+	9.73897i	0.247619	+	0.207777i	−0.510527	+	0.859862i	$0.670550\pi$
$14$	24.8767	−	43.0877i	0.474898	−	0.822548i
$15$	24.3288	+	137.975i	0.418778	+	2.37501i
$16$	2.77837	+	15.7569i	0.0434120	+	0.246202i
$17$	−22.3514	+	18.7550i	−0.318883	+	0.267575i	−0.788152	−	0.615481i	$-0.788962\pi$
$17$	−22.3514	+	18.7550i	−0.318883	+	0.267575i	0.469269	+	0.883055i	$0.344517\pi$
$18$	−37.0927	+	13.5006i	−0.485713	+	0.176785i
$19$	145.227	−	52.8583i	1.75354	−	0.638238i	0.753723	−	0.657192i	$-0.228256\pi$
$19$	145.227	−	52.8583i	1.75354	−	0.638238i	0.999820	+	0.0189544i	$0.00603373\pi$
$20$	−62.7965	+	52.6925i	−0.702086	+	0.589120i
$21$	29.5319	+	167.484i	0.306876	+	1.74038i
$22$	7.99836	+	45.3610i	0.0775117	+	0.439591i
$23$	91.8331	−	159.060i	0.832545	−	1.44201i	−0.0634687	−	0.997984i	$-0.520216\pi$
$23$	91.8331	−	159.060i	0.832545	−	1.44201i	0.896014	−	0.444026i	$-0.146450\pi$
$24$	−41.8960	−	35.1549i	−0.356333	−	0.298999i
$25$	−277.204	−	100.894i	−2.21763	−	0.807151i
$26$	−15.1511	−	26.2426i	−0.114284	−	0.197946i
$27$	−24.8277	+	43.0029i	−0.176967	+	0.306515i
$28$	−76.2266	+	63.9617i	−0.514481	+	0.431701i
$29$	−24.9419	−	43.2007i	−0.159710	−	0.276626i	0.775054	−	0.631895i	$-0.217723\pi$
$29$	−24.9419	−	43.2007i	−0.159710	−	0.276626i	−0.934764	+	0.355269i	$0.884389\pi$
$30$	48.6576	−	275.951i	0.296121	−	1.67938i
$31$	171.742			0.995024			0.497512	−	0.867457i	$-0.334247\pi$
$31$	171.742			0.995024			0.497512	+	0.867457i	$0.334247\pi$
$32$	5.55674	−	31.5138i	0.0306970	−	0.174091i
$33$	−120.610	−	101.204i	−0.636228	−	0.533859i
$34$	54.8361	−	19.9587i	0.276597	−	0.100673i
$35$	−479.071	−	174.368i	−2.31365	−	0.842100i
$36$	78.9465			0.365493
$37$	222.482	−	33.9799i	0.988537	−	0.150980i
$37$	222.482	−	33.9799i	0.988537	−	0.150980i
$38$	−309.094			−1.31952
$39$	97.3330	+	35.4263i	0.399635	+	0.145455i
$40$	154.063	−	56.0742i	0.608986	−	0.221653i
$41$	−50.7025	−	42.5445i	−0.193132	−	0.162057i	0.541094	−	0.840962i	$-0.318010\pi$
$41$	−50.7025	−	42.5445i	−0.193132	−	0.162057i	−0.734226	+	0.678905i	$0.762455\pi$
$42$	59.0638	−	334.967i	0.216994	−	1.23063i
$43$	−22.3507			−0.0792662			−0.0396331	−	0.999214i	$-0.512619\pi$
$43$	−22.3507			−0.0792662			−0.0396331	+	0.999214i	$0.512619\pi$
$44$	15.9967	−	90.7220i	0.0548090	−	0.310837i
$45$	202.239	+	350.288i	0.669955	+	1.16040i
$46$	−281.393	+	236.117i	−0.901938	+	0.756816i
$47$	−242.360	+	419.780i	−0.752166	+	1.30279i	0.194604	+	0.980882i	$0.437658\pi$
$47$	−242.360	+	419.780i	−0.752166	+	1.30279i	−0.946771	+	0.321909i	$0.895676\pi$
$48$	54.6914	+	94.7282i	0.164459	+	0.284851i
$49$	−259.214	−	94.3460i	−0.755725	−	0.275061i
$50$	451.957	+	379.237i	1.27833	+	1.07264i
$51$	−99.7354	+	172.747i	−0.273838	+	0.474302i
$52$	10.5239	+	59.6839i	0.0280654	+	0.159167i
$53$	−0.712563	−	4.04115i	−0.00184676	−	0.0104735i	0.983870	−	0.178882i	$-0.0572482\pi$
$53$	−0.712563	−	4.04115i	−0.00184676	−	0.0104735i	−0.985717	+	0.168409i	$0.946137\pi$
$54$	76.0766	−	63.8358i	0.191717	−	0.160870i
$55$	443.515	−	161.426i	1.08734	−	0.395758i
$56$	187.011	−	68.0666i	0.446258	−	0.162425i
$57$	809.364	−	679.137i	1.88075	−	1.57814i
$58$	17.3245	+	98.2520i	0.0392209	+	0.222433i
$59$	45.6270	+	258.764i	0.100680	+	0.570986i	0.992858	+	0.119302i	$0.0380656\pi$
$59$	45.6270	+	258.764i	0.100680	+	0.570986i	−0.892178	+	0.451684i	$0.850823\pi$
$60$	−280.208	+	485.334i	−0.602911	+	1.04427i
$61$	137.758	+	115.593i	0.289149	+	0.242625i	0.775811	−	0.630965i	$-0.217341\pi$
$61$	137.758	+	115.593i	0.289149	+	0.242625i	−0.486662	+	0.873591i	$0.661785\pi$
$62$	−322.769	−	117.478i	−0.661157	−	0.240641i
$63$	245.491	+	425.203i	0.490936	+	0.850326i
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−237.860	+	199.588i	−0.453890	+	0.380859i
$66$	157.445	+	272.703i	0.293639	+	0.508598i
$67$	65.9225	−	373.865i	0.120205	−	0.681715i	−0.863836	−	0.503773i	$-0.831945\pi$
$67$	65.9225	−	373.865i	0.120205	−	0.681715i	0.984041	−	0.177942i	$-0.0569440\pi$
$68$	−116.711			−0.208136
$69$	218.036	−	1236.54i	0.380412	−	2.15743i
$70$	781.084	+	655.408i	1.33368	+	1.11909i
$71$	−896.955	+	326.465i	−1.49928	+	0.545694i	−0.955875	−	0.293775i	$-0.905088\pi$
$71$	−896.955	+	326.465i	−1.49928	+	0.545694i	−0.543407	+	0.839469i	$0.682866\pi$
$72$	−148.371	−	54.0026i	−0.242857	−	0.0883926i
$73$	733.867			1.17661			0.588306	−	0.808639i	$-0.299795\pi$
$73$	733.867			1.17661			0.588306	+	0.808639i	$0.299795\pi$
$74$	−441.374	−	88.3256i	−0.693360	−	0.138752i
$75$	−2016.70			−3.10492
$76$	580.907	+	211.433i	0.876772	+	0.319119i
$77$	538.368	−	195.950i	0.796789	−	0.290007i
$78$	−158.693	−	133.159i	−0.230365	−	0.193299i
$79$	93.2873	−	529.058i	0.132856	−	0.753465i	−0.843472	−	0.537172i	$-0.819492\pi$
$79$	93.2873	−	529.058i	0.132856	−	0.753465i	0.976329	−	0.216292i	$-0.0693964\pi$
$80$	−327.900			−0.458254
$81$	−151.483	+	859.101i	−0.207795	+	1.17847i
$82$	66.1874	+	114.640i	0.0891363	+	0.154389i
$83$	574.713	−	482.241i	0.760035	−	0.637745i	−0.178101	−	0.984012i	$-0.556995\pi$
$83$	574.713	−	482.241i	0.760035	−	0.637745i	0.938136	+	0.346267i	$0.112551\pi$
$84$	−340.135	+	589.131i	−0.441807	+	0.765231i
$85$	−298.980	−	517.849i	−0.381517	−	0.660807i
$86$	42.0056	+	15.2888i	0.0526695	+	0.0191701i
$87$	−261.242	−	219.208i	−0.321932	−	0.270133i
$88$	−92.1215	+	159.559i	−0.111593	+	0.193285i
$89$	−124.766	−	707.585i	−0.148598	−	0.842740i	−0.964408	−	0.264420i	$-0.914820\pi$
$89$	−124.766	−	707.585i	−0.148598	−	0.842740i	0.815810	−	0.578320i	$-0.196292\pi$
$90$	−140.474	−	796.665i	−0.164525	−	0.933066i
$91$	−288.730	+	242.273i	−0.332606	+	0.279089i
$92$	690.359	−	251.270i	0.782336	−	0.284747i
$93$	1103.29	−	401.566i	1.23017	−	0.447746i
$94$	742.634	−	623.144i	0.814860	−	0.683749i
$95$	549.988	+	3119.13i	0.593974	+	3.36859i
$96$	−37.9882	−	215.442i	−0.0403870	−	0.229046i
$97$	−189.655	+	328.493i	−0.198521	+	0.343849i	−0.948049	−	0.318124i	$-0.896947\pi$
$97$	−189.655	+	328.493i	−0.198521	+	0.343849i	0.749528	+	0.661973i	$0.230281\pi$
$98$	422.626	+	354.625i	0.435629	+	0.365536i
$99$	−427.130	−	155.462i	−0.433618	−	0.157824i
$100$	−589.988	−	1021.89i	−0.589988	−	1.02189i
$101$	632.541	−	1095.59i	0.623170	−	1.07936i	−0.365722	−	0.930724i	$-0.619178\pi$
$101$	632.541	−	1095.59i	0.623170	−	1.07936i	0.988892	−	0.148638i	$-0.0474889\pi$
$102$	305.607	−	256.435i	0.296663	−	0.248930i
$103$	724.579	+	1255.01i	0.693155	+	1.20058i	0.970799	+	0.239895i	$0.0771130\pi$
$103$	724.579	+	1255.01i	0.693155	+	1.20058i	−0.277644	+	0.960684i	$0.589554\pi$
$104$	21.0478	−	119.368i	0.0198452	−	0.112548i
$105$	−3485.32			−3.23936
$106$	−1.42513	+	8.08230i	−0.00130585	+	0.00740587i
$107$	−527.377	−	442.522i	−0.476481	−	0.399815i	0.372671	−	0.927963i	$-0.378442\pi$
$107$	−527.377	−	442.522i	−0.476481	−	0.399815i	−0.849152	+	0.528149i	$0.822886\pi$
$108$	−186.643	+	67.9327i	−0.166294	+	0.0605261i
$109$	−1164.29	−	423.768i	−1.02311	−	0.372381i	−0.224656	−	0.974438i	$-0.572126\pi$
$109$	−1164.29	−	423.768i	−1.02311	−	0.372381i	−0.798453	+	0.602057i	$0.794348\pi$
$110$	−943.958			−0.818207
$111$	1349.80	−	738.498i	1.15421	−	0.631487i
$112$	−398.027			−0.335804
$113$	−453.549	−	165.078i	−0.377578	−	0.137427i	0.146258	−	0.989247i	$-0.453277\pi$
$113$	−453.549	−	165.078i	−0.377578	−	0.137427i	−0.523835	+	0.851819i	$0.675499\pi$
$114$	−1985.66	+	722.722i	−1.63135	+	0.593764i
$115$	2883.40	+	2419.46i	2.33807	+	1.96188i
$116$	34.6489	−	196.504i	0.0277334	−	0.157284i
$117$	299.033			0.236287
$118$	91.2541	−	517.528i	0.0711917	−	0.403748i
$119$	−362.922	−	628.599i	−0.279571	−	0.484232i
$120$	858.607	−	720.456i	0.653164	−	0.548070i
$121$	400.301	−	693.342i	0.300752	−	0.520918i
$122$	−179.830	−	311.475i	−0.133451	−	0.231145i
$123$	−425.197	−	154.759i	−0.311697	−	0.113448i
$124$	526.248	+	441.574i	0.381116	+	0.319795i
$125$	1741.91	−	3017.07i	1.24641	−	2.15884i
$126$	−170.516	−	967.045i	−0.120562	−	0.683740i
$127$	−185.271	−	1050.72i	−0.129450	−	0.734146i	−0.978565	−	0.205938i	$-0.933975\pi$
$127$	−185.271	−	1050.72i	−0.129450	−	0.734146i	0.849115	−	0.528208i	$-0.177136\pi$
$128$	98.0537	−	82.2768i	0.0677094	−	0.0568149i
$129$	−143.584	+	52.2602i	−0.0979988	+	0.0356687i
$130$	583.556	−	212.397i	0.393702	−	0.143296i
$131$	18.5419	−	15.5585i	0.0123665	−	0.0103768i	−0.636583	−	0.771208i	$-0.719653\pi$
$131$	18.5419	−	15.5585i	0.0123665	−	0.0103768i	0.648950	+	0.760831i	$0.275208\pi$
$132$	−109.360	−	620.213i	−0.0721106	−	0.408959i
$133$	667.612	+	3786.21i	0.435258	+	2.46847i
