LMFDB - Embedded newform 114.4.i.d.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.i (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:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 603 x^{16} - 1528 x^{15} + 240417 x^{14} - 786198 x^{13} + 54822410 x^{12} + \cdots + 11\!\cdots\!24 $ x^18 + 603x^16 - 1528x^15 + 240417x^14 - 786198x^13 + 54822410x^12 - 261322128x^11 + 9122210535x^10 - 45012474508x^9 + 1000170346788x^8 - 5035551052410x^7 + 79008124941737x^6 - 336274219954836x^5 + 3621639622047612x^4 - 11991799127581216x^3 + 107004711561222960x^2 - 278928948783924960x + 1161091951621493824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$4.82899 + 8.36405i$ of defining polynomial
Character	$\chi$	$=$	114.61
Dual form			114.4.i.d.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 - 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-3.92666 + 3.29486i) q^{5} +(1.04189 - 5.90885i) q^{6} +(16.8093 - 29.1145i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +O(q^{10})$	\(q+(-1.87939 - 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-3.92666 + 3.29486i) q^{5} +(1.04189 - 5.90885i) q^{6} +(16.8093 - 29.1145i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +(9.63351 - 3.50631i) q^{10} +(28.3762 + 49.1490i) q^{11} +(-6.00000 + 10.3923i) q^{12} +(-8.06433 + 45.7351i) q^{13} +(-51.5067 + 43.2192i) q^{14} +(-11.7800 - 9.88457i) q^{15} +(2.77837 + 15.7569i) q^{16} +(65.1304 + 23.7055i) q^{17} +18.0000 q^{18} +(34.1860 - 75.4342i) q^{19} -20.5035 q^{20} +(94.7734 + 34.4947i) q^{21} +(-19.7099 - 111.780i) q^{22} +(146.811 + 123.189i) q^{23} +(18.3851 - 15.4269i) q^{24} +(-17.1435 + 97.2254i) q^{25} +(46.4406 - 80.4375i) q^{26} +(-13.5000 - 23.3827i) q^{27} +(126.365 - 45.9929i) q^{28} +(-90.8298 + 33.0594i) q^{29} +(15.3777 + 26.6349i) q^{30} +(15.3608 - 26.6058i) q^{31} +(5.55674 - 31.5138i) q^{32} +(-130.425 + 109.439i) q^{33} +(-106.190 - 89.1036i) q^{34} +(29.9239 + 169.707i) q^{35} +(-33.8289 - 12.3127i) q^{36} +346.394 q^{37} +(-115.849 + 118.385i) q^{38} -139.322 q^{39} +(38.5341 + 14.0253i) q^{40} +(-50.8704 - 288.500i) q^{41} +(-154.520 - 129.658i) q^{42} +(105.298 - 88.3557i) q^{43} +(-39.4198 + 223.561i) q^{44} +(23.0665 - 39.9523i) q^{45} +(-191.648 - 331.945i) q^{46} +(-497.974 + 181.248i) q^{47} +(-45.1052 + 16.4170i) q^{48} +(-393.605 - 681.743i) q^{49} +(98.7253 - 170.997i) q^{50} +(-36.1068 + 204.772i) q^{51} +(-142.302 + 119.406i) q^{52} +(-224.643 - 188.498i) q^{53} +(9.37700 + 53.1796i) q^{54} +(-273.362 - 99.4958i) q^{55} -268.949 q^{56} +(240.674 + 61.7029i) q^{57} +193.318 q^{58} +(81.1472 + 29.5352i) q^{59} +(-10.6812 - 60.5761i) q^{60} +(622.360 + 522.222i) q^{61} +(-47.0684 + 39.4950i) q^{62} +(-52.5403 + 297.971i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-119.025 - 206.157i) q^{65} +(319.979 - 116.463i) q^{66} +(-409.599 + 149.082i) q^{67} +(138.621 + 240.098i) q^{68} +(-287.472 + 497.917i) q^{69} +(59.8479 - 339.414i) q^{70} +(31.8079 - 26.6900i) q^{71} +(55.1552 + 46.2807i) q^{72} +(-115.233 - 653.521i) q^{73} +(-651.009 - 236.948i) q^{74} -296.176 q^{75} +(298.705 - 143.246i) q^{76} +1907.93 q^{77} +(261.840 + 95.3018i) q^{78} +(-88.0234 - 499.205i) q^{79} +(-62.8265 - 52.7177i) q^{80} +(62.0496 - 52.0658i) q^{81} +(-101.741 + 577.001i) q^{82} +(103.456 - 179.191i) q^{83} +(201.712 + 349.375i) q^{84} +(-333.851 + 121.512i) q^{85} +(-258.335 + 94.0262i) q^{86} +(-144.989 - 251.128i) q^{87} +(227.009 - 393.192i) q^{88} +(183.513 - 1040.76i) q^{89} +(-70.6798 + 59.3074i) q^{90} +(1196.00 + 1003.56i) q^{91} +(133.118 + 754.947i) q^{92} +(86.6068 + 31.5223i) q^{93} +1059.87 q^{94} +(114.308 + 408.842i) q^{95} +96.0000 q^{96} +(-1014.58 - 369.277i) q^{97} +(273.395 + 1550.50i) q^{98} +(-391.274 - 328.317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 15 q^{5} - 72 q^{8}+O(q^{10}) $ 18 * q + 15 * q^5 - 72 * q^8	\( 18 q + 15 q^{5} - 72 q^{8} - 6 q^{10} - 39 q^{11} - 108 q^{12} - 42 q^{14} + 45 q^{15} + 159 q^{17} + 324 q^{18} + 159 q^{19} + 216 q^{20} + 99 q^{21} - 246 q^{22} + 300 q^{23} - 267 q^{25} - 198 q^{26} - 243 q^{27} + 132 q^{28} - 231 q^{29} - 162 q^{30} - 243 q^{31} - 126 q^{33} - 618 q^{34} + 774 q^{35} + 1422 q^{37} - 270 q^{38} + 594 q^{39} - 24 q^{40} - 69 q^{41} - 126 q^{42} - 60 q^{43} - 492 q^{44} - 243 q^{45} - 456 q^{46} + 540 q^{47} - 2229 q^{49} - 348 q^{50} + 450 q^{51} - 180 q^{52} - 750 q^{53} - 450 q^{55} + 297 q^{57} + 1836 q^{58} + 1263 q^{59} - 144 q^{60} + 1518 q^{61} - 390 q^{62} - 108 q^{63} - 576 q^{64} + 237 q^{65} + 990 q^{66} - 4812 q^{67} - 228 q^{68} - 684 q^{69} + 1548 q^{70} - 1371 q^{71} + 672 q^{73} + 186 q^{74} + 1044 q^{75} - 84 q^{76} - 270 q^{77} + 270 q^{78} - 2301 q^{79} + 240 q^{80} - 138 q^{82} - 2490 q^{83} + 5757 q^{85} + 96 q^{86} - 1377 q^{87} - 312 q^{88} + 7203 q^{89} + 270 q^{90} + 1284 q^{91} + 156 q^{92} - 207 q^{93} - 264 q^{94} + 3270 q^{95} + 1728 q^{96} - 1977 q^{97} + 498 q^{98} - 378 q^{99}+O(q^{100}) \) 18 * q + 15 * q^5 - 72 * q^8 - 6 * q^10 - 39 * q^11 - 108 * q^12 - 42 * q^14 + 45 * q^15 + 159 * q^17 + 324 * q^18 + 159 * q^19 + 216 * q^20 + 99 * q^21 - 246 * q^22 + 300 * q^23 - 267 * q^25 - 198 * q^26 - 243 * q^27 + 132 * q^28 - 231 * q^29 - 162 * q^30 - 243 * q^31 - 126 * q^33 - 618 * q^34 + 774 * q^35 + 1422 * q^37 - 270 * q^38 + 594 * q^39 - 24 * q^40 - 69 * q^41 - 126 * q^42 - 60 * q^43 - 492 * q^44 - 243 * q^45 - 456 * q^46 + 540 * q^47 - 2229 * q^49 - 348 * q^50 + 450 * q^51 - 180 * q^52 - 750 * q^53 - 450 * q^55 + 297 * q^57 + 1836 * q^58 + 1263 * q^59 - 144 * q^60 + 1518 * q^61 - 390 * q^62 - 108 * q^63 - 576 * q^64 + 237 * q^65 + 990 * q^66 - 4812 * q^67 - 228 * q^68 - 684 * q^69 + 1548 * q^70 - 1371 * q^71 + 672 * q^73 + 186 * q^74 + 1044 * q^75 - 84 * q^76 - 270 * q^77 + 270 * q^78 - 2301 * q^79 + 240 * q^80 - 138 * q^82 - 2490 * q^83 + 5757 * q^85 + 96 * q^86 - 1377 * q^87 - 312 * q^88 + 7203 * q^89 + 270 * q^90 + 1284 * q^91 + 156 * q^92 - 207 * q^93 - 264 * q^94 + 3270 * q^95 + 1728 * q^96 - 1977 * q^97 + 498 * q^98 - 378 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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
$3$	0.520945	+	2.95442i	0.100256	+	0.568579i
$3$	0.520945	+	2.95442i	0.100256	+	0.568579i
$4$	3.06418	+	2.57115i	0.383022	+	0.321394i
$5$	−3.92666	+	3.29486i	−0.351211	+	0.294701i	−0.801276	−	0.598295i	$-0.795845\pi$
$5$	−3.92666	+	3.29486i	−0.351211	+	0.294701i	0.450065	+	0.892996i	$0.351401\pi$
$6$	1.04189	−	5.90885i	0.0708916	−	0.402046i
$7$	16.8093	−	29.1145i	0.907616	−	1.57204i	0.0902504	−	0.995919i	$-0.471233\pi$
$7$	16.8093	−	29.1145i	0.907616	−	1.57204i	0.817366	−	0.576119i	$-0.195433\pi$
$8$	−4.00000	−	6.92820i	−0.176777	−	0.306186i
$9$	−8.45723	+	3.07818i	−0.313231	+	0.114007i
$10$	9.63351	−	3.50631i	0.304638	−	0.110879i
$11$	28.3762	+	49.1490i	0.777795	+	1.34718i	0.933210	+	0.359331i	$0.116995\pi$
$11$	28.3762	+	49.1490i	0.777795	+	1.34718i	−0.155416	+	0.987849i	$0.549672\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	−8.06433	+	45.7351i	−0.172049	+	0.975741i	0.769445	+	0.638713i	$0.220533\pi$
$13$	−8.06433	+	45.7351i	−0.172049	+	0.975741i	−0.941495	+	0.337028i	$0.890578\pi$
$14$	−51.5067	+	43.2192i	−0.983267	+	0.825059i
$15$	−11.7800	−	9.88457i	−0.202772	−	0.170146i
$16$	2.77837	+	15.7569i	0.0434120	+	0.246202i
$17$	65.1304	+	23.7055i	0.929202	+	0.338202i	0.761893	−	0.647703i	$-0.224270\pi$
$17$	65.1304	+	23.7055i	0.929202	+	0.338202i	0.167309	+	0.985905i	$0.446492\pi$
$18$	18.0000			0.235702
$19$	34.1860	−	75.4342i	0.412779	−	0.910831i
$19$	34.1860	−	75.4342i	0.412779	−	0.910831i
$20$	−20.5035			−0.229237
$21$	94.7734	+	34.4947i	0.984822	+	0.358446i
$22$	−19.7099	−	111.780i	−0.191007	−	1.08326i
$23$	146.811	+	123.189i	1.33097	+	1.11681i	0.983851	+	0.178992i	$0.0572835\pi$
$23$	146.811	+	123.189i	1.33097	+	1.11681i	0.347116	+	0.937822i	$0.387161\pi$