$134$	−379.633	+	657.543i	−0.244741	+	0.423903i
$135$	−779.547	−	654.118i	−0.496983	−	0.417019i
$136$	219.344	+	79.8348i	0.138299	+	0.0503366i
$137$	−803.669	−	1391.99i	−0.501183	−	0.868074i	−0.999999	−	0.00136632i	$-0.999565\pi$
$137$	−803.669	−	1391.99i	−0.501183	−	0.868074i	0.498816	−	0.866708i	$-0.333768\pi$
$138$	−1255.62	+	2174.80i	−0.774532	+	1.34153i
$139$	−661.453	+	555.025i	−0.403624	+	0.338681i	−0.821892	−	0.569643i	$-0.807082\pi$
$139$	−661.453	+	555.025i	−0.403624	+	0.338681i	0.418268	+	0.908323i	$0.362637\pi$
$140$	−1019.63	−	1766.06i	−0.615534	−	1.06614i
$141$	−575.426	+	3263.40i	−0.343685	+	1.94914i
$142$	1909.04			1.12819
$143$	60.5922	−	343.635i	0.0354334	−	0.200953i
$144$	241.906	+	202.983i	0.139992	+	0.117467i
$145$	960.654	−	349.650i	0.550193	−	0.200254i
$146$	−1379.22	−	501.995i	−0.781815	−	0.284557i
$147$	−1885.82			−1.05809
$148$	769.093	+	467.915i	0.427156	+	0.259881i
$149$	2025.24			1.11352			0.556760	−	0.830674i	$-0.312044\pi$
$149$	2025.24			1.11352			0.556760	+	0.830674i	$0.312044\pi$
$150$	3790.16	+	1379.51i	2.06310	+	0.750908i
$151$	−1296.06	+	471.727i	−0.698488	+	0.254229i	−0.666765	−	0.745268i	$-0.732322\pi$
$151$	−1296.06	+	471.727i	−0.698488	+	0.254229i	−0.0317230	+	0.999497i	$0.510099\pi$
$152$	−947.120	−	794.728i	−0.505405	−	0.424085i
$153$	−99.9986	+	567.120i	−0.0528393	+	0.299666i
$154$	−1145.84			−0.599573
$155$	−611.178	+	3466.16i	−0.316716	+	1.79619i
$156$	207.159	+	358.810i	0.106321	+	0.184153i
$157$	−2757.20	+	2313.56i	−1.40158	+	1.17607i	−0.441188	+	0.897414i	$0.645443\pi$
$157$	−2757.20	+	2313.56i	−1.40158	+	1.17607i	−0.960392	+	0.278651i	$0.910113\pi$
$158$	−537.220	+	930.492i	−0.270499	+	0.468519i
$159$	−14.0266	−	24.2948i	−0.00699610	−	0.0121176i
$160$	616.251	+	224.297i	0.304493	+	0.110826i
$161$	3500.06	+	2936.90i	1.71331	+	1.43764i
$162$	872.354	−	1510.96i	0.423078	−	0.732793i
$163$	91.2991	+	517.783i	0.0438718	+	0.248809i	0.998854	−	0.0478525i	$-0.0152378\pi$
$163$	91.2991	+	517.783i	0.0438718	+	0.248809i	−0.954983	+	0.296662i	$0.904127\pi$
$164$	−45.9733	−	260.728i	−0.0218897	−	0.124143i
$165$	2471.75	−	2074.05i	1.16622	−	0.978572i
$166$	−1409.98	+	513.191i	−0.659251	+	0.239948i
$167$	629.933	−	229.277i	0.291890	−	0.106239i	−0.191925	−	0.981410i	$-0.561473\pi$
$167$	629.933	−	229.277i	0.291890	−	0.106239i	0.483815	+	0.875170i	$0.339251\pi$
$168$	1042.23	−	874.538i	0.478631	−	0.401619i
$169$	−341.643	−	1937.55i	−0.155504	−	0.881908i
$170$	207.669	+	1177.75i	0.0936913	+	0.531350i
$171$	1525.12	−	2641.59i	0.682040	−	1.18133i
$172$	−68.4865	−	57.4670i	−0.0303607	−	0.0254757i
$173$	1531.03	+	557.251i	0.672846	+	0.244896i	0.655773	−	0.754958i	$-0.272343\pi$
$173$	1531.03	+	557.251i	0.672846	+	0.244896i	0.0170734	+	0.999854i	$0.494565\pi$
$174$	341.027	+	590.676i	0.148581	+	0.257351i
$175$	3669.24	−	6355.30i	1.58496	−	2.74523i
$176$	282.277	−	236.858i	0.120894	−	0.101442i
$177$	898.154	+	1555.65i	0.381409	+	0.660620i
$178$	−249.533	+	1415.17i	−0.105075	+	0.595907i
$179$	−417.136			−0.174180			−0.0870900	−	0.996200i	$-0.527757\pi$
$179$	−417.136			−0.174180			−0.0870900	+	0.996200i	$0.527757\pi$
$180$	−280.947	+	1593.33i	−0.116336	+	0.659777i
$181$	−3503.27	−	2939.60i	−1.43865	−	1.20717i	−0.940367	−	0.340161i	$-0.889518\pi$
$181$	−3503.27	−	2939.60i	−1.43865	−	1.20717i	−0.498287	−	0.867012i	$-0.666037\pi$
$182$	708.360	−	257.822i	0.288501	−	0.105006i
$183$	1155.25	+	420.478i	0.466660	+	0.169851i
$184$	−1469.33			−0.588698
$185$	−105.953	+	4611.15i	−0.0421071	+	1.83253i
$186$	−2348.20			−0.925690
$187$	631.448	+	229.828i	0.246931	+	0.0898754i
$188$	−1821.95	+	663.136i	−0.706805	+	0.257256i
$189$	−946.266	−	794.012i	−0.364184	−	0.305587i
$190$	1099.98	−	6238.27i	0.420003	−	2.38196i
$191$	−3975.24			−1.50596			−0.752980	−	0.658044i	$-0.771384\pi$
$191$	−3975.24			−1.50596			−0.752980	+	0.658044i	$0.771384\pi$
$192$	−75.9764	+	430.884i	−0.0285580	+	0.161960i
$193$	−24.4803	−	42.4010i	−0.00913019	−	0.0158140i	0.861424	−	0.507886i	$-0.169573\pi$
$193$	−24.4803	−	42.4010i	−0.00913019	−	0.0158140i	−0.870554	+	0.492072i	$0.836240\pi$
$194$	581.138	−	487.632i	0.215068	−	0.180464i
$195$	−1061.37	+	1838.34i	−0.389775	+	0.675110i
$196$	−551.699	−	955.570i	−0.201056	−	0.348240i
$197$	107.560	+	39.1487i	0.0389002	+	0.0141585i	0.361397	−	0.932412i	$-0.382300\pi$
$197$	107.560	+	39.1487i	0.0389002	+	0.0141585i	−0.322497	+	0.946571i	$0.604522\pi$
$198$	696.399	+	584.348i	0.249954	+	0.209736i
$199$	−700.441	+	1213.20i	−0.249512	+	0.432168i	−0.963391	−	0.268102i	$-0.913604\pi$
$199$	−700.441	+	1213.20i	−0.249512	+	0.432168i	0.713878	+	0.700270i	$0.246937\pi$
$200$	409.801	+	2324.10i	0.144887	+	0.821693i
$201$	−450.674	−	2555.90i	−0.158150	−	0.896911i
$202$	−1938.22	+	1626.36i	−0.675111	+	0.566486i
$203$	1166.11	−	424.428i	0.403175	−	0.146744i
$204$	−749.765	+	272.892i	−0.257324	+	0.0936582i
$205$	1039.08	−	871.896i	0.354014	−	0.297053i
$206$	−503.287	−	2854.29i	−0.170222	−	0.965376i
$207$	−629.467	−	3569.88i	−0.211357	−	1.19867i
$208$	−121.209	+	209.940i	−0.0404055	+	0.0699844i
$209$	−2726.57	−	2287.86i	−0.902395	−	0.757199i
$210$	6550.26	+	2384.10i	2.15243	+	0.783421i
$211$	−1859.04	−	3219.96i	−0.606549	−	1.05057i	−0.991805	−	0.127764i	$-0.959220\pi$
$211$	−1859.04	−	3219.96i	−0.606549	−	1.05057i	0.385256	−	0.922810i	$-0.374113\pi$
$212$	8.20698	−	14.2149i	0.00265876	−	0.00460511i
$213$	−4998.82	+	4194.51i	−1.60805	+	1.34931i
$214$	688.441	+	1192.42i	0.219911	+	0.380897i
$215$	79.5395	−	451.091i	0.0252304	−	0.143089i
$216$	397.244			0.125134
$217$	−741.889	+	4207.46i	−0.232086	+	1.31623i
$218$	1898.28	+	1592.85i	0.589760	+	0.494867i
$219$	4714.46	−	1715.92i	1.45467	−	0.529458i
$220$	1774.06	+	645.705i	0.543669	+	0.197879i
$221$	−442.075			−0.134557
$222$	−3041.96	+	464.601i	−0.919654	+	0.140459i
$223$	−654.397			−0.196510			−0.0982548	−	0.995161i	$-0.531326\pi$
$223$	−654.397			−0.196510			−0.0982548	+	0.995161i	$0.531326\pi$
$224$	748.046	+	272.266i	0.223129	+	0.0812124i
$225$	−5471.07	+	1991.31i	−1.62106	+	0.590016i
$226$	739.473	+	620.491i	0.217650	+	0.182630i
$227$	−604.325	+	3427.30i	−0.176698	+	1.00210i	0.759468	+	0.650545i	$0.225460\pi$
$227$	−604.325	+	3427.30i	−0.176698	+	1.00210i	−0.936166	+	0.351559i	$0.885652\pi$
$228$	4226.20			1.22757
$229$	565.289	−	3205.91i	0.163124	−	0.925121i	−0.787854	−	0.615862i	$-0.788808\pi$
$229$	565.289	−	3205.91i	0.163124	−	0.925121i	0.950978	−	0.309259i	$-0.100081\pi$
$230$	−3764.01	−	6519.46i	−1.07909	−	1.86905i
$231$	3000.38	−	2517.62i	0.854591	−	0.717087i
$232$	−199.535	+	345.605i	−0.0564661	+	0.0978022i
$233$	100.440	+	173.967i	0.0282405	+	0.0489140i	0.879800	−	0.475344i	$-0.157676\pi$
$233$	100.440	+	173.967i	0.0282405	+	0.0489140i	−0.851560	+	0.524258i	$0.824343\pi$
$234$	−561.997	−	204.550i	−0.157004	−	0.0571448i
$235$	−7609.68	−	6385.28i	−2.11234	−	1.77247i
$236$	−525.511	+	910.212i	−0.144949	+	0.251058i
$237$	−637.751	−	3616.86i	−0.174795	−	0.991311i
$238$	252.083	+	1429.63i	0.0686559	+	0.389367i
$239$	5169.20	−	4337.47i	1.39903	−	1.17392i	0.437499	−	0.899219i	$-0.355864\pi$
$239$	5169.20	−	4337.47i	1.39903	−	1.17392i	0.961529	−	0.274704i	$-0.0885800\pi$
$240$	−2106.47	+	766.694i	−0.566551	+	0.206208i
$241$	1585.00	−	576.894i	0.423647	−	0.154195i	−0.121394	−	0.992604i	$-0.538736\pi$
$241$	1585.00	−	576.894i	0.423647	−	0.154195i	0.545041	+	0.838409i	$0.316514\pi$
$242$	−1226.59	+	1029.23i	−0.325820	+	0.273395i
$243$	802.790	+	4552.85i	0.211930	+	1.20192i
$244$	124.909	+	708.394i	0.0327724	+	0.185862i
$245$	2826.59	−	4895.80i	0.737079	−	1.27666i
$246$	693.247	+	581.704i	0.179674	+	0.150764i
$247$	2200.35	+	800.863i	0.566822	+	0.206307i
$248$	−686.967	−	1189.86i	−0.175897	−	0.304663i
$249$	2564.46	−	4441.77i	0.652675	−	1.13047i
$250$	−5337.51	+	4478.71i	−1.35030	+	1.13303i
$251$	196.500	+	340.348i	0.0494142	+	0.0855879i	0.889675	−	0.456595i	$-0.150931\pi$
$251$	196.500	+	340.348i	0.0494142	+	0.0855879i	−0.840260	+	0.542183i	$0.817598\pi$
$252$	−341.032	+	1934.09i	−0.0852501	+	0.483477i
$253$	−4229.90			−1.05111
$254$	−370.541	+	2101.44i	−0.0915348	+	0.519120i
$255$	−3131.52	−	2627.66i	−0.769032	−	0.645295i
$256$	−240.561	+	87.5572i	−0.0587308	+	0.0213763i
$257$	4286.94	+	1560.32i	1.04051	+	0.378716i	0.805075	−	0.593173i	$-0.202125\pi$
$257$	4286.94	+	1560.32i	1.04051	+	0.378716i	0.235438	+	0.971889i	$0.424347\pi$
$258$	305.597			0.0737429
$259$	−128.613	+	5597.32i	−0.0308556	+	1.34286i
$260$	−1242.02			−0.296256
$261$	−925.164	−	336.732i	−0.219411	−	0.0798590i
$262$	−45.4901	+	16.5571i	−0.0107267	+	0.00390419i
$263$	4387.91	+	3681.90i	1.02878	+	0.863253i	0.990706	−	0.136022i	$-0.0434317\pi$
$263$	4387.91	+	3681.90i	1.02878	+	0.863253i	0.0380789	+	0.999275i	$0.487876\pi$
$264$	−218.721	+	1240.43i	−0.0509899	+	0.289178i
$265$	84.0959			0.0194942
$266$	1335.22	−	7572.43i	0.307774	−	1.74547i
$267$	−2455.99	−	4253.89i	−0.562936	−	0.975034i
$268$	1163.26	−	976.093i	0.265140	−	0.222479i
$269$	−3298.95	+	5713.95i	−0.747734	+	1.29511i	0.201172	+	0.979556i	$0.435525\pi$
$269$	−3298.95	+	5713.95i	−0.747734	+	1.29511i	−0.948906	+	0.315558i	$0.897808\pi$
$270$	1017.63	+	1762.58i	0.229373	+	0.397286i
$271$	5571.80	+	2027.97i	1.24894	+	0.454577i	0.880044	−	0.474893i	$-0.157513\pi$
$271$	5571.80	+	2027.97i	1.24894	+	0.454577i	0.368897	+	0.929470i	$0.379735\pi$
$272$	−357.622	−	300.081i	−0.0797207	−	0.0668936i
$273$	−1288.36	+	2231.50i	−0.285623	+	0.494713i
$274$	558.222	+	3165.84i	0.123078	+	0.698012i
$275$	1179.73	+	6690.61i	0.258693	+	1.46712i
$276$	3847.44	−	3228.39i	0.839090	−	0.704080i
$277$	−1092.85	+	397.765i	−0.237050	+	0.0862793i	−0.457814	−	0.889048i	$-0.651367\pi$
$277$	−1092.85	+	397.765i	−0.237050	+	0.0862793i	0.220763	+	0.975327i	$0.429145\pi$
$278$	1622.79	−	590.646i	0.350101	−	0.127426i
$279$	2596.59	−	2178.80i	0.557182	−	0.467531i
$280$	708.230	+	4016.57i	0.151160	+	0.857271i
$281$	−995.979	−	5648.48i	−0.211442	−	1.19915i	−0.886975	−	0.461817i	$-0.847198\pi$
$281$	−995.979	−	5648.48i	−0.211442	−	1.19915i	0.675534	−	0.737329i	$-0.263913\pi$
$282$	3313.75	−	5739.58i	0.699755	−	1.21201i
$283$	2286.76	+	1918.82i	0.480332	+	0.403047i	0.850547	−	0.525900i	$-0.176271\pi$
$283$	2286.76	+	1918.82i	0.480332	+	0.403047i	−0.370214	+	0.928946i	$0.620716\pi$
$284$	−3587.82	−	1305.86i	−0.749641	−	0.272847i
$285$	10826.3	+	18751.8i	2.25016	+	3.89740i
$286$	−348.937	+	604.376i	−0.0721435	+	0.124956i
$287$	1261.31	−	1058.37i	0.259417	−	0.217677i
$288$	−315.786	−	546.957i	−0.0646107	−	0.111909i
$289$	−705.300	+	3999.96i	−0.143558	+	0.814158i
$290$	−2044.61			−0.414013
$291$	−450.292	+	2553.73i	−0.0907099	+	0.514441i
$292$	2248.70	+	1886.88i	0.450668	+	0.378156i
$293$	−1420.72	+	517.101i	−0.283275	+	0.103104i	−0.479750	−	0.877405i	$-0.659273\pi$
$293$	−1420.72	+	517.101i	−0.283275	+	0.103104i	0.196475	+	0.980509i	$0.437050\pi$
$294$	3544.18	+	1289.98i	0.703065	+	0.255895i
$295$	−5384.85			−1.06277
$296$	−1125.35	−	1405.48i	−0.220978	−	0.275987i
$297$	1143.58			0.223426
$298$	−3806.21	−	1385.35i	−0.739892	−	0.269299i
$299$	2614.93	−	951.758i	0.505771	−	0.184086i
$300$	−6179.54	−	5185.25i	−1.18925	−	0.997901i
$301$	96.5503	−	547.564i	0.0184886	−	0.104854i
$302$	2758.47			0.525604
$303$	1501.82	−	8517.24i	0.284743	−	1.61486i
$304$	1236.38	+	2141.47i	0.233260	+	0.404019i
$305$	−2823.18	+	2368.93i	−0.530016	+	0.444736i
$306$	575.869	−	997.434i	0.107582	−	0.186338i
$307$	3040.82	+	5266.85i	0.565305	+	0.979136i	0.997021	+	0.0771269i	$0.0245747\pi$
$307$	3040.82	+	5266.85i	0.565305	+	0.979136i	−0.431717	+	0.902009i	$0.642092\pi$
$308$	2153.47	+	783.800i	0.398394	+	0.145004i
$309$	7589.24	+	6368.13i	1.39721	+	1.17240i
$310$	3519.64	−	6096.19i	0.644845	−	1.11690i
$311$	541.963	+	3073.62i	0.0988164	+	0.560415i	0.993511	+	0.113737i	$0.0362821\pi$
$311$	541.963	+	3073.62i	0.0988164	+	0.560415i	−0.894695	+	0.446678i	$0.852607\pi$
$312$	−143.891	−	816.048i	−0.0261097	−	0.148076i
$313$	2190.67	−	1838.19i	0.395604	−	0.331951i	−0.423188	−	0.906042i	$-0.639089\pi$
$313$	2190.67	−	1838.19i	0.395604	−	0.331951i	0.818792	+	0.574091i	$0.194644\pi$
$314$	6764.40	−	2462.04i	1.21572	−	0.442487i
$315$	−9455.24	+	3441.43i	−1.69125	+	0.615563i
$316$	1646.14	−	1381.27i	0.293046	−	0.245895i
$317$	−256.315	−	1453.63i	−0.0454135	−	0.257553i	0.953645	−	0.300933i	$-0.0972982\pi$
$317$	−256.315	−	1453.63i	−0.0454135	−	0.257553i	−0.999059	+	0.0433809i	$0.986187\pi$
$318$	9.74276	+	55.2540i	0.00171807	+	0.00974367i
$319$	−574.422	+	994.927i	−0.100820	+	0.174625i
$320$	−1004.74	−	843.080i	−0.175522	−	0.147280i
$321$	−4422.64	−	1609.71i	−0.768996	−	0.279892i
$322$	−4569.01	−	7913.75i	−0.790748	−	1.36962i
$323$	−2254.66	+	3905.19i	−0.388399	+	0.672727i
$324$	−2673.05	+	2242.95i	−0.458342	+	0.384594i
$325$	−2234.75	−	3870.70i	−0.381420	−	0.660639i
$326$	182.598	−	1035.57i	0.0310220	−	0.175935i
$327$	−8470.42			−1.43246
$328$	−91.9466	+	521.455i	−0.0154784	+	0.0877821i
$329$	−9237.13	−	7750.87i	−1.54790	−	1.29884i
$330$	−6064.11	+	2207.16i	−1.01157	+	0.368181i
$331$	−9684.14	−	3524.74i	−1.60812	−	0.585308i	−0.627054	−	0.778976i	$-0.715740\pi$
$331$	−9684.14	−	3524.74i	−1.60812	−	0.585308i	−0.981067	+	0.193667i	$0.937962\pi$
$332$	3000.94			0.496078
$333$	2932.66	−	3336.26i	0.482608	−	0.549027i
$334$	−1340.72			−0.219644
$335$	7310.90	+	2660.95i	1.19235	+	0.433980i
$336$	−2556.98	+	930.664i	−0.415162	+	0.151107i
$337$	−869.366	−	729.484i	−0.140526	−	0.117916i	0.569815	−	0.821773i	$-0.307015\pi$
$337$	−869.366	−	729.484i	−0.140526	−	0.117916i	−0.710341	+	0.703858i	$0.751459\pi$
$338$	−683.286	+	3875.11i	−0.109958	+	0.623603i
$339$	−3299.64			−0.528649
$340$	415.339	−	2355.50i	0.0662497	−	0.375721i
$341$	−1977.64	−	3425.37i	−0.314062	−	0.543972i
$342$	−4673.24	+	3921.31i	−0.738888	+	0.620001i
$343$	−835.243	+	1446.68i	−0.131484	+	0.227736i
$344$	89.4028	+	154.850i	0.0140124	+	0.0242702i
$345$	24180.5	+	8800.99i	3.77343	+	1.37342i
$346$	−2496.22	−	2094.58i	−0.387855	−	0.325449i
$347$	3077.60	−	5330.56i	0.476122	−	0.824667i	−0.523504	−	0.852023i	$-0.675376\pi$
$347$	3077.60	−	5330.56i	0.476122	−	0.824667i	0.999626	+	0.0273562i	$0.00870885\pi$
$348$	−236.875	−	1343.38i	−0.0364880	−	0.206934i
$349$	277.890	+	1575.99i	0.0426221	+	0.241722i	0.998674	−	0.0514747i	$-0.0163921\pi$
$349$	277.890	+	1575.99i	0.0426221	+	0.241722i	−0.956052	+	0.293196i	$0.905281\pi$
$350$	−11243.2	+	9434.16i	−1.71707	+	1.44079i
$351$	−706.966	+	257.314i	−0.107507	+	0.0391294i
$352$	−692.527	+	252.059i	−0.104863	+	0.0381671i
$353$	355.393	−	298.210i	0.0535855	−	0.0449636i	−0.615602	−	0.788058i	$-0.711087\pi$
$353$	355.393	−	298.210i	0.0535855	−	0.0449636i	0.669187	+	0.743094i	$0.266642\pi$
$354$	−623.851	−	3538.04i	−0.0936647	−	0.531199i
$355$	−3396.85	−	19264.5i	−0.507849	−	2.88015i
$356$	1437.00	−	2488.96i	0.213935	−	0.370547i
$357$	−3801.24	−	3189.62i	−0.563538	−	0.472865i
$358$	783.960	+	285.338i	0.115736	+	0.0421245i
$359$	−2786.86	−	4826.98i	−0.409707	−	0.709633i	0.585150	−	0.810925i	$-0.301036\pi$
$359$	−2786.86	−	4826.98i	−0.409707	−	0.709633i	−0.994857	+	0.101292i	$0.967702\pi$
$360$	1617.91	−	2802.30i	0.236865	−	0.410262i
$361$	13042.5	−	10944.0i	1.90152	−	1.59557i
$362$	4573.20	+	7921.01i	0.663984	+	1.15005i
$363$	950.420	−	5390.10i	0.137422	−	0.779358i
$364$	−1507.64			−0.217093
$365$	−2611.62	+	14811.2i	−0.374516	+	2.12398i
$366$	−1883.54	−	1580.48i	−0.269001	−	0.225719i
$367$	250.390	−	91.1345i	0.0356138	−	0.0129624i	−0.324152	−	0.946005i	$-0.605079\pi$
$367$	250.390	−	91.1345i	0.0356138	−	0.0129624i	0.359766	+	0.933043i	$0.382857\pi$
$368$	2761.44	+	1005.08i	0.391168	+	0.142374i
$369$	−1306.32			−0.184293
$370$	3353.34	−	8593.66i	0.471167	−	1.20747i
$371$	102.081			0.0142852
$372$	4413.17	+	1606.26i	0.615087	+	0.223873i
$373$	−6959.62	+	2533.10i	−0.966101	+	0.351632i	−0.776421	−	0.630214i	$-0.782967\pi$
$373$	−6959.62	+	2533.10i	−0.966101	+	0.351632i	−0.189679	+	0.981846i	$0.560745\pi$
$374$	−1029.52	−	863.871i	−0.142340	−	0.119438i
$375$	4135.75	−	23455.0i	0.569518	−	3.22989i
$376$	3877.76			0.531862
$377$	131.243	−	744.315i	0.0179293	−	0.101682i
$378$	1235.26	+	2139.54i	0.168082	+	0.291127i
$379$	−7880.94	+	6612.90i	−1.06812	+	0.896258i	−0.994881	−	0.101057i	$-0.967778\pi$
$379$	−7880.94	+	6612.90i	−1.06812	+	0.896258i	−0.0732376	+	0.997315i	$0.523333\pi$
$380$	−6334.50	+	10971.7i	−0.855140	+	1.48115i
$381$	−3647.00	−	6316.78i	−0.490397	−	0.849392i
$382$	7471.01	+	2719.22i	1.00065	+	0.364208i
$383$	3061.48	+	2568.89i	0.408445	+	0.342726i	0.823747	−	0.566958i	$-0.191880\pi$
$383$	3061.48	+	2568.89i	0.408445	+	0.342726i	−0.415302	+	0.909683i	$0.636324\pi$
$384$	437.531	−	757.826i	0.0581449	−	0.100710i
$385$	2038.85	+	11562.9i	0.269895	+	1.53065i
$386$	17.0038	+	96.4334i	0.00224215	+	0.0127159i
$387$	−337.923	+	283.551i	−0.0443866	+	0.0372447i
$388$	−1425.74	+	518.928i	−0.186549	+	0.0678983i
$389$	−6256.70	+	2277.25i	−0.815495	+	0.296816i	−0.715892	−	0.698211i	$-0.753980\pi$