$24$	18.3851	−	15.4269i	0.156368	−	0.131208i
$25$	−17.1435	+	97.2254i	−0.137148	+	0.777803i
$26$	46.4406	−	80.4375i	0.350298	−	0.606735i
$27$	−13.5000	−	23.3827i	−0.0962250	−	0.166667i
$28$	126.365	−	45.9929i	0.852880	−	0.310423i
$29$	−90.8298	+	33.0594i	−0.581610	+	0.211689i	−0.616035	−	0.787719i	$-0.711262\pi$
$29$	−90.8298	+	33.0594i	−0.581610	+	0.211689i	0.0344256	+	0.999407i	$0.489040\pi$
$30$	15.3777	+	26.6349i	0.0935854	+	0.162095i
$31$	15.3608	−	26.6058i	0.0889964	−	0.154146i	−0.818091	−	0.575089i	$-0.804967\pi$
$31$	15.3608	−	26.6058i	0.0889964	−	0.154146i	0.907087	+	0.420943i	$0.138301\pi$
$32$	5.55674	−	31.5138i	0.0306970	−	0.174091i
$33$	−130.425	+	109.439i	−0.688000	+	0.577300i
$34$	−106.190	−	89.1036i	−0.535628	−	0.449445i
$35$	29.9239	+	169.707i	0.144516	+	0.819592i
$36$	−33.8289	−	12.3127i	−0.156615	−	0.0570034i
$37$	346.394			1.53911			0.769553	−	0.638583i	$-0.220479\pi$
$37$	346.394			1.53911			0.769553	+	0.638583i	$0.220479\pi$
$38$	−115.849	+	118.385i	−0.494556	+	0.505385i
$39$	−139.322			−0.572035
$40$	38.5341	+	14.0253i	0.152319	+	0.0554397i
$41$	−50.8704	−	288.500i	−0.193771	−	1.09893i	−0.914158	−	0.405359i	$-0.867147\pi$
$41$	−50.8704	−	288.500i	−0.193771	−	1.09893i	0.720386	−	0.693573i	$-0.243965\pi$
$42$	−154.520	−	129.658i	−0.567689	−	0.476348i
$43$	105.298	−	88.3557i	0.373438	−	0.313352i	−0.436682	−	0.899616i	$-0.643846\pi$
$43$	105.298	−	88.3557i	0.373438	−	0.313352i	0.810120	+	0.586264i	$0.199402\pi$
$44$	−39.4198	+	223.561i	−0.135063	+	0.765978i
$45$	23.0665	−	39.9523i	0.0764122	−	0.132350i
$46$	−191.648	−	331.945i	−0.614283	−	1.06397i
$47$	−497.974	+	181.248i	−1.54547	+	0.562504i	−0.967349	−	0.253448i	$-0.918435\pi$
$47$	−497.974	+	181.248i	−1.54547	+	0.562504i	−0.578119	+	0.815953i	$0.696213\pi$
$48$	−45.1052	+	16.4170i	−0.135633	+	0.0493664i
$49$	−393.605	−	681.743i	−1.14754	−	1.98759i
$50$	98.7253	−	170.997i	0.279237	−	0.483653i
$51$	−36.1068	+	204.772i	−0.0991366	+	0.562232i
$52$	−142.302	+	119.406i	−0.379496	+	0.318435i
$53$	−224.643	−	188.498i	−0.582209	−	0.488532i	0.303462	−	0.952843i	$-0.401857\pi$
$53$	−224.643	−	188.498i	−0.582209	−	0.488532i	−0.885672	+	0.464312i	$0.846302\pi$
$54$	9.37700	+	53.1796i	0.0236305	+	0.134015i
$55$	−273.362	−	99.4958i	−0.670185	−	0.243927i
$56$	−268.949			−0.641782
$57$	240.674	+	61.7029i	0.559263	+	0.143382i
$58$	193.318			0.437654
$59$	81.1472	+	29.5352i	0.179059	+	0.0651721i	0.429994	−	0.902832i	$-0.358516\pi$
$59$	81.1472	+	29.5352i	0.179059	+	0.0651721i	−0.250935	+	0.968004i	$0.580738\pi$
$60$	−10.6812	−	60.5761i	−0.0229823	−	0.130339i
$61$	622.360	+	522.222i	1.30631	+	1.09613i	0.989017	+	0.147799i	$0.0472187\pi$
$61$	622.360	+	522.222i	1.30631	+	1.09613i	0.317294	+	0.948327i	$0.397226\pi$
$62$	−47.0684	+	39.4950i	−0.0964143	+	0.0809012i
$63$	−52.5403	+	297.971i	−0.105071	+	0.595885i
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−119.025	−	206.157i	−0.227126	−	0.393394i
$66$	319.979	−	116.463i	0.596767	−	0.217206i
$67$	−409.599	+	149.082i	−0.746873	+	0.271839i	−0.687289	−	0.726384i	$-0.741199\pi$
$67$	−409.599	+	149.082i	−0.746873	+	0.271839i	−0.0595834	+	0.998223i	$0.518977\pi$
$68$	138.621	+	240.098i	0.247209	+	0.428179i
$69$	−287.472	+	497.917i	−0.501560	+	0.868727i
$70$	59.8479	−	339.414i	0.102188	−	0.579539i
$71$	31.8079	−	26.6900i	0.0531677	−	0.0446130i	−0.615817	−	0.787890i	$-0.711174\pi$
$71$	31.8079	−	26.6900i	0.0531677	−	0.0446130i	0.668984	+	0.743277i	$0.266729\pi$
$72$	55.1552	+	46.2807i	0.0902792	+	0.0757532i
$73$	−115.233	−	653.521i	−0.184754	−	1.04779i	−0.926271	−	0.376859i	$-0.877004\pi$
$73$	−115.233	−	653.521i	−0.184754	−	1.04779i	0.741517	−	0.670934i	$-0.234107\pi$
$74$	−651.009	−	236.948i	−1.02268	−	0.372225i
$75$	−296.176			−0.455993
$76$	298.705	−	143.246i	0.450839	−	0.216204i
$77$	1907.93			2.82376
$78$	261.840	+	95.3018i	0.380096	+	0.138344i
$79$	−88.0234	−	499.205i	−0.125360	−	0.710949i	−0.981094	−	0.193533i	$-0.938005\pi$
$79$	−88.0234	−	499.205i	−0.125360	−	0.710949i	0.855734	−	0.517416i	$-0.173106\pi$
$80$	−62.8265	−	52.7177i	−0.0878027	−	0.0736752i
$81$	62.0496	−	52.0658i	0.0851160	−	0.0714208i
$82$	−101.741	+	577.001i	−0.137017	+	0.777062i
$83$	103.456	−	179.191i	0.136817	−	0.236973i	−0.789473	−	0.613785i	$-0.789646\pi$
$83$	103.456	−	179.191i	0.136817	−	0.236973i	0.926290	+	0.376812i	$0.122980\pi$
$84$	201.712	+	349.375i	0.262006	+	0.453808i
$85$	−333.851	+	121.512i	−0.426014	+	0.155057i
$86$	−258.335	+	94.0262i	−0.323918	+	0.117897i
$87$	−144.989	−	251.128i	−0.178671	−	0.309468i
$88$	227.009	−	393.192i	0.274992	−	0.476300i
$89$	183.513	−	1040.76i	0.218566	−	1.23955i	−0.656044	−	0.754723i	$-0.727771\pi$
$89$	183.513	−	1040.76i	0.218566	−	1.23955i	0.874610	−	0.484827i	$-0.161118\pi$
$90$	−70.6798	+	59.3074i	−0.0827812	+	0.0694617i
$91$	1196.00	+	1003.56i	1.37775	+	1.15607i
$92$	133.118	+	754.947i	0.150853	+	0.855529i
$93$	86.6068	+	31.5223i	0.0965668	+	0.0351474i
$94$	1059.87			1.16294
$95$	114.308	+	408.842i	0.123450	+	0.441540i
$96$	96.0000			0.102062
$97$	−1014.58	−	369.277i	−1.06201	−	0.386540i	−0.248828	−	0.968548i	$-0.580045\pi$
$97$	−1014.58	−	369.277i	−1.06201	−	0.386540i	−0.813184	+	0.582007i	$0.802268\pi$
$98$	273.395	+	1550.50i	0.281807	+	1.59821i
$99$	−391.274	−	328.317i	−0.397217	−	0.333305i
$100$	−302.512	+	253.838i	−0.302512	+	0.253838i
$101$	33.0849	−	187.634i	0.0325948	−	0.184854i	−0.964163	−	0.265309i	$-0.914526\pi$
$101$	33.0849	−	187.634i	0.0325948	−	0.184854i	0.996758	+	0.0804546i	$0.0256372\pi$
$102$	207.931	−	360.147i	0.201845	−	0.349606i
$103$	646.242	+	1119.32i	0.618215	+	1.07078i	0.989811	+	0.142385i	$0.0454771\pi$
$103$	646.242	+	1119.32i	0.618215	+	1.07078i	−0.371597	+	0.928394i	$0.621190\pi$
$104$	349.119	−	127.069i	0.329173	−	0.119809i
$105$	−485.798	+	176.816i	−0.451514	+	0.164338i
$106$	293.251	+	507.925i	0.268708	+	0.465416i
$107$	−27.7246	+	48.0204i	−0.0250489	+	0.0433860i	−0.878278	−	0.478150i	$-0.841307\pi$
$107$	−27.7246	+	48.0204i	−0.0250489	+	0.0433860i	0.853229	+	0.521536i	$0.174641\pi$
$108$	18.7540	−	106.359i	0.0167093	−	0.0947632i
$109$	857.586	−	719.600i	0.753595	−	0.632341i	−0.182856	−	0.983140i	$-0.558534\pi$
$109$	857.586	−	719.600i	0.753595	−	0.632341i	0.936451	+	0.350799i	$0.114090\pi$
$110$	445.694	+	373.982i	0.386321	+	0.324161i
$111$	180.452	+	1023.40i	0.154304	+	0.875103i
$112$	505.458	+	183.972i	0.426440	+	0.155212i
$113$	−1920.49			−1.59880			−0.799401	−	0.600798i	$-0.794850\pi$
$113$	−1920.49			−1.59880			−0.799401	+	0.600798i	$0.794850\pi$
$114$	−410.111	−	280.594i	−0.336933	−	0.230527i
$115$	−982.367			−0.796576
$116$	−363.319	−	132.237i	−0.290805	−	0.105844i
$117$	−72.5790	−	411.616i	−0.0573498	−	0.325247i
$118$	−132.304	−	111.016i	−0.103216	−	0.0866089i
$119$	1784.97	−	1497.77i	1.37503	−	1.15378i
$120$	−21.3624	+	121.152i	−0.0162509	+	0.0921637i
$121$	−944.916	+	1636.64i	−0.709929	+	1.22963i
$122$	−812.433	−	1407.18i	−0.602904	−	1.04426i
$123$	825.852	−	300.585i	0.605403	−	0.220349i
$124$	115.476	−	42.0298i	0.0836293	−	0.0304386i
$125$	−573.395	−	993.150i	−0.410288	−	0.710640i
$126$	302.567	−	524.062i	0.213927	−	0.370533i
$127$	−385.932	+	2188.73i	−0.269653	+	1.52928i	0.485796	+	0.874072i	$0.338530\pi$
$127$	−385.932	+	2188.73i	−0.269653	+	1.52928i	−0.755449	+	0.655207i	$0.772581\pi$
$128$	98.0537	−	82.2768i	0.0677094	−	0.0568149i
$129$	315.895	+	265.067i	0.215605	+	0.180914i
$130$	82.6737	+	468.866i	0.0557766	+	0.316325i
$131$	731.147	+	266.116i	0.487638	+	0.177486i	0.574126	−	0.818767i	$-0.305342\pi$
$131$	731.147	+	266.116i	0.487638	+	0.177486i	−0.0864877	+	0.996253i	$0.527564\pi$
$132$	−681.028			−0.449060
$133$	−1621.59	−	2263.31i	−1.05722	−	1.47559i
$134$	871.772			0.562012
$135$	130.052	+	47.3352i	0.0829121	+	0.0301775i
$136$	−96.2849	−	546.059i	−0.0607085	−	0.344295i
$137$	−271.669	−	227.957i	−0.169418	−	0.142158i	0.554137	−	0.832426i	$-0.313048\pi$
$137$	−271.669	−	227.957i	−0.169418	−	0.142158i	−0.723554	+	0.690267i	$0.757493\pi$
$138$	880.867	−	739.135i	0.543365	−	0.455937i
$139$	−131.545	+	746.026i	−0.0802695	+	0.455231i	0.918008	+	0.396562i	$0.129797\pi$
$139$	−131.545	+	746.026i	−0.0802695	+	0.455231i	−0.998277	+	0.0586691i	$0.981314\pi$
$140$	−344.650	+	596.951i	−0.208059	+	0.360369i
$141$	−794.899	−	1376.81i	−0.474770	−	0.822326i
$142$	−78.0364	+	28.4029i	−0.0461174	+	0.0167854i
$143$	−2476.67	+	901.434i	−1.44832	+	0.527145i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	247.732	−	429.084i	0.141883	−	0.245748i
$146$	−230.467	+	1307.04i	−0.130641	+	0.740902i
$147$	1809.11	−	1518.02i	1.01505	−	0.851732i
$148$	1061.41	+	890.632i	0.589511	+	0.494659i
$149$	283.857	+	1609.83i	0.156070	+	0.885118i	0.957801	+	0.287433i	$0.0928018\pi$
$149$	283.857	+	1609.83i	0.156070	+	0.885118i	−0.801731	+	0.597686i	$0.796087\pi$
$150$	556.629	+	202.596i	0.302990	+	0.110279i
$151$	−649.932			−0.350270			−0.175135	−	0.984544i	$-0.556036\pi$
$151$	−649.932			−0.350270			−0.175135	+	0.984544i	$0.556036\pi$
$152$	−659.367	+	64.8891i	−0.351854	+	0.0346263i
$153$	−623.793			−0.329612
$154$	−3585.74	−	1305.10i	−1.87628	−	0.682911i
$155$	27.3454	+	155.083i	0.0141706	+	0.0803652i
$156$	−426.907	−	358.218i	−0.219102	−	0.183848i
$157$	−176.615	+	148.198i	−0.0897799	+	0.0753343i	−0.686573	−	0.727061i	$-0.740886\pi$
$157$	−176.615	+	148.198i	−0.0897799	+	0.0753343i	0.596793	+	0.802395i	$0.296441\pi$
$158$	−176.047	+	998.411i	−0.0886426	+	0.502717i
$159$	439.876	−	761.888i	0.219399	−	0.380010i
$160$	82.0142	+	142.053i	0.0405237	+	0.0701891i
$161$	6054.39	−	2203.62i	2.96368	−	1.07869i
$162$	−152.230	+	55.4073i	−0.0738292	+	0.0268716i
$163$	−1213.96	−	2102.64i	−0.583342	−	1.01038i	−0.995080	−	0.0990752i	$-0.968412\pi$
$163$	−1213.96	−	2102.64i	−0.583342	−	1.01038i	0.411738	−	0.911302i	$-0.364922\pi$
$164$	585.902	−	1014.81i	0.278971	−	0.483192i
$165$	151.546	−	859.460i	0.0715021	−	0.405508i
$166$	−317.008	+	266.001i	−0.148220	+	0.124372i
$167$	−1649.26	−	1383.89i	−0.764212	−	0.641250i	0.175008	−	0.984567i	$-0.444005\pi$
$167$	−1649.26	−	1383.89i	−0.764212	−	0.641250i	−0.939219	+	0.343317i	$0.888449\pi$
$168$	−140.107	−	794.588i	−0.0643424	−	0.364904i
$169$	37.8394	+	13.7724i	0.0172232	+	0.00626874i
$170$	710.554			0.320570
$171$	−56.9190	+	743.195i	−0.0254544	+	0.332360i
$172$	549.828			0.243744
$173$	−534.682	−	194.608i	−0.234978	−	0.0855248i	0.221848	−	0.975081i	$-0.428791\pi$
$173$	−534.682	−	194.608i	−0.234978	−	0.0855248i	−0.456825	+	0.889557i	$0.651013\pi$
$174$	100.708	+	571.144i	0.0438773	+	0.248841i
$175$	2542.50	+	2133.41i	1.09826	+	0.921549i
$176$	−695.597	+	583.676i	−0.297913	+	0.249978i
$177$	−44.9862	+	255.129i	−0.0191038	+	0.108343i
$178$	−1056.81	+	1830.45i	−0.445008	+	0.770776i
$179$	33.6376	+	58.2621i	0.0140458	+	0.0243280i	0.872963	−	0.487787i	$-0.162196\pi$
$179$	33.6376	+	58.2621i	0.0140458	+	0.0243280i	−0.858917	+	0.512115i	$0.828862\pi$
$180$	173.403	−	63.1136i	0.0718040	−	0.0261345i
$181$	−257.585	+	93.7532i	−0.105780	+	0.0385007i	−0.394368	−	0.918953i	$-0.629036\pi$
$181$	−257.585	+	93.7532i	−0.105780	+	0.0385007i	0.288588	+	0.957453i	$0.406814\pi$
$182$	−1561.27	−	2704.20i	−0.635873	−	1.10136i
$183$	−1218.65	+	2110.76i	−0.492269	+	0.852634i
$184$	266.235	−	1509.89i	0.106669	−	0.604950i
$185$	−1360.17	+	1141.32i	−0.540550	+	0.453576i
$186$	−141.205	−	118.485i	−0.0556648	−	0.0467083i
$187$	683.049	+	3873.77i	0.267110	+	1.51485i
$188$	−1991.90	−	724.991i	−0.772734	−	0.281252i
$189$	−907.702			−0.349342
$190$	64.8356	−	846.563i	0.0247562	−	0.323243i
$191$	−3035.08			−1.14979			−0.574897	−	0.818225i	$-0.694958\pi$
$191$	−3035.08			−1.14979			−0.574897	+	0.818225i	$0.694958\pi$
$192$	−180.421	−	65.6679i	−0.0678165	−	0.0246832i
$193$	252.782	+	1433.60i	0.0942778	+	0.534676i	0.994966	+	0.100211i	$0.0319516\pi$
$193$	252.782	+	1433.60i	0.0942778	+	0.534676i	−0.900688	+	0.434466i	$0.856937\pi$
$194$	1654.19	+	1388.03i	0.612184	+	0.513684i
$195$	547.069	−	459.046i	0.200905	−	0.168579i
$196$	546.790	−	3101.00i	0.199267	−	1.13010i
$197$	906.830	−	1570.68i	0.327964	−	0.568051i	−0.654143	−	0.756371i	$-0.726971\pi$
$197$	906.830	−	1570.68i	0.327964	−	0.568051i	0.982108	+	0.188320i	$0.0603041\pi$
$198$	510.771	+	884.682i	0.183328	+	0.317533i
$199$	1127.44	−	410.354i	0.401618	−	0.146177i	−0.133310	−	0.991074i	$-0.542561\pi$
$199$	1127.44	−	410.354i	0.401618	−	0.146177i	0.534929	+	0.844897i	$0.320338\pi$
$200$	742.171	−	270.128i	0.262397	−	0.0955048i
$201$	−653.829	−	1132.47i	−0.229441	−	0.397403i
$202$	−190.528	+	330.005i	−0.0663640	+	0.114946i
$203$	−564.277	+	3200.17i	−0.195096	+	1.10644i
$204$	−637.137	+	534.622i	−0.218669	+	0.183485i
$205$	1150.32	+	965.232i	0.391911	+	0.328852i
$206$	−448.875	−	2545.70i	−0.151818	−	0.861005i
$207$	−1620.81	−	589.928i	−0.544224	−	0.198081i
$208$	−743.050			−0.247698
$209$	4677.58	−	460.326i	1.54811	−	0.152351i
$210$	1033.95			0.339759
$211$	−2401.47	−	874.065i	−0.783528	−	0.285181i	−0.0808848	−	0.996723i	$-0.525775\pi$
$211$	−2401.47	−	874.065i	−0.783528	−	0.285181i	−0.702643	+	0.711543i	$0.747997\pi$
$212$	−203.690	−	1155.18i	−0.0659881	−	0.374237i
$213$	95.4238	+	80.0701i	0.0306964	+	0.0257573i
$214$	84.9530	−	71.2841i	0.0271368	−	0.0227705i
$215$	−122.351	+	693.885i	−0.0388105	+	0.220105i
$216$	−108.000	+	187.061i	−0.0340207	+	0.0589256i
$217$	−516.410	−	894.448i	−0.161549	−	0.279812i
$218$	−2103.97	+	765.782i	−0.653664	+	0.237914i
$219$	1870.75	−	680.897i	0.577230	−	0.210095i
$220$	−581.812	−	1007.73i	−0.178299	−	0.308823i
$221$	−1609.41	+	2787.58i	−0.489866	+	0.848473i
$222$	360.905	−	2046.79i	0.109110	−	0.618791i
$223$	−2002.72	+	1680.48i	−0.601398	+	0.504633i	−0.891895	−	0.452243i	$-0.850624\pi$
$223$	−2002.72	+	1680.48i	−0.601398	+	0.504633i	0.290497	+	0.956876i	$0.406179\pi$
$224$	−824.107	−	691.508i	−0.245817	−	0.206265i
$225$	−154.291	−	875.029i	−0.0457159	−	0.259268i
$226$	3609.34	+	1313.69i	1.06234	+	0.386662i
$227$	2306.64			0.674437			0.337219	−	0.941426i	$-0.390514\pi$
$227$	2306.64			0.674437			0.337219	+	0.941426i	$0.390514\pi$
$228$	578.819	+	807.877i	0.168128	+	0.234662i
$229$	−1441.46			−0.415958			−0.207979	−	0.978133i	$-0.566689\pi$
$229$	−1441.46			−0.415958			−0.207979	+	0.978133i	$0.566689\pi$
$230$	1846.25	+	671.979i	0.529295	+	0.192648i
$231$	993.928	+	5636.85i	0.283098	+	1.60553i
$232$	592.361	+	497.050i	0.167631	+	0.140659i
$233$	1421.03	−	1192.39i	0.399550	−	0.335262i	−0.420770	−	0.907167i	$-0.638240\pi$
$233$	1421.03	−	1192.39i	0.399550	−	0.335262i	0.820320	+	0.571905i	$0.193796\pi$
$234$	−145.158	+	823.232i	−0.0405524	+	0.229984i
$235$	1358.19	−	2352.45i	0.377015	−	0.653008i
$236$	172.710	+	299.143i	0.0476376	+	0.0825108i
$237$	1429.01	−	520.117i	0.391663	−	0.142554i
$238$	−4379.18	+	1593.89i	−1.19269	+	0.434104i
$239$	−1677.36	−	2905.27i	−0.453972	−	0.786302i	0.544657	−	0.838659i	$-0.316660\pi$
$239$	−1677.36	−	2905.27i	−0.453972	−	0.786302i	−0.998628	+	0.0523568i	$0.983327\pi$
$240$	123.021	−	213.079i	0.0330875	−	0.0573091i
$241$	714.262	−	4050.78i	0.190911	−	1.08271i	−0.727210	−	0.686415i	$-0.759184\pi$
$241$	714.262	−	4050.78i	0.190911	−	1.08271i	0.918122	−	0.396298i	$-0.129705\pi$
$242$	2895.39	−	2429.52i	0.769102	−	0.645353i
$243$	186.149	+	156.197i	0.0491418	+	0.0412348i
$244$	564.310	+	3200.36i	0.148058	+	0.839681i
$245$	3791.80	+	1380.10i	0.988771	+	0.359883i
$246$	−1757.71			−0.455558
$247$	3174.30	+	2171.83i	0.817717	+	0.559474i
$248$	−245.774			−0.0629300
$249$	583.301	+	212.304i	0.148455	+	0.0540331i
$250$	398.276	+	2258.74i	0.100757	+	0.571420i
$251$	2011.57	+	1687.91i	0.505854	+	0.424462i	0.859667	−	0.510854i	$-0.170671\pi$
$251$	2011.57	+	1687.91i	0.505854	+	0.424462i	−0.353814	+	0.935316i	$0.615115\pi$
$252$	−927.120	+	777.946i	−0.231758	+	0.194468i