$389$	−6256.70	+	2277.25i	−0.815495	+	0.296816i	−0.0996032	+	0.995027i	$0.531757\pi$
$390$	3252.22	−	2728.94i	0.422263	−	0.354321i
$391$	930.573	+	5277.54i	0.120361	+	0.682600i
$392$	383.206	+	2173.27i	0.0493745	+	0.280017i
$393$	82.7371	−	143.305i	0.0106197	−	0.0183938i
$394$	−175.368	−	147.151i	−0.0224236	−	0.0188156i
$395$	10345.7	+	3765.52i	1.31784	+	0.479656i
$396$	−909.084	−	1574.58i	−0.115362	−	0.199812i
$397$	−2342.58	+	4057.46i	−0.296147	+	0.512942i	−0.975251	−	0.221100i	$-0.929035\pi$
$397$	−2342.58	+	4057.46i	−0.296147	+	0.512942i	0.679104	+	0.734042i	$0.262369\pi$
$398$	2146.27	−	1800.94i	0.270309	−	0.226816i
$399$	13141.7	+	22762.1i	1.64889	+	2.85597i
$400$	819.603	−	4648.20i	0.102450	−	0.581025i
$401$	8477.08			1.05567			0.527837	−	0.849346i	$-0.323003\pi$
$401$	8477.08			1.05567			0.527837	+	0.849346i	$0.323003\pi$
$402$	−901.348	+	5111.80i	−0.111829	+	0.634212i
$403$	1993.31	+	1672.59i	0.246387	+	0.206743i
$404$	4755.15	−	1730.73i	0.585588	−	0.213137i
$405$	−16799.7	−	6114.57i	−2.06119	−	0.750211i
$406$	−2481.89			−0.303384
$407$	−3239.65	−	4046.10i	−0.394554	−	0.492771i
$408$	1595.77			0.193633
$409$	−14700.5	−	5350.53i	−1.77724	−	0.646863i	−0.999841	−	0.0178572i	$-0.994316\pi$
$409$	−14700.5	−	5350.53i	−1.77724	−	0.646863i	−0.777401	−	0.629006i	$-0.783462\pi$
$410$	−2549.25	+	927.852i	−0.307070	+	0.111764i
$411$	−8417.63	−	7063.23i	−1.01025	−	0.847697i
$412$	−1006.57	+	5708.57i	−0.120365	+	0.682624i
$413$	−6536.49			−0.778788
$414$	−1258.93	+	7139.76i	−0.149452	+	0.847585i
$415$	7687.56	+	13315.2i	0.909319	+	1.57499i
$416$	371.406	−	311.647i	0.0437733	−	0.0367302i
$417$	−2951.51	+	5112.16i	−0.346609	+	0.600344i
$418$	3559.28	+	6164.85i	0.416483	+	0.721370i
$419$	−4912.13	−	1787.87i	−0.572728	−	0.208456i	0.0393878	−	0.999224i	$-0.487459\pi$
$419$	−4912.13	−	1787.87i	−0.572728	−	0.208456i	−0.612116	+	0.790768i	$0.709681\pi$
$420$	−10679.6	−	8961.28i	−1.24075	−	1.04111i
$421$	926.687	−	1605.07i	0.107278	−	0.185811i	−0.807389	−	0.590020i	$-0.799120\pi$
$421$	926.687	−	1605.07i	0.107278	−	0.185811i	0.914667	+	0.404209i	$0.132453\pi$
$422$	1291.28	+	7323.20i	0.148954	+	0.844758i
$423$	1661.25	+	9421.39i	0.190952	+	1.08294i
$424$	−25.1476	+	21.1014i	−0.00288037	+	0.00241692i
$425$	8088.16	−	2943.85i	0.923137	−	0.335994i
$426$	12263.9	−	4463.70i	1.39481	−	0.507669i
$427$	−3426.96	+	2875.56i	−0.388390	+	0.325898i
$428$	−478.186	−	2711.93i	−0.0540047	−	0.306276i
$429$	−414.234	−	2349.24i	−0.0466186	−	0.264387i
$430$	−458.050	+	793.365i	−0.0513700	+	0.0889755i
$431$	3385.62	+	2840.87i	0.378375	+	0.317494i	0.812064	−	0.583568i	$-0.198344\pi$
$431$	3385.62	+	2840.87i	0.378375	+	0.317494i	−0.433689	+	0.901063i	$0.642788\pi$
$432$	−746.574	−	271.731i	−0.0831471	−	0.0302631i
$433$	−5161.31	−	8939.66i	−0.572834	−	0.992177i	−0.996273	−	0.0862527i	$-0.972511\pi$
$433$	−5161.31	−	8939.66i	−0.572834	−	0.992177i	0.423440	−	0.905924i	$-0.360823\pi$
$434$	4272.37	−	7399.96i	0.472535	−	0.818455i
$435$	5353.82	−	4492.39i	0.590106	−	0.495158i
$436$	−2478.03	−	4292.07i	−0.272193	−	0.471451i
$437$	4929.02	−	27953.9i	0.539559	−	3.05999i
$438$	−10034.0			−1.09462
$439$	2321.06	−	13163.4i	0.252342	−	1.43110i	−0.550462	−	0.834860i	$-0.685548\pi$
$439$	2321.06	−	13163.4i	0.252342	−	1.43110i	0.802804	−	0.596243i	$-0.203340\pi$
$440$	−2892.45	−	2427.06i	−0.313392	−	0.262967i
$441$	−5116.00	+	1862.07i	−0.552424	+	0.201066i
$442$	830.830	+	302.397i	0.0894085	+	0.0325420i
$443$	6485.51			0.695566			0.347783	−	0.937575i	$-0.386935\pi$
$443$	6485.51			0.695566			0.347783	+	0.937575i	$0.386935\pi$
$444$	6034.83	+	1207.66i	0.645046	+	0.129084i
$445$	14724.8			1.56859
$446$	1229.86	+	447.634i	0.130573	+	0.0475248i
$447$	13010.4	−	4735.41i	1.37667	−	0.501067i
$448$	−1219.63	−	1023.39i	−0.128620	−	0.107925i
$449$	−63.2028	+	358.441i	−0.00664303	+	0.0376745i	−0.987949	−	0.154779i	$-0.950533\pi$
$449$	−63.2028	+	358.441i	−0.00664303	+	0.0376745i	0.981306	+	0.192454i	$0.0616445\pi$
$450$	11644.4			1.21982
$451$	−264.696	+	1501.16i	−0.0276364	+	0.156734i
$452$	−965.313	−	1671.97i	−0.100452	−	0.173989i
$453$	−7223.06	+	6060.87i	−0.749159	+	0.628619i
$454$	3480.17	−	6027.83i	0.359763	−	0.623128i
$455$	−3862.15	−	6689.45i	−0.397935	−	0.689244i
$456$	−7942.65	−	2890.89i	−0.815677	−	0.296882i
$457$	−1807.61	−	1516.77i	−0.185025	−	0.155255i	0.545570	−	0.838065i	$-0.316313\pi$
$457$	−1807.61	−	1516.77i	−0.185025	−	0.155255i	−0.730596	+	0.682810i	$0.760758\pi$
$458$	−3255.37	+	5638.47i	−0.332125	+	0.575258i
$459$	−251.587	−	1426.82i	−0.0255840	−	0.145094i
$460$	2614.46	+	14827.3i	0.264999	+	1.50288i
$461$	−10138.7	+	8507.35i	−1.02431	+	0.859494i	−0.990162	−	0.139923i	$-0.955315\pi$
$461$	−10138.7	+	8507.35i	−1.02431	+	0.859494i	−0.0341429	+	0.999417i	$0.510870\pi$
$462$	−7361.02	+	2679.19i	−0.741267	+	0.269799i
$463$	12902.5	−	4696.14i	1.29510	−	0.471378i	0.399703	−	0.916645i	$-0.369113\pi$
$463$	12902.5	−	4696.14i	1.29510	−	0.471378i	0.895398	+	0.445267i	$0.146891\pi$
$464$	611.412	−	513.035i	0.0611726	−	0.0513299i
$465$	4178.27	+	23696.2i	0.416694	+	2.36319i
$466$	−69.7649	−	395.656i	−0.00693518	−	0.0393314i
$467$	2417.91	−	4187.95i	0.239588	−	0.414979i	−0.721008	−	0.692927i	$-0.756321\pi$
$467$	2417.91	−	4187.95i	0.239588	−	0.414979i	0.960596	+	0.277948i	$0.0896542\pi$
$468$	916.289	+	768.858i	0.0905031	+	0.0759412i
$469$	8874.46	+	3230.04i	0.873741	+	0.318016i
$470$	9933.73	+	17205.7i	0.974912	+	1.68860i
$471$	−12303.0	+	21309.5i	−1.20360	+	2.08469i
$472$	1610.26	−	1351.17i	0.157030	−	0.131764i
$473$	257.372	+	445.782i	0.0250190	+	0.0433342i
$474$	−1275.50	+	7233.73i	−0.123599	+	0.700962i
$475$	−45590.5			−4.40386
$476$	504.166	−	2859.27i	0.0485471	−	0.275324i
$477$	−62.0412	−	52.0588i	−0.00595529	−	0.00499708i
$478$	−12681.9	+	4615.84i	−1.21351	+	0.441681i
$479$	10863.7	+	3954.06i	1.03627	+	0.377172i	0.803466	−	0.595351i	$-0.202987\pi$
$479$	10863.7	+	3954.06i	1.03627	+	0.377172i	0.232806	+	0.972523i	$0.425209\pi$
$480$	4483.32			0.426323
$481$	2913.16	+	1772.36i	0.276151	+	0.168010i
$482$	−3373.45			−0.318789
$483$	29351.9	+	10683.2i	2.76513	+	1.00643i
$484$	3009.28	−	1095.29i	0.282614	−	0.102863i
$485$	−5954.85	−	4996.71i	−0.557517	−	0.467812i
$486$	1605.58	−	9105.70i	0.149857	−	0.849882i
$487$	8360.43			0.777920			0.388960	−	0.921255i	$-0.372834\pi$
$487$	8360.43			0.777920			0.388960	+	0.921255i	$0.372834\pi$
$488$	249.818	−	1416.79i	0.0231736	−	0.131424i
$489$	1797.19	+	3112.83i	0.166200	+	0.287867i
$490$	−8661.19	+	7267.60i	−0.798515	+	0.670034i
$491$	−5595.96	+	9692.49i	−0.514342	+	0.890867i	0.485519	+	0.874226i	$0.338631\pi$
$491$	−5595.96	+	9692.49i	−0.514342	+	0.890867i	−0.999862	+	0.0166411i	$0.994703\pi$
$492$	−904.970	−	1567.45i	−0.0829252	−	0.143631i
$493$	1367.72	+	497.808i	0.124947	+	0.0454770i
$494$	−3587.49	−	3010.26i	−0.326738	−	0.274166i
$495$	4657.63	−	8067.26i	0.422919	−	0.732518i
$496$	477.163	+	2706.12i	0.0431960	+	0.244977i
$497$	−4123.33	−	23384.5i	−0.372146	−	2.11054i
$498$	−7857.96	+	6593.61i	−0.707075	+	0.593307i
$499$	−5320.75	+	1936.59i	−0.477334	+	0.173735i	−0.569472	−	0.822011i	$-0.692852\pi$
$499$	−5320.75	+	1936.59i	−0.477334	+	0.173735i	0.0921380	+	0.995746i	$0.470630\pi$
$500$	13094.9	−	4766.14i	1.17124	−	0.426296i
$501$	3510.68	−	2945.81i	0.313065	−	0.262693i
$502$	−136.487	−	774.058i	−0.0121349	−	0.0688205i
$503$	−2799.05	−	15874.2i	−0.248118	−	1.40715i	−0.813138	−	0.582071i	$-0.802243\pi$
$503$	−2799.05	−	15874.2i	−0.248118	−	1.40715i	0.565020	−	0.825077i	$-0.308868\pi$
$504$	1963.93	−	3401.62i	0.173572	−	0.300635i
$505$	19860.7	+	16665.1i	1.75008	+	1.46849i
$506$	7949.62	+	2893.42i	0.698426	+	0.254206i
$507$	−6725.13	−	11648.3i	−0.589100	−	1.02035i
$508$	2133.86	−	3695.96i	0.186368	−	0.322799i
$509$	3968.56	−	3330.01i	0.345586	−	0.289981i	−0.453429	−	0.891292i	$-0.649799\pi$
$509$	3968.56	−	3330.01i	0.345586	−	0.289981i	0.799015	+	0.601312i	$0.205355\pi$
$510$	4087.91	+	7080.46i	0.354932	+	0.614761i
$511$	−3170.15	+	17978.8i	−0.274441	+	1.55643i
$512$	512.000			0.0441942
$513$	−1332.60	+	7557.52i	−0.114689	+	0.650434i
$514$	−6989.49	−	5864.88i	−0.599792	−	0.503285i
$515$	−27907.6	+	10157.6i	−2.38788	+	0.869117i
$516$	−574.335	−	209.041i	−0.0489994	−	0.0178343i
$517$	11163.3			0.949633
$518$	4070.51	−	10431.6i	0.345266	−	0.884819i
$519$	11138.5			0.942056
$520$	2334.23	+	849.589i	0.196851	+	0.0716479i