$253$	−1888.68	+	10711.3i	−0.469330	+	2.66170i
$254$	2222.50	−	3849.48i	0.549023	−	0.950936i
$255$	−532.915	−	923.036i	−0.130872	−	0.226678i
$256$	−240.561	+	87.5572i	−0.0587308	+	0.0213763i
$257$	−1207.85	+	439.623i	−0.293167	+	0.106704i	−0.484417	−	0.874837i	$-0.660968\pi$
$257$	−1207.85	+	439.623i	−0.293167	+	0.106704i	0.191250	+	0.981541i	$0.438746\pi$
$258$	−412.371	−	714.248i	−0.0995082	−	0.172353i
$259$	5822.65	−	10085.1i	1.39692	−	2.41953i
$260$	165.347	−	937.732i	0.0394400	−	0.223676i
$261$	666.406	−	559.181i	0.158044	−	0.132615i
$262$	−1192.07	−	1000.27i	−0.281093	−	0.235865i
$263$	1079.81	+	6123.91i	0.253171	+	1.43580i	0.800725	+	0.599033i	$0.204448\pi$
$263$	1079.81	+	6123.91i	0.253171	+	1.43580i	−0.547554	+	0.836771i	$0.684441\pi$
$264$	1279.91	+	465.851i	0.298384	+	0.108603i
$265$	1503.17			0.348449
$266$	1499.40	+	5362.86i	0.345617	+	1.23616i
$267$	3170.44			0.726695
$268$	−1638.40	−	596.327i	−0.373436	−	0.135920i
$269$	−399.466	−	2265.48i	−0.0905423	−	0.513491i	−0.996022	−	0.0891023i	$-0.971600\pi$
$269$	−399.466	−	2265.48i	−0.0905423	−	0.513491i	0.905480	−	0.424389i	$-0.139511\pi$
$270$	−212.039	−	177.922i	−0.0477937	−	0.0401037i
$271$	4049.06	−	3397.56i	0.907612	−	0.761576i	−0.0640516	−	0.997947i	$-0.520402\pi$
$271$	4049.06	−	3397.56i	0.907612	−	0.761576i	0.971663	+	0.236370i	$0.0759578\pi$
$272$	−192.570	+	1092.12i	−0.0429274	+	0.243453i
$273$	−2341.90	+	4056.29i	−0.519188	+	0.899260i
$274$	354.638	+	614.251i	0.0781915	+	0.135432i
$275$	−5265.00	+	1916.30i	−1.15451	+	0.420209i
$276$	−2161.09	+	786.571i	−0.471312	+	0.171544i
$277$	−779.373	−	1349.91i	−0.169054	−	0.292810i	0.769034	−	0.639208i	$-0.220738\pi$
$277$	−779.373	−	1349.91i	−0.169054	−	0.292810i	−0.938088	+	0.346398i	$0.887405\pi$
$278$	757.535	−	1312.09i	0.163431	−	0.283071i
$279$	−48.0129	+	272.295i	−0.0103027	+	0.0584296i
$280$	1056.07	−	886.147i	0.225401	−	0.189134i
$281$	−3630.21	−	3046.11i	−0.770677	−	0.646675i	0.170205	−	0.985409i	$-0.445557\pi$
$281$	−3630.21	−	3046.11i	−0.770677	−	0.646675i	−0.940882	+	0.338734i	$0.890001\pi$
$282$	552.131	+	3131.29i	0.116592	+	0.661226i
$283$	1712.40	+	623.262i	0.359687	+	0.130915i	0.515542	−	0.856865i	$-0.327591\pi$
$283$	1712.40	+	623.262i	0.359687	+	0.130915i	−0.155854	+	0.987780i	$0.549813\pi$
$284$	166.089			0.0347027
$285$	−1148.34	+	550.698i	−0.238674	+	0.114458i
$286$	5271.23			1.08984
$287$	−9254.66	−	3368.42i	−1.90343	−	0.692793i
$288$	50.0107	+	283.625i	0.0102323	+	0.0580304i
$289$	−83.5607	−	70.1158i	−0.0170081	−	0.0142715i
$290$	−759.094	+	636.956i	−0.153709	+	0.128977i
$291$	562.461	−	3189.87i	0.113306	−	0.642590i
$292$	1327.21	−	2298.79i	0.265989	−	0.460707i
$293$	1212.24	+	2099.67i	0.241706	+	0.418648i	0.961200	−	0.275851i	$-0.0889596\pi$
$293$	1212.24	+	2099.67i	0.241706	+	0.418648i	−0.719494	+	0.694499i	$0.755626\pi$
$294$	−4438.41	+	1615.45i	−0.880453	+	0.320459i
$295$	−415.952	+	151.394i	−0.0820937	+	0.0298797i
$296$	−1385.58	−	2399.89i	−0.272078	−	0.471253i
$297$	766.157	−	1327.02i	0.149687	−	0.259265i
$298$	567.714	−	3219.67i	0.110358	−	0.625873i
$299$	−6818.00	+	5720.98i	−1.31871	+	1.10653i
$300$	−907.536	−	761.513i	−0.174655	−	0.146553i
$301$	−802.448	−	4550.91i	−0.153662	−	0.871462i
$302$	1221.47	+	444.580i	0.232741	+	0.0847109i
$303$	571.585			0.108372
$304$	1283.59	+	329.082i	0.242168	+	0.0620861i
$305$	−4164.44			−0.781820
$306$	1172.35	+	426.699i	0.219015	+	0.0797150i
$307$	259.011	+	1468.93i	0.0481517	+	0.273082i	0.999372	−	0.0354302i	$-0.0112802\pi$
$307$	259.011	+	1468.93i	0.0481517	+	0.273082i	−0.951220	+	0.308512i	$0.900169\pi$
$308$	5846.25	+	4905.59i	1.08156	+	0.907538i
$309$	−2970.30	+	2492.38i	−0.546843	+	0.458856i
$310$	54.6908	−	310.167i	0.0100201	−	0.0568268i
$311$	3665.98	−	6349.66i	0.668420	−	1.15774i	−0.309926	−	0.950761i	$-0.600304\pi$
$311$	3665.98	−	6349.66i	0.668420	−	1.15774i	0.978346	−	0.206977i	$-0.0663625\pi$
$312$	557.288	+	965.250i	0.101122	+	0.175149i
$313$	8653.80	−	3149.73i	1.56275	−	0.568796i	0.591388	−	0.806387i	$-0.298580\pi$
$313$	8653.80	−	3149.73i	1.56275	−	0.568796i	0.971365	+	0.237591i	$0.0763578\pi$
$314$	433.302	−	157.709i	0.0778747	−	0.0283441i
$315$	−775.463	−	1343.14i	−0.138706	−	0.240246i
$316$	1013.81	−	1755.98i	0.180479	−	0.312599i
$317$	483.441	−	2741.73i	0.0856553	−	0.485776i	−0.911558	−	0.411172i	$-0.865120\pi$
$317$	483.441	−	2741.73i	0.0856553	−	0.485776i	0.997213	−	0.0746038i	$-0.0237692\pi$
$318$	−1347.86	+	1130.99i	−0.237686	+	0.199442i
$319$	−4202.24	−	3526.10i	−0.737555	−	0.618882i
$320$	−56.9665	−	323.073i	−0.00995163	−	0.0564385i
$321$	−156.315	−	56.8942i	−0.0271797	−	0.00989260i
$322$	−12885.9			−2.23013
$323$	4014.76	−	4102.66i	0.691600	−	0.706743i
$324$	324.000			0.0555556
$325$	−4308.36	−	1568.12i	−0.735338	−	0.267641i
$326$	843.208	+	4782.07i	0.143254	+	0.812436i
$327$	2572.76	+	2158.80i	0.435088	+	0.365082i
$328$	−1795.31	+	1506.44i	−0.302224	+	0.253596i
$329$	−3093.65	+	17544.9i	−0.518414	+	2.94007i
$330$	−872.719	+	1511.59i	−0.145581	+	0.252153i
$331$	−5264.24	−	9117.93i	−0.874165	−	1.51410i	−0.857649	−	0.514235i	$-0.828076\pi$
$331$	−5264.24	−	9117.93i	−0.874165	−	1.51410i	−0.0165158	−	0.999864i	$-0.505257\pi$
$332$	777.735	−	283.072i	0.128566	−	0.0467940i
$333$	−2929.54	+	1066.26i	−0.482095	+	0.175468i
$334$	2152.95	+	3729.02i	0.352707	+	0.610907i
$335$	1117.15	−	1934.96i	0.182198	−	0.315577i
$336$	−280.215	+	1589.18i	−0.0454969	+	0.258026i
$337$	3296.48	−	2766.07i	0.532851	−	0.447115i	−0.336234	−	0.941779i	$-0.609153\pi$
$337$	3296.48	−	2766.07i	0.532851	−	0.447115i	0.869084	+	0.494664i	$0.164709\pi$
$338$	−61.6940	−	51.7674i	−0.00992813	−	0.00833069i
$339$	−1000.47	−	5673.94i	−0.160289	−	0.909045i
$340$	−1335.40	−	486.047i	−0.213007	−	0.0775283i
$341$	1743.53			0.276884
$342$	615.348	−	1357.82i	0.0972930	−	0.214685i
$343$	−14933.7			−2.35085
$344$	−1033.34	−	376.105i	−0.161959	−	0.0589483i
$345$	−511.759	−	2902.33i	−0.0798614	−	0.452916i
$346$	871.753	+	731.488i	0.135450	+	0.113656i
$347$	755.136	−	633.635i	0.116824	−	0.0980268i	−0.582504	−	0.812828i	$-0.697927\pi$
$347$	755.136	−	633.635i	0.116824	−	0.0980268i	0.699328	+	0.714801i	$0.253483\pi$
$348$	201.416	−	1142.29i	0.0310260	−	0.175957i
$349$	4862.57	−	8422.22i	0.745810	−	1.29178i	−0.204006	−	0.978970i	$-0.565396\pi$
$349$	4862.57	−	8422.22i	0.745810	−	1.29178i	0.949816	−	0.312811i	$-0.101271\pi$
$350$	−3319.00	−	5748.68i	−0.506881	−	0.877943i
$351$	1178.28	−	428.858i	0.179179	−	0.0652158i
$352$	1706.55	−	621.134i	0.258408	−	0.0940528i
$353$	−1334.72	−	2311.81i	−0.201247	−	0.348570i	0.747683	−	0.664055i	$-0.231166\pi$
$353$	−1334.72	−	2311.81i	−0.201247	−	0.348570i	−0.948931	+	0.315485i	$0.897833\pi$
$354$	259.065	−	448.714i	0.0388959	−	0.0673698i
$355$	−36.9590	+	209.605i	−0.00552558	+	0.0313371i
$356$	3238.26	−	2717.22i	0.482099	−	0.404529i
$357$	5354.91	+	4493.31i	0.793871	+	0.666137i
$358$	−23.3645	−	132.506i	−0.00344930	−	0.0195620i
$359$	−6181.17	−	2249.76i	−0.908718	−	0.330746i	−0.154977	−	0.987918i	$-0.549530\pi$
$359$	−6181.17	−	2249.76i	−0.908718	−	0.330746i	−0.753741	+	0.657172i	$0.771753\pi$
$360$	−369.064			−0.0540316
$361$	−4521.63	−	5157.59i	−0.659226	−	0.751945i
$362$	548.232			0.0795979
$363$	−5327.58	−	1939.08i	−0.770318	−	0.280373i
$364$	1084.45	+	6150.20i	0.156155	+	0.885599i
$365$	2605.74	+	2186.48i	0.373673	+	0.313549i
$366$	3734.16	−	3133.33i	0.533300	−	0.447491i
$367$	1109.01	−	6289.53i	0.157739	−	0.894580i	−0.798500	−	0.601994i	$-0.794373\pi$
$367$	1109.01	−	6289.53i	0.157739	−	0.894580i	0.956239	−	0.292586i	$-0.0945159\pi$
$368$	−1533.19	+	2655.56i	−0.217182	+	0.376170i
$369$	1318.28	+	2283.33i	0.185981	+	0.322128i
$370$	3337.00	−	1214.57i	0.468871	−	0.170655i
$371$	−9264.12	+	3371.87i	−1.29641	+	0.471856i
$372$	184.330	+	319.269i	0.0256911	+	0.0444982i
$373$	−1417.30	+	2454.84i	−0.196743	+	0.340769i	−0.947470	−	0.319843i	$-0.896370\pi$
$373$	−1417.30	+	2454.84i	−0.196743	+	0.340769i	0.750728	+	0.660612i	$0.229703\pi$
$374$	1366.10	−	7747.53i	0.188875	−	1.07116i
$375$	2635.48	−	2211.43i	0.362921	−	0.304527i
$376$	3247.62	+	2725.07i	0.445434	+	0.373763i
$377$	−779.491	−	4420.71i	−0.106488	−	0.603921i
$378$	1705.92	+	620.905i	0.232125	+	0.0844865i
$379$	1008.90			0.136738			0.0683691	−	0.997660i	$-0.478220\pi$
$379$	1008.90			0.136738			0.0683691	+	0.997660i	$0.478220\pi$
$380$	−700.934	+	1546.67i	−0.0946242	+	0.208796i
$381$	−6667.49			−0.896551
$382$	5704.09	+	2076.12i	0.763996	+	0.278072i
$383$	1256.22	+	7124.36i	0.167597	+	0.950490i	0.946346	+	0.323155i	$0.104743\pi$
$383$	1256.22	+	7124.36i	0.167597	+	0.950490i	−0.778749	+	0.627335i	$0.784146\pi$
$384$	294.161	+	246.830i	0.0390920	+	0.0328021i
$385$	−7491.80	+	6286.37i	−0.991734	+	0.832164i
$386$	505.563	−	2867.19i	0.0666645	−	0.378073i
$387$	−618.557	+	1071.37i	−0.0812481	+	0.140726i
$388$	−2159.39	−	3740.17i	−0.282542	−	0.489377i
$389$	−4303.88	+	1566.48i	−0.560964	+	0.204174i	−0.606911	−	0.794770i	$-0.707592\pi$
$389$	−4303.88	+	1566.48i	−0.560964	+	0.204174i	0.0459470	+	0.998944i	$0.485369\pi$
$390$	−1342.16	+	488.506i	−0.174264	+	0.0634268i
$391$	6641.60	+	11503.6i	0.859029	+	1.48788i
$392$	−3148.84	+	5453.95i	−0.405715	+	0.702719i
$393$	−405.331	+	2298.75i	−0.0520261	+	0.295055i
$394$	−2778.69	+	2331.60i	−0.355300	+	0.298132i
$395$	1990.45	+	1670.18i	0.253545	+	0.212750i
$396$	−354.778	−	2012.05i	−0.0450209	−	0.255326i
$397$	3457.22	+	1258.33i	0.437060	+	0.159077i	0.551173	−	0.834391i	$-0.314180\pi$
$397$	3457.22	+	1258.33i	0.437060	+	0.159077i	−0.114113	+	0.993468i	$0.536403\pi$
$398$	−2399.59			−0.302213
$399$	5842.00	−	5969.92i	0.732998	−	0.749047i
$400$	−1579.60			−0.197451
$401$	8076.85	+	2939.73i	1.00583	+	0.366093i	0.791831	−	0.610740i	$-0.209128\pi$
$401$	8076.85	+	2939.73i	1.00583	+	0.366093i	0.214001	+	0.976833i	$0.431350\pi$
$402$	454.145	+	2575.58i	0.0563450	+	0.319548i
$403$	1092.94	+	917.087i	0.135095	+	0.113358i
$404$	583.813	−	489.877i	0.0718955	−	0.0603275i
$405$	−72.0982	+	408.889i	−0.00884589	+	0.0501676i
$406$	3249.54	−	5628.37i	0.397222	−	0.688008i
$407$	9829.35	+	17024.9i	1.19711	+	2.07345i
$408$	1563.13	−	568.933i	0.189673	−	0.0690352i
$409$	−7636.86	+	2779.59i	−0.923272	+	0.336044i	−0.759539	−	0.650461i	$-0.774576\pi$
$409$	−7636.86	+	2779.59i	−0.923272	+	0.336044i	−0.163733	+	0.986505i	$0.552353\pi$
$410$	−1501.63	−	2600.91i	−0.180879	−	0.313292i
$411$	531.957	−	921.377i	0.0638431	−	0.110579i
$412$	−897.750	+	5091.39i	−0.107352	+	0.608823i
$413$	2223.93	−	1866.10i	0.264970	−	0.222336i
$414$	2642.60	+	2217.40i	0.313712	+	0.263236i
$415$	184.173	+	1044.49i	0.0217848	+	0.123548i
$416$	1396.48	+	508.276i	0.164586	+	0.0599045i
$417$	−2272.60			−0.266882
$418$	−9105.86	−	2334.52i	−1.06551	−	0.273171i
$419$	−1378.04			−0.160672			−0.0803362	−	0.996768i	$-0.525599\pi$
$419$	−1378.04			−0.160672			−0.0803362	+	0.996768i	$0.525599\pi$
$420$	−1943.19	−	707.264i	−0.225757	−	0.0821689i
$421$	2678.20	+	15188.8i	0.310042	+	1.75833i	0.598768	+	0.800922i	$0.295657\pi$
$421$	2678.20	+	15188.8i	0.310042	+	1.75833i	−0.288727	+	0.957412i	$0.593232\pi$
$422$	3915.40	+	3285.41i	0.451656	+	0.378984i
$423$	3653.57	−	3065.71i	0.419959	−	0.352387i
$424$	−407.380	+	2310.36i	−0.0466606	+	0.264626i
$425$	−3421.34	+	5925.94i	−0.390493	+	0.676353i
$426$	−124.567	−	215.756i	−0.0141673	−	0.0245385i
$427$	25665.7	−	9341.55i	2.90878	−	1.05871i
$428$	−208.421	+	75.8589i	−0.0235383	+	0.00856724i
$429$	−3953.42	−	6847.53i	−0.444926	−	0.770634i
$430$	704.590	−	1220.38i	0.0790194	−	0.136866i
$431$	2192.45	−	12434.0i	0.245026	−	1.38961i	−0.575405	−	0.817869i	$-0.695156\pi$
$431$	2192.45	−	12434.0i	0.245026	−	1.38961i	0.820431	−	0.571745i	$-0.193733\pi$
$432$	330.931	−	277.684i	0.0368563	−	0.0309261i
$433$	4090.45	+	3432.29i	0.453982	+	0.380936i	0.840911	−	0.541173i	$-0.182020\pi$
$433$	4090.45	+	3432.29i	0.453982	+	0.380936i	−0.386929	+	0.922110i	$0.626464\pi$
$434$	358.695	+	2034.26i	0.0396726	+	0.224994i
$435$	1396.75	+	508.375i	0.153952	+	0.0560339i
$436$	4478.00			0.491874
$437$	14311.6	−	6863.23i	1.56662	−	0.751288i
$438$	−3981.62			−0.434359
$439$	6646.01	+	2418.95i	0.722544	+	0.262984i	0.677005	−	0.735978i	$-0.263277\pi$
$439$	6646.01	+	2418.95i	0.722544	+	0.262984i	0.0455386	+	0.998963i	$0.485500\pi$
$440$	404.123	+	2291.89i	0.0437859	+	0.248322i
$441$	5427.34	+	4554.07i	0.586042	+	0.491748i
$442$	4931.51	−	4138.03i	0.530697	−	0.445308i
$443$	2276.88	−	12912.8i	0.244194	−	1.38489i	−0.578163	−	0.815921i	$-0.696230\pi$
$443$	2276.88	−	12912.8i	0.244194	−	1.38489i	0.822357	−	0.568972i	$-0.192659\pi$
$444$	−2078.37	+	3599.84i	−0.222151	+	0.384776i
$445$	2708.55	+	4691.34i	0.288534	+	0.499755i
$446$	4913.39	−	1788.33i	0.521650	−	0.189865i
$447$	−4608.25	+	1677.27i	−0.487613	+	0.177477i
$448$	1075.79	+	1863.33i	0.113452	+	0.196505i
$449$	2575.18	−	4460.35i	0.270669	−	0.468812i	−0.698364	−	0.715742i	$-0.746088\pi$
$449$	2575.18	−	4460.35i	0.270669	−	0.468812i	0.969033	+	0.246930i	$0.0794218\pi$
$450$	−308.582	+	1750.06i	−0.0323260	+	0.183330i
$451$	12736.0	−	10686.8i	1.32974	−	1.11579i
$452$	−5884.72	−	4937.87i	−0.612376	−	0.513845i
$453$	−338.579	−	1920.17i	−0.0351166	−	0.199156i
$454$	−4335.07	−	1577.84i	−0.448139	−	0.163109i
$455$	−8002.88			−0.824574
$456$	−535.204	−	1914.25i	−0.0549632	−	0.196585i
$457$	−10784.0			−1.10384			−0.551922	−	0.833896i	$-0.686105\pi$
$457$	−10784.0			−1.10384			−0.551922	+	0.833896i	$0.686105\pi$
$458$	2709.06	+	986.016i	0.276389	+	0.100597i
$459$	−324.961	−	1842.95i	−0.0330455	−	0.187411i
$460$	−3010.15	−	2525.81i	−0.305106	−	0.256015i
$461$	−2705.75	+	2270.40i	−0.273361	+	0.229377i	−0.769154	−	0.639064i	$-0.779322\pi$
$461$	−2705.75	+	2270.40i	−0.273361	+	0.229377i	0.495793	+	0.868441i	$0.334878\pi$
$462$	1987.86	−	11273.7i	0.200181	−	1.13528i
$463$	−5740.86	+	9943.46i	−0.576243	+	0.998081i	0.419663	+	0.907680i	$0.362148\pi$
$463$	−5740.86	+	9943.46i	−0.576243	+	0.998081i	−0.995905	+	0.0904014i	$0.971185\pi$
$464$	−773.273	−	1339.35i	−0.0773670	−	0.134004i
$465$	−443.937	+	161.580i	−0.0442733	+	0.0161142i
$466$	−3486.31	+	1268.91i	−0.346567	+	0.126140i
$467$	−5284.08	−	9152.30i	−0.523593	−	0.906890i	−0.999623	−	0.0274611i	$-0.991258\pi$
$467$	−5284.08	−	9152.30i	−0.523593	−	0.906890i	0.476029	−	0.879429i	$-0.342076\pi$
$468$	835.931	−	1447.88i	0.0825661	−	0.143009i
$469$	−2544.62	+	14431.2i	−0.250532	+	1.42084i
$470$	−4161.73	+	3492.11i	−0.408439	+	0.342721i
$471$	−529.846	−	444.594i	−0.0518345	−	0.0434943i
$472$	−119.963	−	680.345i	−0.0116986	−	0.0663463i
$473$	7330.56	+	2668.10i	0.712599	+	0.259365i
$474$	−3041.44			−0.294721
$475$	6748.05	+	4616.95i	0.651836	+	0.445980i
$476$	9320.46			0.897484
$477$	2480.09	+	902.679i	0.238062	+	0.0866474i
$478$	1165.08	+	6607.50i	0.111484	+	0.632260i
$479$	572.113	+	480.060i	0.0545731	+	0.0457923i	0.669666	−	0.742662i	$-0.266437\pi$
$479$	572.113	+	480.060i	0.0545731	+	0.0457923i	−0.615093	+	0.788454i	$0.710882\pi$
$480$	−376.959	+	316.306i	−0.0358453	+	0.0300778i
$481$	−2793.44	+	15842.4i	−0.264802	+	1.50177i
$482$	−4113.27	+	7124.39i	−0.388702	+	0.673252i
$483$	9664.42	+	16739.3i	0.910448	+	1.57694i
$484$	−7103.44	+	2585.44i	−0.667115	+	0.242810i
$485$	5200.63	−	1892.87i	0.486904	−	0.177218i
$486$	−243.000	−	420.888i	−0.0226805	−	0.0392837i
$487$	−9963.13	+	17256.6i	−0.927048	+	1.60569i	−0.138814	+	0.990318i	$0.544329\pi$
$487$	−9963.13	+	17256.6i	−0.927048	+	1.60569i	−0.788234	+	0.615376i	$0.789004\pi$
$488$	1128.62	−	6400.72i	0.104693	−	0.593744i
$489$	5579.68	−	4681.91i	0.515996	−	0.432972i
$490$	−6182.20	−	5187.48i	−0.569966	−	0.478258i
$491$	−497.870	−	2823.56i	−0.0457609	−	0.259523i	0.953341	−	0.301896i	$-0.0976194\pi$
$491$	−497.870	−	2823.56i	−0.0457609	−	0.259523i	−0.999102	+	0.0423728i	$0.986508\pi$
$492$	3303.41	+	1202.34i	0.302701	+	0.110174i