$521$	−14791.5	+	5383.67i	−1.24382	+	0.452712i	−0.878307	−	0.478096i	$-0.841327\pi$
$521$	−14791.5	+	5383.67i	−1.24382	+	0.452712i	−0.365508	+	0.930808i	$0.619105\pi$
$522$	1508.40	+	1265.70i	0.126477	+	0.106127i
$523$	−214.124	+	1214.36i	−0.0179025	+	0.101530i	−0.992450	−	0.122652i	$-0.960860\pi$
$523$	−214.124	+	1214.36i	−0.0179025	+	0.101530i	0.974547	+	0.224182i	$0.0719711\pi$
$524$	96.8192			0.00807169
$525$	8711.73	−	49406.7i	0.724212	−	4.10721i
$526$	−5728.02	−	9921.21i	−0.474816	−	0.822406i
$527$	−3838.67	+	3221.03i	−0.317296	+	0.266243i
$528$	1259.56	−	2181.63i	0.103817	−	0.179816i
$529$	−10783.2	−	18677.0i	−0.886262	−	1.53505i
$530$	−158.049	−	57.5250i	−0.0129532	−	0.00471458i
$531$	3972.64	+	3333.44i	0.324666	+	0.272427i
$532$	−7689.24	+	13318.2i	−0.626637	+	1.08537i
$533$	−174.137	−	987.581i	−0.0141514	−	0.0802568i
$534$	1705.91	+	9674.70i	0.138243	+	0.784017i
$535$	10807.9	−	9068.93i	0.873397	−	0.732867i
$536$	−2853.90	+	1038.74i	−0.229981	+	0.0837063i
$537$	−2679.74	+	975.345i	−0.215343	+	0.0783785i
$538$	10108.6	−	8482.10i	0.810058	−	0.679720i
$539$	1103.17	+	6256.40i	0.0881576	+	0.499967i
$540$	−706.836	−	4008.67i	−0.0563285	−	0.319455i
$541$	−7613.80	+	13187.5i	−0.605070	+	1.04801i	0.386970	+	0.922092i	$0.373522\pi$
$541$	−7613.80	+	13187.5i	−0.605070	+	1.04801i	−0.992040	+	0.125920i	$0.959812\pi$
$542$	−9084.35	−	7622.68i	−0.719938	−	0.604100i
$543$	−29378.8	−	10693.0i	−2.32185	−	0.845086i
$544$	466.843	+	808.595i	0.0367936	+	0.0637284i
$545$	12696.0	−	21990.2i	0.997868	−	1.72836i
$546$	3947.76	−	3312.56i	0.309429	−	0.259642i
$547$	1189.74	+	2060.70i	0.0929977	+	0.161077i	0.908771	−	0.417295i	$-0.137022\pi$
$547$	1189.74	+	2060.70i	0.0929977	+	0.161077i	−0.815773	+	0.578372i	$0.803688\pi$
$548$	1116.44	−	6331.67i	0.0870295	−	0.493569i
$549$	3549.25			0.275916
$550$	2359.47	−	13381.2i	0.182924	−	1.03741i
$551$	−5905.75	−	4955.51i	−0.456612	−	0.383143i
$552$	−9439.17	+	3435.58i	−0.727822	+	0.264906i
$553$	12558.3	+	4570.84i	0.965701	+	0.351486i
$554$	2325.97			0.178377
$555$	10101.1	+	29870.4i	0.772555	+	2.28455i
$556$	−3453.86			−0.263447
$557$	13115.0	+	4773.46i	0.997665	+	0.363121i	0.788684	−	0.614799i	$-0.210763\pi$
$557$	13115.0	+	4773.46i	0.997665	+	0.363121i	0.208982	+	0.977920i	$0.432985\pi$
$558$	−6370.37	+	2318.63i	−0.483296	+	0.175906i
$559$	−259.412	−	217.673i	−0.0196278	−	0.0164697i
$560$	1416.46	−	8033.14i	0.106886	−	0.606182i
$561$	4593.89			0.345729
$562$	−1991.96	+	11297.0i	−0.149512	+	0.847924i
$563$	3228.19	+	5591.39i	0.241655	+	0.418559i	0.961186	−	0.275901i	$-0.0889763\pi$
$563$	3228.19	+	5591.39i	0.241655	+	0.418559i	−0.719531	+	0.694461i	$0.755643\pi$
$564$	−10153.9	+	8520.14i	−0.758079	+	0.636104i
$565$	4945.72	−	8566.24i	0.368262	−	0.637849i
$566$	−2985.16	−	5170.45i	−0.221688	−	0.383975i
$567$	−20392.5	−	7422.28i	−1.51042	−	0.549747i
$568$	5849.64	+	4908.43i	0.432122	+	0.362594i
$569$	1315.84	−	2279.09i	0.0969468	−	0.167917i	−0.813473	−	0.581603i	$-0.802426\pi$
$569$	1315.84	−	2279.09i	0.0969468	−	0.167917i	0.910419	+	0.413686i	$0.135759\pi$
$570$	−7519.89	−	42647.4i	−0.552585	−	3.13387i
$571$	−730.690	−	4143.95i	−0.0535524	−	0.303711i	0.946253	−	0.323427i	$-0.104835\pi$
$571$	−730.690	−	4143.95i	−0.0535524	−	0.303711i	−0.999806	+	0.0197160i	$0.993724\pi$
$572$	1069.20	−	897.168i	0.0781567	−	0.0655813i
$573$	−25537.5	+	9294.88i	−1.86185	+	0.677660i
$574$	−3094.45	+	1126.29i	−0.225017	+	0.0818996i
$575$	−41504.6	+	34826.5i	−3.01020	+	2.52585i
$576$	219.343	+	1243.95i	0.0158668	+	0.0899851i
$577$	−2955.52	−	16761.6i	−0.213241	−	1.20935i	−0.883933	−	0.467613i	$-0.845114\pi$
$577$	−2955.52	−	16761.6i	−0.213241	−	1.20935i	0.670692	−	0.741736i	$-0.265997\pi$
$578$	4061.66	−	7035.01i	0.292289	−	0.506259i
$579$	−256.406	−	215.150i	−0.0184039	−	0.0154427i
$580$	3842.62	+	1398.60i	0.275097	+	0.100127i
$581$	9331.67	+	16162.9i	0.666339	+	1.15413i
$582$	2593.13	−	4491.43i	0.184688	−	0.319889i
$583$	−72.3949	+	60.7466i	−0.00514287	+	0.00431538i
$584$	−2935.47	−	5084.38i	−0.207998	−	0.360262i
$585$	−1064.17	+	6035.20i	−0.0752102	+	0.426538i
$586$	3023.80			0.213161
$587$	−565.666	+	3208.05i	−0.0397743	+	0.225571i	−0.998215	−	0.0597200i	$-0.980979\pi$
$587$	−565.666	+	3208.05i	−0.0397743	+	0.225571i	0.958441	+	0.285291i	$0.0920903\pi$
$588$	−5778.49	−	4848.73i	−0.405274	−	0.340065i
$589$	24941.5	−	9077.97i	1.74482	−	0.635062i
$590$	10120.2	+	3683.45i	0.706173	+	0.257026i
$591$	782.518			0.0544645
$592$	1153.56	+	3411.23i	0.0800859	+	0.236825i
$593$	−27261.4			−1.88785			−0.943923	−	0.330164i	$-0.892896\pi$
$593$	−27261.4			−1.88785			−0.943923	+	0.330164i	$0.892896\pi$
$594$	−2149.23	−	782.257i	−0.148458	−	0.0540344i
$595$	13978.2	−	5087.64i	0.963108	−	0.350543i
$596$	6205.70	+	5207.20i	0.426503	+	0.357878i
$597$	−1663.03	+	9431.51i	−0.114009	+	0.646577i
$598$	−5565.51			−0.380586
$599$	−123.287	+	699.195i	−0.00840963	+	0.0476934i	−0.988724	−	0.149751i	$-0.952153\pi$
$599$	−123.287	+	699.195i	−0.00840963	+	0.0476934i	0.980314	+	0.197444i	$0.0632640\pi$
$600$	8066.81	+	13972.1i	0.548877	+	0.950683i
$601$	11712.8	−	9828.17i	0.794964	−	0.667054i	−0.152005	−	0.988380i	$-0.548573\pi$
$601$	11712.8	−	9828.17i	0.794964	−	0.667054i	0.946969	+	0.321326i	$0.104128\pi$
$602$	−556.011	+	963.039i	−0.0376434	+	0.0652002i
$603$	−3746.33	−	6488.84i	−0.253006	−	0.438219i
$604$	−5184.23	−	1886.91i	−0.349244	−	0.127114i
$605$	12568.8	+	10546.4i	0.844616	+	0.708717i
$606$	−8648.63	+	14979.9i	−0.579747	+	1.00415i
$607$	695.890	+	3946.59i	0.0465326	+	0.263899i	0.999194	−	0.0401327i	$-0.0127781\pi$
$607$	695.890	+	3946.59i	0.0465326	+	0.263899i	−0.952662	+	0.304032i	$0.901667\pi$
$608$	−858.779	−	4870.38i	−0.0572830	−	0.324868i
$609$	6498.83	−	5453.16i	0.432423	−	0.362846i
$610$	6926.29	−	2520.96i	0.459733	−	0.167329i
$611$	−6901.16	+	2511.82i	−0.456941	+	0.166313i
$612$	−1764.56	+	1480.65i	−0.116550	+	0.0977967i
$613$	963.114	+	5462.09i	0.0634581	+	0.359889i	0.999957	+	0.00921946i	$0.00293469\pi$
$613$	963.114	+	5462.09i	0.0634581	+	0.359889i	−0.936499	+	0.350669i	$0.885954\pi$
$614$	−2112.13	−	11978.5i	−0.138825	−	0.787316i
$615$	4636.56	−	8030.76i	0.304007	−	0.526555i
$616$	−3511.05	−	2946.12i	−0.229650	−	0.192699i
$617$	20657.5	+	7518.70i	1.34787	+	0.490586i	0.912284	−	0.409559i	$-0.134317\pi$
$617$	20657.5	+	7518.70i	1.34787	+	0.490586i	0.435590	+	0.900145i	$0.356540\pi$
$618$	−9907.06	−	17159.5i	−0.644855	−	1.11692i
$619$	−4468.48	+	7739.64i	−0.290151	+	0.502557i	−0.973845	−	0.227212i	$-0.927039\pi$
$619$	−4468.48	+	7739.64i	−0.290151	+	0.502557i	0.683694	+	0.729769i	$0.260372\pi$
$620$	−10784.8	+	9049.51i	−0.698593	+	0.586189i
$621$	4560.02	+	7898.18i	0.294665	+	0.510375i
$622$	1083.93	−	6147.25i	0.0698737	−	0.396274i
$623$	17873.9			1.14944
$624$	−287.783	+	1632.10i	−0.0184624	+	0.104705i
$625$	26445.5	+	22190.4i	1.69251	+	1.42019i
$626$	−5374.51	+	1956.16i	−0.343145	+	0.124895i
$627$	−22865.3	−	8322.28i	−1.45638	−	0.530080i
$628$	−14397.1			−0.914817
$629$	−4335.50	+	4932.16i	−0.274829	+	0.312652i
$630$	20124.1			1.27264
$631$	28490.4	+	10369.6i	1.79744	+	0.654214i	0.998613	+	0.0526523i	$0.0167675\pi$
$631$	28490.4	+	10369.6i	1.79744	+	0.654214i	0.798826	+	0.601562i	$0.205455\pi$
$632$	−4038.57	+	1469.92i	−0.254186	+	0.0925163i
$633$	−19471.6	−	16338.6i	−1.22263	−	1.02591i
$634$	−512.630	+	2907.27i	−0.0321122	+	0.182117i
$635$	21865.4			1.36646
$636$	19.4855	−	110.508i	0.00121486	−	0.00688982i
$637$	−2089.72	−	3619.50i	−0.129981	−	0.225133i
$638$	1760.13	−	1476.92i	0.109223	−	0.0916489i
$639$	−9419.50	+	16315.1i	−0.583145	+	1.01004i
$640$	1311.60	+	2271.76i	0.0810087	+	0.140311i
$641$	6546.47	+	2382.72i	0.403385	+	0.146820i	0.535742	−	0.844382i	$-0.320032\pi$
$641$	6546.47	+	2382.72i	0.403385	+	0.146820i	−0.132356	+	0.991202i	$0.542254\pi$
$642$	7210.74	+	6050.53i	0.443279	+	0.371955i
$643$	4056.40	−	7025.89i	0.248785	−	0.430908i	−0.714404	−	0.699733i	$-0.753302\pi$
$643$	4056.40	−	7025.89i	0.248785	−	0.430908i	0.963189	+	0.268825i	$0.0866354\pi$
$644$	3173.60	+	17998.4i	0.194188	+	1.10130i
$645$	−543.765	−	3083.85i	−0.0331949	−	0.188258i
$646$	6908.69	−	5797.08i	0.420772	−	0.353070i
$647$	14657.7	−	5334.97i	0.890656	−	0.324172i	0.144154	−	0.989555i	$-0.453954\pi$
$647$	14657.7	−	5334.97i	0.890656	−	0.324172i	0.746502	+	0.665383i	$0.231732\pi$
$648$	6557.96	−	2386.90i	0.397563	−	0.144701i
$649$	4635.61	−	3889.74i	0.280375	−	0.235263i
$650$	1552.24	+	8803.19i	0.0936675	+	0.531215i