$493$	−6699.47			−0.612026
$494$	−4480.12	−	6253.05i	−0.408037	−	0.569510i
$495$	2618.16			0.237732
$496$	461.903	+	168.119i	0.0418146	+	0.0152193i
$497$	−242.399	−	1374.71i	−0.0218774	−	0.124073i
$498$	−951.023	−	798.003i	−0.0855750	−	0.0718060i
$499$	10259.5	−	8608.70i	0.920393	−	0.772302i	−0.0536744	−	0.998558i	$-0.517093\pi$
$499$	10259.5	−	8608.70i	0.920393	−	0.772302i	0.974068	+	0.226257i	$0.0726489\pi$
$500$	796.552	−	4517.47i	0.0712458	−	0.404055i
$501$	3229.43	−	5593.53i	0.287984	−	0.498804i
$502$	−2625.92	−	4548.23i	−0.233467	−	0.404377i
$503$	−14738.3	+	5364.29i	−1.30646	+	0.475511i	−0.899094	−	0.437756i	$-0.855773\pi$
$503$	−14738.3	+	5364.29i	−1.30646	+	0.475511i	−0.407362	+	0.913267i	$0.633551\pi$
$504$	2274.56	−	827.873i	0.201026	−	0.0731674i
$505$	488.314	+	845.784i	0.0430290	+	0.0745285i
$506$	10876.5	−	18838.6i	0.955572	−	1.65510i
$507$	−20.9773	+	118.968i	−0.00183755	+	0.0104212i
$508$	−6810.12	+	5714.37i	−0.594784	+	0.499083i
$509$	9585.61	+	8043.28i	0.834724	+	0.700417i	0.956370	−	0.292157i	$-0.0943730\pi$
$509$	9585.61	+	8043.28i	0.834724	+	0.700417i	−0.121646	+	0.992573i	$0.538817\pi$
$510$	370.159	+	2099.28i	0.0321390	+	0.182270i
$511$	−20964.0	−	7630.26i	−1.81486	−	0.660554i
$512$	512.000			0.0441942
$513$	−2225.37	+	219.001i	−0.191525	+	0.0188482i
$514$	2570.74			0.220604
$515$	−6225.58	−	2265.93i	−0.532683	−	0.193881i
$516$	286.430	+	1624.43i	0.0244368	+	0.138588i
$517$	−23038.7	−	19331.8i	−1.95985	−	1.64451i
$518$	−17841.6	+	14970.9i	−1.51335	+	1.26985i
$519$	296.416	−	1681.06i	0.0250698	−	0.142178i
$520$	−952.198	+	1649.25i	−0.0803012	+	0.139086i
$521$	−7200.82	−	12472.2i	−0.605515	−	1.04878i	−0.991970	−	0.126475i	$-0.959634\pi$
$521$	−7200.82	−	12472.2i	−0.605515	−	1.04878i	0.386454	−	0.922308i	$-0.373700\pi$
$522$	−1634.94	+	595.068i	−0.137087	+	0.0498955i
$523$	−14128.6	+	5142.40i	−1.18127	+	0.429946i	−0.856649	−	0.515900i	$-0.827458\pi$
$523$	−14128.6	+	5142.40i	−1.18127	+	0.429946i	−0.324617	+	0.945846i	$0.605235\pi$
$524$	1556.14	+	2695.31i	0.129733	+	0.224705i
$525$	−4978.51	+	8623.03i	−0.413866	+	0.716838i
$526$	2159.62	−	12247.8i	0.179019	−	1.01527i
$527$	1631.16	−	1368.71i	0.134828	−	0.113134i
$528$	−2086.79	−	1751.03i	−0.172000	−	0.144325i
$529$	4265.16	+	24188.9i	0.350551	+	1.98808i
$530$	−2825.04	−	1028.23i	−0.231531	−	0.0842706i
$531$	−777.196			−0.0635168
$532$	850.461	−	11104.5i	0.0693085	−	0.904966i
$533$	13604.8			1.10561
$534$	−5958.47	−	2168.71i	−0.482862	−	0.175747i
$535$	−49.3553	−	279.908i	−0.00398844	−	0.0226196i
$536$	2671.26	+	2241.46i	0.215263	+	0.180627i
$537$	−154.608	+	129.731i	−0.0124242	+	0.0104252i
$538$	−798.932	+	4530.97i	−0.0640231	+	0.363093i
$539$	22338.0	−	38690.5i	1.78509	−	3.09187i
$540$	276.798	+	479.428i	0.0220583	+	0.0382061i
$541$	−340.993	+	124.111i	−0.0270988	+	0.00986314i	−0.355534	−	0.934663i	$-0.615701\pi$
$541$	−340.993	+	124.111i	−0.0270988	+	0.00986314i	0.328435	+	0.944527i	$0.393479\pi$
$542$	−9933.81	+	3615.61i	−0.787258	+	0.286538i
$543$	−411.174	−	712.174i	−0.0324957	−	0.0562842i
$544$	1108.96	−	1920.78i	0.0874016	−	0.151384i
$545$	−996.467	+	5651.24i	−0.0783192	+	0.444170i
$546$	7176.01	−	6021.38i	0.562463	−	0.471962i
$547$	−331.831	−	278.440i	−0.0259380	−	0.0217646i	0.629726	−	0.776817i	$-0.283167\pi$
$547$	−331.831	−	278.440i	−0.0259380	−	0.0217646i	−0.655664	+	0.755052i	$0.727611\pi$
$548$	−246.329	−	1397.00i	−0.0192019	−	0.108900i
$549$	−6870.94	−	2500.82i	−0.534143	−	0.194412i
$550$	11205.8			0.868757
$551$	−611.304	+	7981.84i	−0.0472640	+	0.617129i
$552$	4599.56			0.354656
$553$	−16013.7	−	5828.53i	−1.23142	−	0.448199i
$554$	541.347	+	3070.13i	0.0415155	+	0.235446i
$555$	−4080.52	−	3423.96i	−0.312087	−	0.261872i
$556$	−2321.22	+	1947.74i	−0.177053	+	0.148565i
$557$	292.646	−	1659.68i	0.0222618	−	0.126253i	−0.971652	−	0.236418i	$-0.924027\pi$
$557$	292.646	−	1659.68i	0.0222618	−	0.126253i	0.993913	+	0.110165i	$0.0351378\pi$
$558$	276.495	−	478.904i	0.0209767	−	0.0363326i
$559$	3191.80	+	5528.36i	0.241500	+	0.418291i
$560$	−2590.92	+	943.018i	−0.195511	+	0.0711603i
$561$	−11088.9	+	4036.03i	−0.834535	+	0.303746i
$562$	4738.90	+	8208.02i	0.355691	+	0.616075i
$563$	−5766.04	+	9987.08i	−0.431634	+	0.747612i	−0.997014	−	0.0772187i	$-0.975396\pi$
$563$	−5766.04	+	9987.08i	−0.431634	+	0.747612i	0.565380	+	0.824830i	$0.308729\pi$
$564$	1104.26	−	6262.58i	0.0824430	−	0.467557i
$565$	7541.11	−	6327.74i	0.561516	−	0.471168i
$566$	−2791.92	−	2342.70i	−0.207338	−	0.173977i
$567$	−472.862	−	2681.74i	−0.0350235	−	0.198628i
$568$	−312.146	−	113.612i	−0.0230587	−	0.00839268i
$569$	7109.93			0.523838			0.261919	−	0.965090i	$-0.415645\pi$
$569$	7109.93			0.523838			0.261919	+	0.965090i	$0.415645\pi$
$570$	2534.88	−	249.461i	0.186271	−	0.0183311i
$571$	547.355			0.0401158			0.0200579	−	0.999799i	$-0.493615\pi$
$571$	547.355			0.0401158			0.0200579	+	0.999799i	$0.493615\pi$
$572$	−9906.67	−	3605.73i	−0.724159	−	0.263572i
$573$	−1581.11	−	8966.92i	−0.115274	−	0.653749i
$574$	15088.9	+	12661.1i	1.09721	+	0.920670i
$575$	−14494.0	+	12161.9i	−1.05120	+	0.882062i
$576$	100.021	−	567.249i	0.00723534	−	0.0410337i
$577$	8128.10	−	14078.3i	0.586442	−	1.01575i	−0.408252	−	0.912869i	$-0.633861\pi$
$577$	8128.10	−	14078.3i	0.586442	−	1.01575i	0.994694	−	0.102878i	$-0.0328052\pi$
$578$	109.081	+	188.933i	0.00784976	+	0.0135962i
$579$	−4103.76	+	1493.65i	−0.294554	+	0.107209i
$580$	1862.33	−	677.834i	0.133326	−	0.0485268i
$581$	−3478.05	−	6024.15i	−0.248354	−	0.430162i
$582$	−3239.08	+	5610.26i	−0.230695	+	0.399575i
$583$	2889.97	−	16389.8i	0.205301	−	1.16432i
$584$	−4066.80	+	3412.45i	−0.288160	+	0.241795i
$585$	1641.21	+	1377.14i	0.115992	+	0.0973292i
$586$	−842.015	−	4775.31i	−0.0593572	−	0.336631i
$587$	14107.5	+	5134.70i	0.991955	+	0.361042i	0.786477	−	0.617620i	$-0.211903\pi$
$587$	14107.5	+	5134.70i	0.991955	+	0.361042i	0.205478	+	0.978662i	$0.434125\pi$
$588$	9446.51			0.662530
$589$	−1481.86	−	2068.28i	−0.103665	−	0.144689i
$590$	885.293			0.0617745
$591$	5112.85	+	1860.93i	0.355862	+	0.129523i
$592$	962.412	+	5458.11i	0.0668157	+	0.378931i
$593$	10325.6	+	8664.23i	0.715046	+	0.599995i	0.926010	−	0.377499i	$-0.123216\pi$
$593$	10325.6	+	8664.23i	0.715046	+	0.599995i	−0.210964	+	0.977494i	$0.567660\pi$
$594$	−2347.64	+	1969.90i	−0.162163	+	0.136071i
$595$	−2074.04	+	11762.4i	−0.142903	+	0.810443i
$596$	−3269.33	+	5662.65i	−0.224693	+	0.389180i
$597$	1799.69	+	3117.16i	0.123378	+	0.213697i
$598$	16727.0	−	6088.14i	1.14384	−	0.416325i
$599$	−3387.46	+	1232.93i	−0.231065	+	0.0841007i	−0.454958	−	0.890513i	$-0.650346\pi$
$599$	−3387.46	+	1232.93i	−0.231065	+	0.0841007i	0.223893	+	0.974614i	$0.428123\pi$
$600$	1184.70	+	2051.97i	0.0806089	+	0.139619i
$601$	6933.35	−	12008.9i	0.470578	−	0.815065i	−0.528856	−	0.848712i	$-0.677379\pi$
$601$	6933.35	−	12008.9i	0.470578	−	0.815065i	0.999434	+	0.0336468i	$0.0107121\pi$
$602$	−1604.90	+	9101.82i	−0.108656	+	0.616217i
$603$	3005.17	−	2521.64i	0.202952	−	0.170297i
$604$	−1991.51	−	1671.07i	−0.134161	−	0.112575i
$605$	−1682.14	−	9539.89i	−0.113039	−	0.641077i
$606$	−1074.23	−	390.987i	−0.0720092	−	0.0262092i
$607$	15438.3			1.03232			0.516162	−	0.856491i	$-0.327360\pi$
$607$	15438.3			1.03232			0.516162	+	0.856491i	$0.327360\pi$
$608$	−2187.26	−	1496.50i	−0.145896	−	0.0998209i
$609$	−9748.63			−0.648660
$610$	7826.59	+	2848.64i	0.519491	+	0.189079i
$611$	−4273.55	−	24236.5i	−0.282962	−	1.60475i
$612$	−1911.41	−	1603.87i	−0.126249	−	0.105935i
$613$	−12620.9	+	10590.2i	−0.831569	+	0.697769i	−0.955651	−	0.294503i	$-0.904846\pi$
$613$	−12620.9	+	10590.2i	−0.831569	+	0.697769i	0.124082	+	0.992272i	$0.460401\pi$
$614$	518.023	−	2937.85i	0.0340484	−	0.193098i
$615$	−2252.45	+	3901.36i	−0.147687	+	0.255802i
$616$	−7631.74	−	13218.6i	−0.499174	−	0.864595i
$617$	−17847.3	+	6495.87i	−1.16451	+	0.423848i	−0.850707	−	0.525640i	$-0.823826\pi$
$617$	−17847.3	+	6495.87i	−1.16451	+	0.423848i	−0.313805	+	0.949488i	$0.601604\pi$
$618$	7287.23	−	2652.33i	0.474329	−	0.172642i
$619$	11336.9	+	19636.1i	0.736137	+	1.27503i	0.954223	+	0.299097i	$0.0966856\pi$
$619$	11336.9	+	19636.1i	0.736137	+	1.27503i	−0.218085	+	0.975930i	$0.569981\pi$
$620$	−314.952	+	545.513i	−0.0204012	+	0.0353360i
$621$	898.543	−	5095.89i	0.0580633	−	0.329293i
$622$	−11233.2	+	9425.79i	−0.724133	+	0.607620i
$623$	−27216.4	−	22837.3i	−1.75025	−	1.46863i
$624$	−387.088	−	2195.28i	−0.0248332	−	0.140836i
$625$	−6072.62	−	2210.25i	−0.388648	−	0.141456i
$626$	−18418.4			−1.17595
$627$	3796.76	+	13579.8i	0.241831	+	0.864949i
$628$	−922.221			−0.0585997
$629$	22560.8	+	8211.46i	1.43014	+	0.520528i
$630$	538.631	+	3054.73i	0.0340628	+	0.193180i
$631$	−5669.54	−	4757.31i	−0.357688	−	0.300136i	0.446181	−	0.894943i	$-0.352784\pi$
$631$	−5669.54	−	4757.31i	−0.357688	−	0.300136i	−0.803868	+	0.594807i	$0.797228\pi$
$632$	−3106.50	+	2606.67i	−0.195522	+	0.164063i
$633$	1331.32	−	7550.31i	0.0835946	−	0.474088i
$634$	−2784.02	+	4822.07i	−0.174397	+	0.302065i
$635$	−5696.13	−	9865.99i	−0.355975	−	0.616567i
$636$	3306.79	−	1203.57i	0.206168	−	0.0750389i
$637$	34353.7	−	12503.7i	2.13681	−	0.777734i
$638$	5485.63	+	9501.39i	0.340405	+	0.589598i
$639$	−186.850	+	323.634i	−0.0115676	+	0.0200356i
$640$	−113.933	+	646.146i	−0.00703686	+	0.0399080i
$641$	21667.1	−	18180.9i	1.33510	−	1.12028i	0.352244	−	0.935908i	$-0.385419\pi$
$641$	21667.1	−	18180.9i	1.33510	−	1.12028i	0.982856	−	0.184374i	$-0.0590258\pi$
$642$	254.859	+	213.852i	0.0156674	+	0.0131465i
$643$	−505.259	−	2865.47i	−0.0309883	−	0.175743i	0.965386	−	0.260827i	$-0.0839953\pi$
$643$	−505.259	−	2865.47i	−0.0309883	−	0.175743i	−0.996374	+	0.0850839i	$0.972884\pi$
$644$	24217.6	+	8814.47i	1.48184	+	0.539346i
$645$	−2113.77			−0.129038
$646$	−10351.7	+	4964.23i	−0.630465	+	0.302345i
$647$	4939.67			0.300152			0.150076	−	0.988674i	$-0.452048\pi$
$647$	4939.67			0.300152			0.150076	+	0.988674i	$0.452048\pi$
$648$	−608.921	−	221.629i	−0.0369146	−	0.0134358i
$649$	851.025	+	4826.40i	0.0514725	+	0.291915i
$650$	7024.42	+	5894.19i	0.423878	+	0.355676i
$651$	2373.56	−	1991.65i	0.142899	−	0.119906i
$652$	1686.42	−	9564.14i	0.101296	−	0.574479i
$653$	−11069.1	+	19172.2i	−0.663348	+	1.14895i	0.316382	+	0.948632i	$0.397532\pi$
$653$	−11069.1	+	19172.2i	−0.663348	+	1.14895i	−0.979730	+	0.200321i	$0.935802\pi$
$654$	−3358.50	−	5817.09i	−0.200807	−	0.347807i
$655$	−3747.77	+	1364.08i	−0.223569	+	0.0813724i
$656$	4404.54	−	1603.12i	0.262147	−	0.0954138i
$657$	2986.21	+	5172.27i	0.177326	+	0.307138i
$658$	17815.6	−	30857.5i	1.05551	−	1.82819i
$659$	−3828.24	+	21711.1i	−0.226293	+	1.28337i	0.633904	+	0.773412i	$0.281451\pi$
$659$	−3828.24	+	21711.1i	−0.226293	+	1.28337i	−0.860197	+	0.509961i	$0.829660\pi$
$660$	2674.16	−	2243.89i	0.157715	−	0.132338i
$661$	−16651.7	−	13972.4i	−0.979840	−	0.822184i	0.00422511	−	0.999991i	$-0.498655\pi$
$661$	−16651.7	−	13972.4i	−0.979840	−	0.822184i	−0.984065	+	0.177808i	$0.943100\pi$
$662$	3656.50	+	20737.0i	0.214674	+	1.21747i
$663$	−9074.09	−	3302.70i	−0.531536	−	0.193463i
$664$	−1655.30			−0.0967439
$665$	13824.7	+	3544.32i	0.806163	+	0.206681i
$666$	6235.10			0.362771
$667$	−17407.4	−	6335.77i	−1.01052	−	0.367799i
$668$	−1495.42	−	8480.98i	−0.0866164	−	0.491226i
$669$	−6008.15	−	5041.43i	−0.347217	−	0.291350i
$670$	−3423.15	+	2872.36i	−0.197385	+	0.165625i
$671$	−8006.48	+	45407.0i	−0.460636	+	2.61240i
$672$	1613.69	−	2795.00i	0.0926332	−	0.160445i
$673$	2358.79	+	4085.54i	0.135103	+	0.234006i	0.925637	−	0.378413i	$-0.123530\pi$
$673$	2358.79	+	4085.54i	0.135103	+	0.234006i	−0.790534	+	0.612419i	$0.790197\pi$
$674$	−8087.46	+	2943.59i	−0.462192	+	0.168224i
$675$	2504.83	−	911.683i	0.142831	−	0.0519862i
$676$	80.5358	+	139.492i	0.00458214	+	0.00793651i
$677$	−3999.83	+	6927.91i	−0.227069	+	0.393296i	−0.956938	−	0.290291i	$-0.906248\pi$
$677$	−3999.83	+	6927.91i	−0.227069	+	0.393296i	0.729869	+	0.683587i	$0.239581\pi$
$678$	−2000.94	+	11347.9i	−0.113342	+	0.642792i
$679$	−27805.7	+	23331.8i	−1.57156	+	1.31869i
$680$	2177.26	+	1826.94i	0.122786	+	0.103029i
$681$	1201.63	+	6814.80i	0.0676163	+	0.383471i
$682$	−3276.76	−	1192.64i	−0.183979	−	0.0669629i
$683$	22257.4			1.24693			0.623466	−	0.781851i	$-0.285724\pi$
$683$	22257.4			1.24693			0.623466	+	0.781851i	$0.285724\pi$
$684$	−2085.28	+	2130.94i	−0.116568	+	0.119120i
$685$	1817.83			0.101395
$686$	28066.1	+	10215.2i	1.56206	+	0.568542i
$687$	−750.920	−	4258.68i	−0.0417022	−	0.236505i
$688$	1684.77	+	1413.69i	0.0933595	+	0.0783379i
$689$	10432.6	−	8753.96i	0.576849	−	0.484034i
$690$	−1023.52	+	5804.66i	−0.0564705	+	0.320260i
$691$	−9459.59	+	16384.5i	−0.520781	+	0.902020i	0.478927	+	0.877855i	$0.341026\pi$
$691$	−9459.59	+	16384.5i	−0.520781	+	0.902020i	−0.999708	+	0.0241647i	$0.992307\pi$
$692$	−1137.99	−	1971.06i	−0.0625145	−	0.108278i
$693$	−16135.8	+	5872.97i	−0.884488	+	0.321927i
$694$	−1852.62	+	674.300i	−0.101332	+	0.0368820i
$695$	−1941.52	−	3362.81i	−0.105965	−	0.183538i
$696$	−1159.91	+	2009.02i	−0.0631699	+	0.109413i
$697$	3525.84	−	19996.1i	0.191608	−	1.08666i
$698$	−14899.8	+	12502.4i	−0.807973	+	0.677970i
$699$	4263.10	+	3577.17i	0.230680	+	0.193564i
$700$	2305.36	+	13074.3i	0.124478	+	0.705947i
$701$	−17891.6	−	6512.00i	−0.963988	−	0.350863i	−0.188393	−	0.982094i	$-0.560328\pi$
$701$	−17891.6	−	6512.00i	−0.963988	−	0.350863i	−0.775595	+	0.631231i	$0.782550\pi$
$702$	−2507.79			−0.134830
$703$	11841.8	−	26130.0i	0.635311	−	1.40186i
$704$	−3632.15			−0.194449
$705$	7657.67	+	2787.17i	0.409085	+	0.148895i
$706$	927.090	+	5257.79i	0.0494214	+	0.280283i
$707$	−4906.74	−	4117.25i	−0.261014	−	0.219017i
$708$	−793.822	+	666.096i	−0.0421379	+	0.0353579i
$709$	2510.36	−	14237.0i	0.132974	−	0.754134i	−0.843275	−	0.537483i	$-0.819375\pi$
$709$	2510.36	−	14237.0i	0.132974	−	0.754134i	0.976249	−	0.216651i	$-0.0695135\pi$
$710$	212.839	−	368.647i	0.0112503	−	0.0194860i
$711$	2281.08	+	3950.94i	0.120319	+	0.208399i
$712$	−7944.63	+	2891.61i	−0.418171	+	0.152202i
$713$	5532.68	−	2013.73i	0.290604	−	0.105771i
$714$	−6990.34	−	12107.6i	−0.366396	−	0.634617i
$715$	6754.93	−	11699.9i	0.353315	−	0.611959i
$716$	−46.7289	+	265.013i	−0.00243903	+	0.0138324i
$717$	7709.59	−	6469.11i	0.401562	−	0.336950i
$718$	10077.9	+	8456.34i	0.523820	+	0.439537i
$719$	111.289	+	631.152i	0.00577244	+	0.0327371i	0.987558	−	0.157256i	$-0.0502647\pi$
$719$	111.289	+	631.152i	0.00577244	+	0.0327371i	−0.981785	+	0.189993i	$0.939154\pi$
$720$	693.613	+	252.455i	0.0359020	+	0.0130673i
$721$	43451.5			2.24441
$722$	4969.89	+	12786.1i	0.256178	+	0.659070i
$723$	12339.8			0.634748
$724$	−1030.34	−	375.013i	−0.0528899	−	0.0192503i
$725$	−1657.07	−	9397.72i	−0.0848857	−	0.481411i
$726$	8686.17	+	7288.56i	0.444041	+	0.372595i
$727$	12122.0	−	10171.6i	0.618404	−	0.518902i	−0.278898	−	0.960321i	$-0.589969\pi$
$727$	12122.0	−	10171.6i	0.618404	−	0.518902i	0.897301	+	0.441419i	$0.145525\pi$
$728$	2168.89	−	12300.4i	0.110418	−	0.626213i
$729$	−364.500	+	631.333i	−0.0185185	+	0.0320750i
$730$	−3401.55	−	5891.66i	−0.172462	−	0.298713i
$731$	8952.64	−	3258.49i	0.452976	−	0.164870i
$732$	−9161.25	+	3334.42i	−0.462581	+	0.168366i
$733$	−9198.96	−	15933.1i	−0.463535	−	0.802867i	0.535599	−	0.844473i	$-0.320086\pi$
$733$	−9198.96	−	15933.1i	−0.463535	−	0.802867i	−0.999134	+	0.0416057i	$0.986753\pi$
$734$	−6386.56	+	11061.8i	−0.321161	+	0.556267i
$735$	−2102.09	+	11921.5i	−0.105492	+	0.598275i
$736$	4697.96	−	3942.05i	0.235284	−	0.197427i
$737$	−18950.1	−	15901.0i	−0.947130	−	0.794737i
$738$	−915.668	−	5193.01i	−0.0456723	−	0.259021i
$739$	5783.65	+	2105.08i	0.287896	+	0.104785i	0.481931	−	0.876209i	$-0.339935\pi$
$739$	5783.65	+	2105.08i	0.287896	+	0.104785i	−0.194036	+	0.980994i	$0.562158\pi$
$740$	−7102.31			−0.352819