$651$	5071.86	+	28764.0i	0.305349	+	1.73172i
$652$	−1051.54	+	1821.32i	−0.0631618	+	0.109400i
$653$	−11775.4	−	9880.72i	−0.705676	−	0.592132i	0.217706	−	0.976014i	$-0.430143\pi$
$653$	−11775.4	−	9880.72i	−0.705676	−	0.592132i	−0.923382	+	0.383882i	$0.874587\pi$
$654$	15919.2	+	5794.11i	0.951818	+	0.346433i
$655$	248.024	+	429.589i	0.0147955	+	0.0256266i
$656$	529.499	−	917.120i	0.0315145	−	0.0545846i
$657$	11095.4	−	9310.18i	0.658865	−	0.552853i
$658$	12058.2	+	20885.4i	0.714405	+	1.23739i
$659$	1582.52	−	8974.93i	0.0935453	−	0.530522i	−0.901638	−	0.432491i	$-0.857635\pi$
$659$	1582.52	−	8974.93i	0.0935453	−	0.530522i	0.995183	−	0.0980305i	$-0.0312543\pi$
$660$	12906.6			0.761194
$661$	−2739.68	+	15537.5i	−0.161212	+	0.914281i	0.791672	+	0.610946i	$0.209211\pi$
$661$	−2739.68	+	15537.5i	−0.161212	+	0.914281i	−0.952884	+	0.303334i	$0.901900\pi$
$662$	15789.2	+	13248.7i	0.926984	+	0.777832i
$663$	−2839.95	+	1033.66i	−0.166357	+	0.0605489i
$664$	−5639.92	−	2052.76i	−0.329625	−	0.119974i
$665$	−78790.7			−4.59455
$666$	−7793.72	+	4264.06i	−0.453455	+	0.248092i
$667$	−9161.98			−0.531864
$668$	2519.73	+	917.107i	0.145945	+	0.0531197i
$669$	−4203.93	+	1530.11i	−0.242950	+	0.0884265i
$670$	−11919.8	−	10001.9i	−0.687317	−	0.576727i
$671$	719.175	−	4078.64i	0.0413762	−	0.234656i
$672$	5442.16			0.312404
$673$	−1181.58	+	6701.09i	−0.0676771	+	0.383816i	0.932090	+	0.362227i	$0.117984\pi$
$673$	−1181.58	+	6701.09i	−0.0676771	+	0.383816i	−0.999767	+	0.0215886i	$0.993128\pi$
$674$	1134.88	+	1965.66i	0.0648573	+	0.112336i
$675$	11221.1	−	9415.59i	0.639850	−	0.536898i
$676$	3934.89	−	6815.42i	0.223878	−	0.387769i
$677$	−4313.56	−	7471.30i	−0.244880	−	0.424144i	0.717218	−	0.696849i	$-0.245415\pi$
$677$	−4313.56	−	7471.30i	−0.244880	−	0.424144i	−0.962098	+	0.272705i	$0.912082\pi$
$678$	6201.30	+	2257.09i	0.351268	+	0.127851i
$679$	−7228.39	−	6065.34i	−0.408542	−	0.342808i
$680$	−2391.84	+	4142.79i	−0.134887	+	0.233630i
$681$	4131.42	+	23430.4i	0.232476	+	1.31844i
$682$	1373.65	+	7790.38i	0.0771260	+	0.437403i
$683$	−7237.25	+	6072.78i	−0.405455	+	0.340217i	−0.822598	−	0.568624i	$-0.807476\pi$
$683$	−7237.25	+	6072.78i	−0.405455	+	0.340217i	0.417143	+	0.908841i	$0.363032\pi$
$684$	11465.2	−	4172.97i	0.640908	−	0.233271i
$685$	30953.8	−	11266.3i	1.72655	−	0.628412i
$686$	2559.33	−	2147.54i	0.142443	−	0.119524i
$687$	−3864.55	−	21917.0i	−0.214617	−	1.21715i
$688$	−62.0985	−	352.178i	−0.00344111	−	0.0195155i
$689$	31.0863	−	53.8430i	0.00171886	−	0.00297715i
$690$	−39424.3	−	33080.9i	−2.17515	−	1.82517i
$691$	18772.9	+	6832.78i	1.03351	+	0.376167i	0.802416	−	0.596765i	$-0.203547\pi$
$691$	18772.9	+	6832.78i	1.03351	+	0.376167i	0.231094	+	0.972932i	$0.425770\pi$
$692$	3258.59	+	5644.04i	0.179007	+	0.310049i
$693$	5653.75	−	9792.58i	0.309911	−	0.536781i
$694$	−9430.31	+	7912.97i	−0.515807	+	0.432813i
$695$	−8847.83	−	15324.9i	−0.482903	−	0.836412i
$696$	−473.749	+	2686.77i	−0.0258009	+	0.146324i
$697$	1931.20			0.104949
$698$	555.780	−	3151.98i	0.0301383	−	0.170923i
$699$	1052.01	+	882.740i	0.0569250	+	0.0477658i
$700$	27583.6	−	10039.6i	1.48938	−	0.542089i
$701$	7950.14	+	2893.62i	0.428349	+	0.155906i	0.547193	−	0.837007i	$-0.315696\pi$
$701$	7950.14	+	2893.62i	0.428349	+	0.155906i	−0.118844	+	0.992913i	$0.537919\pi$
$702$	1504.67			0.0808978
$703$	30514.3	−	16694.8i	1.63708	−	0.895671i
$704$	1473.94			0.0789082
$705$	−63815.6	−	23227.0i	−3.40913	−	1.24082i
$706$	−871.909	+	317.349i	−0.0464798	+	0.0169173i
$707$	24108.2	+	20229.2i	1.28244	+	1.07609i
$708$	−1247.70	+	7076.07i	−0.0662310	+	0.375614i
$709$	−23745.2			−1.25778			−0.628892	−	0.777493i	$-0.716491\pi$
$709$	−23745.2			−1.25778			−0.628892	+	0.777493i	$0.716491\pi$
$710$	−6793.71	+	38529.0i	−0.359103	+	2.03658i
$711$	−5301.45	−	9182.39i	−0.279634	−	0.484341i
$712$	−4403.23	+	3694.75i	−0.231767	+	0.194475i
$713$	15771.6	−	27317.2i	0.828402	−	1.43483i
$714$	4962.17	+	8594.73i	0.260091	+	0.450490i
$715$	6719.76	+	2445.79i	0.351475	+	0.127927i
$716$	−1278.18	−	1072.52i	−0.0667148	−	0.0559804i
$717$	23065.8	−	39951.1i	1.20140	−	2.08089i
$718$	1935.73	+	10978.1i	0.100614	+	0.570611i
$719$	1508.03	+	8552.48i	0.0782199	+	0.443607i	0.998615	+	0.0526170i	$0.0167562\pi$
$719$	1508.03	+	8552.48i	0.0782199	+	0.443607i	−0.920395	+	0.390990i	$0.872133\pi$
$720$	−4957.57	+	4159.89i	−0.256608	+	0.215319i
$721$	−33876.2	+	12329.9i	−1.74981	+	0.636879i
$722$	−31998.1	+	11646.4i	−1.64937	+	0.600322i
$723$	8833.37	−	7412.08i	0.454380	−	0.381270i
$724$	−3176.51	−	18014.9i	−0.163058	−	0.924749i
$725$	2555.31	+	14491.9i	0.130899	+	0.742365i
$726$	−5473.25	+	9479.95i	−0.279795	+	0.484620i
$727$	−5998.95	−	5033.72i	−0.306037	−	0.256795i	0.476815	−	0.879004i	$-0.341791\pi$
$727$	−5998.95	−	5033.72i	−0.306037	−	0.256795i	−0.782852	+	0.622208i	$0.786236\pi$
$728$	2833.44	+	1031.29i	0.144250	+	0.0525028i
$729$	4025.88	+	6973.03i	0.204536	+	0.354267i
$730$	15039.7	−	26049.5i	0.762526	−	1.32073i
$731$	499.569	−	419.188i	0.0252766	−	0.0212096i
$732$	2458.79	+	4258.75i	0.124152	+	0.215038i
$733$	−5474.79	+	31049.1i	−0.275874	+	1.56456i	0.460296	+	0.887765i	$0.347743\pi$
$733$	−5474.79	+	31049.1i	−0.275874	+	1.56456i	−0.736171	+	0.676796i	$0.763368\pi$
$734$	−532.919			−0.0267989
$735$	6711.08	−	38060.4i	0.336792	−	1.91004i
$736$	−4502.29	−	3777.87i	−0.225484	−	0.189204i
$737$	−8215.81	+	2990.31i	−0.410628	+	0.149457i
$738$	2455.07	+	893.573i	0.122456	+	0.0445703i
$739$	−2543.49			−0.126609			−0.0633044	−	0.997994i	$-0.520164\pi$
$739$	−2543.49			−0.126609			−0.0633044	+	0.997994i	$0.520164\pi$
$740$	−12180.6	+	13857.0i	−0.605093	+	0.688368i
$741$	16007.9			0.793612
$742$	−191.850	−	69.8276i	−0.00949196	−	0.00345479i
$743$	−14076.7	+	5123.49i	−0.695051	+	0.252978i	−0.665296	−	0.746579i	$-0.731695\pi$
$743$	−14076.7	+	5123.49i	−0.695051	+	0.252978i	−0.0297544	+	0.999557i	$0.509473\pi$
$744$	−7195.30	−	6037.57i	−0.354560	−	0.297511i
$745$	−7207.24	+	40874.3i	−0.354433	+	2.01009i
$746$	14812.6			0.726979
$747$	2571.23	−	14582.1i	0.125939	−	0.714234i
$748$	1343.95	+	2327.78i	0.0656945	+	0.113786i
$749$	13119.4	−	11008.5i	0.640016	−	0.537037i
$750$	−23816.8	+	41251.9i	−1.15956	+	2.00841i
$751$	−3698.56	−	6406.10i	−0.179710	−	0.311267i	0.762071	−	0.647493i	$-0.224183\pi$
$751$	−3698.56	−	6406.10i	−0.179710	−	0.311267i	−0.941781	+	0.336226i	$0.890849\pi$
$752$	−7287.80	−	2652.54i	−0.353403	−	0.128628i
$753$	2058.14	+	1726.98i	0.0996053	+	0.0835787i
$754$	−755.797	+	1309.08i	−0.0365047	+	0.0632279i
$755$	−4908.29	−	27836.3i	−0.236597	−	1.34181i
$756$	−858.005	−	4865.99i	−0.0412769	−	0.234093i
$757$	−15771.6	+	13233.9i	−0.757237	+	0.635398i	−0.937406	−	0.348238i	$-0.886780\pi$
$757$	−15771.6	+	13233.9i	−0.757237	+	0.635398i	0.180169	+	0.983636i	$0.442336\pi$
$758$	19334.8	−	7037.30i	0.926480	−	0.337211i
$759$	−27173.5	+	9890.33i	−1.29952	+	0.472986i
$760$	19410.0	−	16287.0i	0.926416	−	0.777356i
$761$	293.900	+	1666.79i	0.0139998	+	0.0793970i	0.991007	−	0.133809i	$-0.0427207\pi$
$761$	293.900	+	1666.79i	0.0139998	+	0.0793970i	−0.977007	+	0.213206i	$0.931610\pi$
$762$	2533.18	+	14366.4i	0.120430	+	0.682990i
$763$	15411.3	−	26693.1i	0.731226	−	1.26652i
$764$	−12180.8	−	10220.9i	−0.576816	−	0.484006i
$765$	−11090.0	−	4036.42i	−0.524130	−	0.190768i
$766$	−3996.48	−	6922.10i	−0.188510	−	0.326509i
$767$	−1990.52	+	3447.69i	−0.0937075	+	0.162306i
$768$	−1340.67	+	1124.96i	−0.0629913	+	0.0528560i
$769$	−115.142	−	199.431i	−0.00539937	−	0.00935199i	0.863313	−	0.504669i	$-0.168385\pi$
$769$	−115.142	−	199.431i	−0.00539937	−	0.00935199i	−0.868712	+	0.495317i	$0.835052\pi$
$770$	4077.70	−	23125.8i	0.190844	−	1.08233i
$771$	31188.2			1.45683
$772$	34.0076	−	192.867i	0.00158544	−	0.00899148i
$773$	−3583.72	−	3007.10i	−0.166750	−	0.139920i	0.555594	−	0.831454i	$-0.312491\pi$
$773$	−3583.72	−	3007.10i	−0.166750	−	0.139920i	−0.722344	+	0.691534i	$0.756935\pi$
$774$	829.048	−	301.749i	0.0385007	−	0.0140131i
$775$	−47607.5	−	17327.7i	−2.20659	−	0.803135i
$776$	3034.49			0.140376
$777$	12261.4	+	36258.7i	0.566120	+	1.67410i
$778$	13316.5			0.613650
$779$	−9612.19	−	3498.55i	−0.442096	−	0.160910i
$780$	−7978.87	+	2904.07i	−0.366269	+	0.133311i
$781$	16839.9	+	14130.4i	0.771549	+	0.647406i
$782$	1861.15	−	10555.1i	0.0851080	−	0.482671i
$783$	2477.00			0.113054
$784$	766.412	−	4346.54i	0.0349131	−	0.198002i
$785$	−36881.2	−	63880.1i	−1.67687	−	2.90443i
$786$	−253.521	+	212.729i	−0.0115048	+	0.00965370i
$787$	3152.22	−	5459.80i	0.142776	−	0.247295i	−0.785765	−	0.618525i	$-0.787731\pi$
$787$	3152.22	−	5459.80i	0.142776	−	0.247295i	0.928541	+	0.371230i	$0.121064\pi$
$788$	228.926	+	396.512i	0.0103492	+	0.0179253i
$789$	36797.5	+	13393.2i	1.66036	+	0.604323i
$790$	−16867.8	−	14153.7i	−0.759656	−	0.637427i
$791$	6003.45	−	10398.3i	0.269858	−	0.467408i
$792$	631.443	+	3581.09i	0.0283300	+	0.160667i
$793$	473.128	+	2683.24i	0.0211870	+	0.120157i
$794$	7178.07	−	6023.11i	0.320831	−	0.269209i
$795$	540.243	−	196.632i	0.0241012	−	0.00877212i
$796$	−5265.59	+	1916.52i	−0.234465	+	0.0853382i
$797$	−1684.72	+	1413.65i	−0.0748756	+	0.0628281i	−0.679457	−	0.733715i	$-0.737785\pi$
$797$	−1684.72	+	1413.65i	−0.0748756	+	0.0628281i	0.604582	+	0.796543i	$0.293340\pi$
$798$	−9128.14	−	51768.3i	−0.404928	−	2.29646i
$799$	−2455.91	−	13928.1i	−0.108741	−	0.616698i
$800$	−4719.90	+	8175.11i	−0.208592	+	0.361292i
$801$	−10863.1	−	9115.23i	−0.479187	−	0.402086i
$802$	−15931.7	−	5798.66i	−0.701456	−	0.255309i
$803$	−8450.62	−	14636.9i	−0.371377	−	0.643244i
$804$	5190.66	−	8990.48i	0.227687	−	0.394365i
$805$	−71729.4	+	60188.1i	−3.14053	+	2.63522i
$806$	−2602.09	−	4506.95i	−0.113715	−	0.196961i
$807$	−7832.58	+	44420.8i	−0.341660	+	1.93765i
$808$	−10120.7			−0.440648
$809$	−3518.24	+	19952.9i	−0.152898	+	0.867128i	0.807784	+	0.589478i	$0.200667\pi$
$809$	−3518.24	+	19952.9i	−0.152898	+	0.867128i	−0.960682	+	0.277650i	$0.910444\pi$
$810$	27390.4	+	22983.3i	1.18815	+	0.996976i
$811$	−10712.5	+	3899.02i	−0.463829	+	0.168820i	−0.563355	−	0.826215i	$-0.690490\pi$
$811$	−10712.5	+	3899.02i	−0.463829	+	0.168820i	0.0995257	+	0.995035i	$0.468267\pi$
$812$	4664.42	+	1697.71i	0.201588	+	0.0733719i
$813$	40535.8			1.74865
$814$	3320.85	+	9820.23i	0.142992	+	0.422849i
$815$	−10775.0			−0.463107
$816$	−2999.06	−	1091.57i	−0.128662	−	0.0468291i
$817$	−3245.92	+	1181.42i	−0.138997	+	0.0505907i
$818$	23967.9	+	20111.4i	1.02447	+	0.859633i
$819$	−1291.76	+	7325.92i	−0.0551132	+	0.312562i
$820$	5425.72			0.231066
$821$	5851.72	−	33186.8i	0.248753	−	1.41075i	−0.562859	−	0.826553i	$-0.690298\pi$
$821$	5851.72	−	33186.8i	0.248753	−	1.41075i	0.811612	−	0.584197i	$-0.198590\pi$
$822$	10988.4	+	19032.5i	0.466260	+	0.807586i
$823$	25915.3	−	21745.5i	1.09763	−	0.921022i	0.100368	−	0.994950i	$-0.467998\pi$
$823$	25915.3	−	21745.5i	1.09763	−	0.921022i	0.997264	+	0.0739284i	$0.0235536\pi$
$824$	5796.63	−	10040.1i	0.245067	−	0.424469i
$825$	23222.7	+	40222.9i	0.980013	+	1.69743i
$826$	12284.6	+	4471.22i	0.517476	+	0.188346i
$827$	32065.5	+	26906.2i	1.34828	+	1.13134i	0.979415	+	0.201858i	$0.0646979\pi$
$827$	32065.5	+	26906.2i	1.34828	+	1.13134i	0.368865	+	0.929483i	$0.379747\pi$
$828$	7249.91	−	12557.2i	0.304289	−	0.527045i
$829$	−5948.11	−	33733.4i	−0.249200	−	1.41328i	−0.810534	−	0.585692i	$-0.800823\pi$
$829$	−5948.11	−	33733.4i	−0.249200	−	1.41328i	0.561334	−	0.827589i	$-0.310288\pi$
$830$	−5339.72	−	30283.1i	−0.223307	−	1.26643i
$831$	−6090.56	+	5110.59i	−0.254247	+	0.213339i
$832$	−911.195	+	331.648i	−0.0379688	+	0.0138195i
$833$	7563.25	−	2752.80i	0.314587	−	0.114500i
$834$	9043.94	−	7588.77i	0.375499	−	0.315081i
$835$	2385.61	+	13529.5i	0.0988714	+	0.560727i
$836$	−2472.25	−	14020.8i	−0.102278	−	0.580048i
$837$	−4263.96	+	7385.40i	−0.176086	+	0.304990i
$838$	8008.81	+	6720.19i	0.330143	+	0.277023i
$839$	−41929.5	−	15261.1i	−1.72535	−	0.627976i	−0.727067	−	0.686567i	$-0.759117\pi$
$839$	−41929.5	−	15261.1i	−1.72535	−	0.627976i	−0.998282	+	0.0585913i	$0.981339\pi$
$840$	13941.3	+	24147.0i	0.572643	+	0.991846i
$841$	10950.3	−	18966.5i	0.448985	−	0.777665i
$842$	−2839.53	+	2382.65i	−0.116219	+	0.0975197i
$843$	−19605.5	−	33957.8i	−0.801009	−	1.38739i
$844$	2582.56	−	14646.4i	0.105326	−	0.597334i
$845$	40320.3			1.64149
$846$	3322.49	−	18842.8i	0.135023	−	0.765755i
$847$	15256.8	+	12802.0i	0.618925	+	0.519340i
$848$	61.6963	−	22.4556i	0.00249842	−	0.000909350i
$849$	19177.1	+	6979.88i	0.775212	+	0.282154i
$850$	−17214.5			−0.694649
$851$	15026.4	−	38508.4i	0.605287	−	1.55118i
$852$	−26102.0			−1.04958
$853$	−13946.3	−	5076.04i	−0.559804	−	0.203752i	0.0465932	−	0.998914i	$-0.485164\pi$
$853$	−13946.3	−	5076.04i	−0.559804	−	0.203752i	−0.606397	+	0.795162i	$0.707386\pi$
$854$	8407.59	−	3060.11i	0.336887	−	0.122617i
$855$	47886.1	+	40181.2i	1.91540	+	1.60721i
$856$	−956.373	+	5423.86i	−0.0381871	+	0.216570i
$857$	−20614.7			−0.821685			−0.410842	−	0.911706i	$-0.634765\pi$
$857$	−20614.7			−0.821685			−0.410842	+	0.911706i	$0.634765\pi$
$858$	−828.467	+	4698.47i	−0.0329643	+	0.186950i
$859$	−15214.2	−	26351.8i	−0.604310	−	1.04670i	−0.992160	−	0.124974i	$-0.960115\pi$
$859$	−15214.2	−	26351.8i	−0.604310	−	1.04670i	0.387850	−	0.921723i	$-0.373218\pi$
$860$	1403.55	−	1177.71i	0.0556517	−	0.0466974i
$861$	5628.16	−	9748.26i	0.222773	−	0.385854i
$862$	−4419.61	−	7655.00i	−0.174632	−	0.302471i
$863$	3326.43	+	1210.72i	0.131209	+	0.0477560i	0.406790	−	0.913522i	$-0.366648\pi$
$863$	3326.43	+	1210.72i	0.131209	+	0.0477560i	−0.275581	+	0.961278i	$0.588870\pi$
$864$	1217.23	+	1021.37i	0.0479292	+	0.0402174i
$865$	−16695.2	+	28916.9i	−0.656246	+	1.13665i
$866$	3585.01	+	20331.6i	0.140674	+	0.797802i
$867$	4821.73	+	27345.4i	0.188875	+	1.07116i
$868$	−13091.3	+	10984.9i	−0.511921	+	0.429553i
$869$	−11626.2	+	4231.60i	−0.453847	+	0.165187i
$870$	−13134.9	+	4780.70i	−0.511855	+	0.186300i
$871$	4406.19	−	3697.23i	0.171410	−	0.143830i
$872$	1721.22	+	9761.52i	0.0668439	+	0.379090i
$873$	1299.98	+	7372.58i	0.0503984	+	0.285824i
$874$	−28385.1	+	49164.5i	−1.09856	+	1.90276i
$875$	66389.8	+	55707.7i	2.56501	+	2.15230i
$876$	18857.8	+	6863.69i	0.727337	+	0.264729i
$877$	5748.26	+	9956.28i	0.221328	+	0.383352i	0.955212	−	0.295924i	$-0.0956274\pi$
$877$	5748.26	+	9956.28i	0.221328	+	0.383352i	−0.733883	+	0.679276i	$0.762294\pi$
$878$	−13366.5	+	23151.4i	−0.513777	+	0.889887i
$879$	−7917.83	+	6643.85i	−0.303824	+	0.254939i
$880$	3775.83	+	6539.93i	0.144640	+	0.250524i
$881$	−4748.62	+	26930.7i	−0.181595	+	1.02987i	0.748658	+	0.662956i	$0.230698\pi$
$881$	−4748.62	+	26930.7i	−0.181595	+	1.02987i	−0.930253	+	0.366919i	$0.880413\pi$
$882$	10888.7			0.415692
$883$	3431.47	−	19460.8i	0.130779	−	0.741686i	−0.846927	−	0.531709i	$-0.821550\pi$
$883$	3431.47	−	19460.8i	0.130779	−	0.741686i	0.977706	−	0.209977i	$-0.0673390\pi$
$884$	−1354.60	−	1136.64i	−0.0515385	−	0.0432459i
$885$	−34593.0	+	12590.8i	−1.31393	+	0.478232i
$886$	−12188.8	−	4436.35i	−0.462178	−	0.168219i
$887$	−4960.97			−0.187794			−0.0938970	−	0.995582i	$-0.529932\pi$
$887$	−4960.97			−0.187794			−0.0938970	+	0.995582i	$0.529932\pi$
$888$	−10515.7	−	6397.73i	−0.397391	−	0.241772i
$889$	26541.7			1.00133
$890$	−27673.5	−	10072.3i	−1.04227	−	0.379355i
$891$	18879.0	−	6871.41i	0.709844	−	0.258362i
$892$	−2005.19	−	1682.55i	−0.0752675	−	0.0631570i
$893$	−13008.3	+	73774.0i	−0.487467	+	2.76456i
$894$	−27690.8			−1.03593
$895$	1484.46	−	8418.82i	0.0554415	−	0.314425i
$896$	1592.11	+	2757.61i	0.0593623	+	0.102818i
$897$	14573.3	−	12228.4i	0.542462	−	0.455179i
$898$	363.970	−	630.415i	0.0135254	−	0.0234267i
$899$	−4283.57	−	7419.36i	−0.158916	−	0.275250i
$900$	−21884.3	−	7965.22i	−0.810528	−	0.295008i
$901$	91.7187	+	76.9611i	0.00339134	+	0.00284567i
$902$	1524.32	−	2640.20i	0.0562687	−	0.0974602i
$903$	−660.058	−	3743.38i	−0.0243249	−	0.137953i
$904$	670.499	+	3802.59i	0.0246687	+	0.139903i
$905$	71795.2	−	60243.4i	2.63708	−	2.21277i
$906$	17720.8	−	6449.84i	0.649817	−	0.236514i
$907$	13570.1	−	4939.13i	0.496791	−	0.180817i	−0.0814593	−	0.996677i	$-0.525958\pi$
$907$	13570.1	−	4939.13i	0.496791	−	0.180817i	0.578250	+	0.815860i	$0.303736\pi$
$908$	−10663.9	+	8948.04i	−0.389750	+	0.327039i
$909$	−4335.73	−	24589.1i	−0.158203	−	0.897216i
$910$	2682.62	+	15213.9i	0.0977232	+	0.554216i
$911$	−24407.8	+	42275.5i	−0.887669	+	1.53749i	−0.0450452	+	0.998985i	$0.514343\pi$
$911$	−24407.8	+	42275.5i	−0.887669	+	1.53749i	−0.842624	+	0.538503i	$0.818990\pi$
$912$	12949.8	+	10866.2i	0.470188	+	0.394535i
$913$	−16236.2	−	5909.49i	−0.588542	−	0.214212i
$914$	2359.67	+	4087.07i	0.0853950	+	0.147909i
$915$	−12597.5	+	21819.5i	−0.455147	+	0.788338i
$916$	9975.03	−	8370.04i	0.359808	−	0.301915i
$917$	301.067	+	521.464i	0.0108420	+	0.0187789i
$918$	−503.174	+	2853.64i	−0.0180906	+	0.102597i
$919$	−9914.30			−0.355868			−0.177934	−	0.984042i	$-0.556941\pi$
$919$	−9914.30			−0.355868			−0.177934	+	0.984042i	$0.556941\pi$
$920$	5228.91	−	29654.6i	0.187383	−	1.06270i
$921$	31849.5	+	26724.9i	1.13950	+	0.956152i
$922$	24873.8	−	9053.33i	0.888477	−	0.323379i
$923$	−13589.9	−	4946.32i	−0.484634	−	0.176392i
$924$	15666.9			0.557794
$925$	−65101.3	−	13027.8i	−2.31407	−	0.463081i
$926$	−27461.2			−0.974547
$927$	26876.6	+	9782.29i	0.952259	+	0.346594i
$928$	−1500.01	+	545.961i	−0.0530608	+	0.0193125i
$929$	29448.7	+	24710.4i	1.04002	+	0.872683i	0.992009	−	0.126164i	$-0.0402665\pi$
$929$	29448.7	+	24710.4i	1.04002	+	0.872683i	0.0480135	+	0.998847i	$0.484711\pi$
$930$	8356.54	−	47392.3i	0.294647	−	1.67103i
$931$	−42631.7			−1.50075
$932$	−139.530	+	791.312i	−0.00490391	+	0.0278115i
$933$	10668.4	+	18478.2i	0.374348	+	0.648390i
$934$	−7408.92	+	6216.82i	−0.259558	+	0.217795i
$935$	−6885.62	+	11926.2i	−0.240838	+	0.417144i
$936$	−1196.13	−	2071.76i	−0.0417700	−	0.0723478i
$937$	−35130.0	−	12786.3i	−1.22481	−	0.445795i	−0.352993	−	0.935626i	$-0.614836\pi$
$937$	−35130.0	−	12786.3i	−1.22481	−	0.445795i	−0.871817	+	0.489831i	$0.837058\pi$
$938$	−14469.0	−	12141.0i	−0.503658	−	0.422619i
$939$	9775.11	−	16931.0i	0.339722	−	0.588415i
$940$	−6899.90	−	39131.3i	−0.239415	−	1.35779i
$941$	−5718.77	−	32432.8i	−0.198115	−	1.12357i	−0.907912	−	0.419161i	$-0.862324\pi$
$941$	−5718.77	−	32432.8i	−0.198115	−	1.12357i	0.709796	−	0.704407i	$-0.248787\pi$
$942$	37698.7	−	31633.0i	1.30392	−	1.09412i
$943$	−11423.3	+	4157.73i	−0.394478	+	0.143578i
$944$	−3950.55	+	1437.88i	−0.136207	+	0.0495753i
$945$	19392.5	−	16272.3i	0.667555	−	0.560145i
$946$	−178.769	−	1013.85i	−0.00614406	−	0.0348447i
$947$	60.7211	+	344.366i	0.00208360	+	0.0118167i	0.985832	−	0.167737i	$-0.0536458\pi$
$947$	60.7211	+	344.366i	0.00208360	+	0.0118167i	−0.983748	+	0.179553i	$0.942535\pi$
$948$	7345.32	−	12722.5i	0.251651	−	0.435872i
$949$	8517.59	+	7147.11i	0.291352	+	0.244473i
$950$	85682.1	+	31185.7i	2.92620	+	1.06505i
$951$	−5045.48	−	8739.02i	−0.172041	−	0.297983i
$952$	−2903.37	+	5028.79i	−0.0988434	+	0.171202i
$953$	18611.2	−	15616.7i	0.632609	−	0.530822i	−0.269129	−	0.963104i	$-0.586736\pi$
$953$	18611.2	−	15616.7i	0.632609	−	0.530822i	0.901738	+	0.432282i	$0.142291\pi$
$954$	80.9890	+	140.277i	0.00274855	+	0.00476063i
$955$	14146.7	−	80229.9i	0.479347	−	2.71851i
$956$	26991.6			0.913150
$957$	−1363.83	+	7734.65i	−0.0460672	+	0.261260i
$958$	−17712.3	−	14862.4i	−0.597347	−	0.501234i
$959$	37573.8	−	13675.7i	1.26519	−	0.460493i
$960$	−8425.89	−	3066.77i	−0.283276	−	0.103104i
$961$	−295.734			−0.00992696
$962$	−4262.58	−	5323.67i	−0.142860	−	0.178422i
$963$	−13587.5			−0.454674
$964$	6340.01	+	2307.57i	0.211824	+	0.0770975i
$965$	942.873	−	343.178i	0.0314530	−	0.0114480i
$966$	−47855.8	−	40155.8i	−1.59393	−	1.33746i
$967$	−1054.46	+	5980.14i	−0.0350663	+	0.198871i	−0.997308	−	0.0733252i	$-0.976639\pi$
$967$	−1054.46	+	5980.14i	−0.0350663	+	0.198871i	0.962242	+	0.272196i	$0.0877500\pi$
$968$	−6404.82			−0.212664
$969$	−5353.17	+	30359.3i	−0.177470	+	1.00648i
$970$	7773.50	+	13464.1i	0.257311	+	0.445676i
$971$	−26339.4	+	22101.4i	−0.870517	+	0.730450i	−0.964207	−	0.265151i	$-0.914578\pi$
$971$	−26339.4	+	22101.4i	−0.870517	+	0.730450i	0.0936900	+	0.995601i	$0.470134\pi$
$972$	−9246.17	+	16014.8i	−0.305114	+	0.528473i
$973$	−10740.1	−	18602.4i	−0.353866	−	0.612913i
$974$	−15712.5	−	5718.87i	−0.516899	−	0.188136i
$975$	−23406.8	−	19640.6i	−0.768837	−	0.645131i
$976$	−1438.64	+	2491.80i	−0.0471822	+	0.0817220i
$977$	7537.32	+	42746.2i	0.246817	+	1.39977i	0.816235	+	0.577720i	$0.196057\pi$
$977$	7537.32	+	42746.2i	0.246817	+	1.39977i	−0.569418	+	0.822048i	$0.692831\pi$
$978$	−1248.32	−	7079.56i	−0.0408147	−	0.231472i
$979$	−12676.0	+	10636.4i	−0.413817	+	0.347233i
$980$	21249.0	−	7734.02i	0.692628	−	0.252096i
$981$	−22979.2	+	8363.74i	−0.747879	+	0.272206i
$982$	17147.0	−	14388.1i	0.557213	−	0.467557i
$983$	9695.12	+	54983.8i	0.314574	+	1.78404i	0.574597	+	0.818436i	$0.305159\pi$
$983$	9695.12	+	54983.8i	0.314574	+	1.78404i	−0.260023	+	0.965602i	$0.583730\pi$
$984$	628.586	+	3564.89i	0.0203644	+	0.115492i
$985$	−1172.89	+	2031.51i	−0.0379405	+	0.0657149i
$986$	−2229.95	−	1871.15i	−0.0720243	−	0.0604356i
$987$	−77463.6	−	28194.4i	−2.49817	−	0.909259i
$988$	4683.13	+	8111.43i	0.150800	+	0.261193i
$989$	−2052.53	+	3555.09i	−0.0659927	+	0.114303i
$990$	−14271.8	+	11975.5i	−0.458170	+	0.384450i
$991$	11783.4	+	20409.5i	0.377713	+	0.654218i	0.990729	−	0.135852i	$-0.0433773\pi$
$991$	11783.4	+	20409.5i	0.377713	+	0.654218i	−0.613016	+	0.790070i	$0.710044\pi$
$992$	954.325	−	5412.25i	0.0305442	−	0.173225i
$993$	−70453.7			−2.25154
$994$	−8246.65	+	46769.1i	−0.263147	+	1.49238i
$995$	−21992.6	−	18454.0i	−0.700716	−	0.587971i
$996$	19278.4	−	7016.77i	0.613313	−	0.223228i
$997$	29903.6	+	10884.0i	0.949906	+	0.345737i	0.770070	−	0.637959i	$-0.220221\pi$
$997$	29903.6	+	10884.0i	0.949906	+	0.345737i	0.179836	+	0.983697i	$0.442443\pi$
$998$	11324.4			0.359187
$999$	−4062.50	+	10411.0i	−0.128660	+	0.329720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.f.b.53.4	yes	30
37.7	even	9	inner	74.4.f.b.7.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.f.b.7.4	✓	30	37.7	even	9	inner
74.4.f.b.53.4	yes	30	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87939 - 0.684040i) q^{2} +(6.42413 - 2.33819i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-3.55870 + 20.1824i) q^{5} -13.6728 q^{6} +(-4.31979 + 24.4987i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(15.1191 - 12.6865i) q^{9} +O(q^{10})\)	\(q+(-1.87939 - 0.684040i) q^{2} +(6.42413 - 2.33819i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-3.55870 + 20.1824i) q^{5} -13.6728 q^{6} +(-4.31979 + 24.4987i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(15.1191 - 12.6865i) q^{9} +(20.4938 - 35.4962i) q^{10} +(-11.5152 - 19.9449i) q^{11} +(25.6965 + 9.35277i) q^{12} +(11.6065 + 9.73897i) q^{13} +(24.8767 - 43.0877i) q^{14} +(24.3288 + 137.975i) q^{15} +(2.77837 + 15.7569i) q^{16} +(-22.3514 + 18.7550i) q^{17} +(-37.0927 + 13.5006i) q^{18} +(145.227 - 52.8583i) q^{19} +(-62.7965 + 52.6925i) q^{20} +(29.5319 + 167.484i) q^{21} +(7.99836 + 45.3610i) q^{22} +(91.8331 - 159.060i) q^{23} +(-41.8960 - 35.1549i) q^{24} +(-277.204 - 100.894i) q^{25} +(-15.1511 - 26.2426i) q^{26} +(-24.8277 + 43.0029i) q^{27} +(-76.2266 + 63.9617i) q^{28} +(-24.9419 - 43.2007i) q^{29} +(48.6576 - 275.951i) q^{30} +171.742 q^{31} +(5.55674 - 31.5138i) q^{32} +(-120.610 - 101.204i) q^{33} +(54.8361 - 19.9587i) q^{34} +(-479.071 - 174.368i) q^{35} +78.9465 q^{36} +(222.482 - 33.9799i) q^{37} -309.094 q^{38} +(97.3330 + 35.4263i) q^{39} +(154.063 - 56.0742i) q^{40} +(-50.7025 - 42.5445i) q^{41} +(59.0638 - 334.967i) q^{42} -22.3507 q^{43} +(15.9967 - 90.7220i) q^{44} +(202.239 + 350.288i) q^{45} +(-281.393 + 236.117i) q^{46} +(-242.360 + 419.780i) q^{47} +(54.6914 + 94.7282i) q^{48} +(-259.214 - 94.3460i) q^{49} +(451.957 + 379.237i) q^{50} +(-99.7354 + 172.747i) q^{51} +(10.5239 + 59.6839i) q^{52} +(-0.712563 - 4.04115i) q^{53} +(76.0766 - 63.8358i) q^{54} +(443.515 - 161.426i) q^{55} +(187.011 - 68.0666i) q^{56} +(809.364 - 679.137i) q^{57} +(17.3245 + 98.2520i) q^{58} +(45.6270 + 258.764i) q^{59} +(-280.208 + 485.334i) q^{60} +(137.758 + 115.593i) q^{61} +(-322.769 - 117.478i) q^{62} +(245.491 + 425.203i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-237.860 + 199.588i) q^{65} +(157.445 + 272.703i) q^{66} +(65.9225 - 373.865i) q^{67} -116.711 q^{68} +(218.036 - 1236.54i) q^{69} +(781.084 + 655.408i) q^{70} +(-896.955 + 326.465i) q^{71} +(-148.371 - 54.0026i) q^{72} +733.867 q^{73} +(-441.374 - 88.3256i) q^{74} -2016.70 q^{75} +(580.907 + 211.433i) q^{76} +(538.368 - 195.950i) q^{77} +(-158.693 - 133.159i) q^{78} +(93.2873 - 529.058i) q^{79} -327.900 q^{80} +(-151.483 + 859.101i) q^{81} +(66.1874 + 114.640i) q^{82} +(574.713 - 482.241i) q^{83} +(-340.135 + 589.131i) q^{84} +(-298.980 - 517.849i) q^{85} +(42.0056 + 15.2888i) q^{86} +(-261.242 - 219.208i) q^{87} +(-92.1215 + 159.559i) q^{88} +(-124.766 - 707.585i) q^{89} +(-140.474 - 796.665i) q^{90} +(-288.730 + 242.273i) q^{91} +(690.359 - 251.270i) q^{92} +(1103.29 - 401.566i) q^{93} +(742.634 - 623.144i) q^{94} +(549.988 + 3119.13i) q^{95} +(-37.9882 - 215.442i) q^{96} +(-189.655 + 328.493i) q^{97} +(422.626 + 354.625i) q^{98} +(-427.130 - 155.462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

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