$741$	−4762.86	+	10509.6i	−0.236124	+	0.521027i
$742$	19717.3			0.975535
$743$	23894.2	+	8696.78i	1.17980	+	0.429413i	0.856132	−	0.516757i	$-0.172861\pi$
$743$	23894.2	+	8696.78i	1.17980	+	0.429413i	0.323671	+	0.946170i	$0.395083\pi$
$744$	−128.034	−	726.119i	−0.00630910	−	0.0357807i
$745$	−6418.78	−	5385.99i	−0.315659	−	0.264869i
$746$	4342.86	−	3644.09i	0.213141	−	0.178847i
$747$	−323.369	+	1833.92i	−0.0158386	+	0.0898254i
$748$	−7867.05	+	13626.1i	−0.384556	+	0.666070i
$749$	932.061	+	1614.38i	0.0454697	+	0.0787557i
$750$	−6465.78	+	2353.35i	−0.314796	+	0.114576i
$751$	26770.6	−	9743.70i	1.30076	−	0.473439i	0.403518	−	0.914972i	$-0.367787\pi$
$751$	26770.6	−	9743.70i	1.30076	−	0.473439i	0.897245	+	0.441533i	$0.145565\pi$
$752$	−4239.46	−	7342.97i	−0.205582	−	0.356078i
$753$	−3938.88	+	6822.34i	−0.190625	+	0.330172i
$754$	−1558.98	+	8841.42i	−0.0752981	+	0.427037i
$755$	2552.06	−	2141.43i	0.123019	−	0.103225i
$756$	−2781.36	−	2333.84i	−0.133806	−	0.112276i
$757$	2878.50	+	16324.8i	0.138204	+	0.783796i	0.972575	+	0.232591i	$0.0747205\pi$
$757$	2878.50	+	16324.8i	0.138204	+	0.783796i	−0.834370	+	0.551205i	$0.814168\pi$
$758$	−1896.12	−	690.130i	−0.0908575	−	0.0330694i
$759$	−32629.5			−1.56044
$760$	2375.31	−	2427.32i	0.113370	−	0.115853i
$761$	−8226.43			−0.391863			−0.195932	−	0.980618i	$-0.562773\pi$
$761$	−8226.43			−0.391863			−0.195932	+	0.980618i	$0.562773\pi$
$762$	12530.8	+	4560.83i	0.595725	+	0.216826i
$763$	−6535.42	−	37064.2i	−0.310089	−	1.75860i
$764$	−9300.03	−	7803.65i	−0.440397	−	0.369537i
$765$	2449.42	−	2055.31i	0.115763	−	0.0971370i
$766$	2512.43	−	14248.7i	0.118509	−	0.672098i
$767$	−2005.19	+	3473.10i	−0.0943980	+	0.163502i
$768$	−384.000	−	665.108i	−0.0180422	−	0.0312500i
$769$	19333.0	−	7036.62i	0.906586	−	0.329970i	0.153697	−	0.988118i	$-0.450882\pi$
$769$	19333.0	−	7036.62i	0.906586	−	0.329970i	0.752889	+	0.658148i	$0.228660\pi$
$770$	18380.1	−	6689.81i	0.860225	−	0.313096i
$771$	−1928.06	−	3339.49i	−0.0900614	−	0.155991i
$772$	−2911.42	+	5042.73i	−0.135731	+	0.235093i
$773$	−4482.05	+	25419.0i	−0.208549	+	1.18274i	0.683208	+	0.730224i	$0.260584\pi$
$773$	−4482.05	+	25419.0i	−0.208549	+	1.18274i	−0.891757	+	0.452515i	$0.850527\pi$
$774$	1895.37	−	1590.40i	0.0880202	−	0.0738577i
$775$	2323.42	+	1949.58i	0.107690	+	0.0903626i
$776$	1499.90	+	8506.33i	0.0693855	+	0.393505i
$777$	32829.0	+	11948.8i	1.51574	+	0.551686i
$778$	9160.18			0.422119
$779$	−23501.9	−	6025.31i	−1.08093	−	0.277124i
$780$	2856.59			0.131131
$781$	2214.37	+	805.967i	0.101455	+	0.0369267i
$782$	−4613.21	−	26162.8i	−0.210957	−	1.19639i
$783$	1999.22	+	1677.54i	0.0912468	+	0.0765652i
$784$	9648.60	−	8096.13i	0.439532	−	0.368811i
$785$	205.217	−	1163.85i	0.00933060	−	0.0529165i
$786$	2334.21	−	4042.97i	0.105927	−	0.183471i
$787$	12343.4	+	21379.4i	0.559079	+	0.968353i	0.997574	+	0.0696195i	$0.0221785\pi$
$787$	12343.4	+	21379.4i	0.559079	+	0.968353i	−0.438495	+	0.898734i	$0.644488\pi$
$788$	6817.13	−	2481.23i	0.308186	−	0.112170i
$789$	−17530.1	+	6380.43i	−0.790986	+	0.287895i
$790$	−2598.34	−	4500.46i	−0.117019	−	0.202683i
$791$	−32282.1	+	55914.2i	−1.45110	+	2.51338i
$792$	−709.556	+	4024.09i	−0.0318346	+	0.180543i
$793$	−28902.8	+	24252.3i	−1.29428	+	1.08603i
$794$	−5636.71	−	4729.76i	−0.251939	−	0.211402i
$795$	783.068	+	4441.00i	0.0349340	+	0.198121i
$796$	4509.76	+	1641.42i	0.200809	+	0.0730885i
$797$	−13149.0			−0.584395			−0.292198	−	0.956358i	$-0.594386\pi$
$797$	−13149.0			−0.584395			−0.292198	+	0.956358i	$0.594386\pi$
$798$	−15063.0	+	7223.61i	−0.668203	+	0.320442i
$799$	−36729.8			−1.62629
$800$	2968.69	+	1080.51i	0.131199	+	0.0477524i
$801$	1651.62	+	9366.81i	0.0728554	+	0.413183i
$802$	−13168.6	−	11049.8i	−0.579801	−	0.486511i
$803$	28850.0	−	24208.1i	1.26786	−	1.06386i
$804$	908.290	−	5151.17i	0.0398419	−	0.225955i
$805$	−16512.9	+	28601.2i	−0.722985	+	1.25225i
$806$	−1426.73	−	2471.18i	−0.0623506	−	0.107994i
$807$	6485.10	−	2360.38i	0.282883	−	0.102961i
$808$	−1432.31	+	521.316i	−0.0623618	+	0.0226978i
$809$	−6755.83	−	11701.4i	−0.293600	−	0.508530i	0.681058	−	0.732229i	$-0.261520\pi$
$809$	−6755.83	−	11701.4i	−0.293600	−	0.508530i	−0.974658	+	0.223699i	$0.928187\pi$
$810$	415.197	−	719.142i	0.0180105	−	0.0311951i
$811$	320.891	−	1819.86i	0.0138940	−	0.0787966i	−0.977072	−	0.212907i	$-0.931707\pi$
$811$	320.891	−	1819.86i	0.0138940	−	0.0787966i	0.990966	+	0.134111i	$0.0428178\pi$
$812$	−9957.17	+	8355.06i	−0.430330	+	0.361090i
$813$	12147.2	+	10192.7i	0.524010	+	0.439696i
$814$	−6827.40	−	38720.1i	−0.293980	−	1.66725i
$815$	11694.7	+	4256.52i	0.502635	+	0.182944i
$816$	−3326.89			−0.142726
$817$	−3065.32	−	10963.6i	−0.131263	−	0.469484i
$818$	16253.9			0.694751
$819$	−13204.0	−	4805.87i	−0.563352	−	0.205043i
$820$	1043.02	+	5915.28i	0.0444195	+	0.251915i
$821$	−19207.0	−	16116.6i	−0.816481	−	0.685109i	0.135664	−	0.990755i	$-0.456683\pi$
$821$	−19207.0	−	16116.6i	−0.816481	−	0.685109i	−0.952145	+	0.305646i	$0.901128\pi$
$822$	−1630.01	+	1367.74i	−0.0691644	+	0.0580359i
$823$	−1952.42	+	11072.7i	−0.0826937	+	0.468979i	0.915137	+	0.403144i	$0.132082\pi$
$823$	−1952.42	+	11072.7i	−0.0826937	+	0.468979i	−0.997830	+	0.0658358i	$0.979029\pi$
$824$	5169.94	−	8954.59i	0.218572	−	0.378578i
$825$	−8404.34	−	14556.7i	−0.354669	−	0.614304i
$826$	−5456.11	+	1985.86i	−0.229833	+	0.0836525i
$827$	13503.5	−	4914.86i	0.567789	−	0.206658i	−0.0421437	−	0.999112i	$-0.513419\pi$
$827$	13503.5	−	4914.86i	0.567789	−	0.206658i	0.609933	+	0.792453i	$0.291197\pi$
$828$	−3449.67	−	5975.00i	−0.144788	−	0.250780i
$829$	17343.7	−	30040.2i	0.726624	−	1.25855i	−0.231678	−	0.972793i	$-0.574421\pi$
$829$	17343.7	−	30040.2i	0.726624	−	1.25855i	0.958302	−	0.285758i	$-0.0922453\pi$
$830$	368.345	−	2088.99i	0.0154042	−	0.0873613i
$831$	3582.20	−	3005.83i	0.149537	−	0.125476i
$832$	−2276.84	−	1910.49i	−0.0948740	−	0.0796087i
$833$	−9474.54	−	53732.8i	−0.394086	−	2.23497i
$834$	4271.10	+	1554.55i	0.177333	+	0.0645441i
$835$	11035.8			0.457376
$836$	15516.5	+	10616.2i	0.641926	+	0.439199i
$837$	−829.486			−0.0342547
$838$	2589.87	+	942.636i	0.106761	+	0.0388578i
$839$	1424.95	+	8081.32i	0.0586352	+	0.332537i	0.999988	−	0.00488714i	$-0.00155563\pi$
$839$	1424.95	+	8081.32i	0.0586352	+	0.332537i	−0.941353	+	0.337424i	$0.890445\pi$
$840$	3168.21	+	2658.44i	0.130135	+	0.109196i
$841$	−11525.9	+	9671.40i	−0.472587	+	0.396547i
$842$	5356.40	−	30377.7i	0.219233	−	1.24333i
$843$	7108.35	−	12312.0i	0.290421	−	0.503023i
$844$	−5111.19	−	8852.84i	−0.208453	−	0.361052i
$845$	−193.961	+	70.5959i	−0.00789639	+	0.00287405i
$846$	−8963.53	+	3262.46i	−0.364270	+	0.132584i
$847$	31766.7	+	55021.6i	1.28869	+	2.23207i
$848$	2346.01	−	4063.40i	0.0950026	−	0.164549i
$849$	−949.315	+	5383.83i	−0.0383751	+	0.217636i
$850$	10483.6	−	8796.78i	0.423040	−	0.354973i
$851$	50854.6	+	42672.0i	2.04850	+	1.71889i
$852$	86.5233	+	490.698i	0.00347915	+	0.0197313i
$853$	−43458.1	−	15817.5i	−1.74441	−	0.634912i	−0.744925	−	0.667148i	$-0.767515\pi$
$853$	−43458.1	−	15817.5i	−1.74441	−	0.634912i	−0.999480	+	0.0322364i	$0.989737\pi$
$854$	−54625.7			−2.18882
$855$	−2225.22	−	3105.81i	−0.0890069	−	0.124230i
$856$	443.593			0.0177123
$857$	−41453.2	−	15087.7i	−1.65229	−	0.601385i	−0.663169	−	0.748470i	$-0.730789\pi$
$857$	−41453.2	−	15087.7i	−1.65229	−	0.601385i	−0.989124	+	0.147084i	$0.953011\pi$
$858$	2746.02	+	15573.4i	0.109263	+	0.619661i
$859$	−10288.3	−	8632.88i	−0.408651	−	0.342899i	0.415175	−	0.909741i	$-0.363720\pi$
$859$	−10288.3	−	8632.88i	−0.408651	−	0.342899i	−0.823826	+	0.566843i	$0.808165\pi$
$860$	−2158.99	+	1811.61i	−0.0856057	+	0.0718317i
$861$	5130.57	−	29096.9i	0.203077	−	1.15171i
$862$	−12625.8	+	21868.5i	−0.498882	+	0.864089i
$863$	20855.8	+	36123.3i	0.822641	+	1.42486i	0.903709	+	0.428148i	$0.140834\pi$
$863$	20855.8	+	36123.3i	0.822641	+	1.42486i	−0.0810673	+	0.996709i	$0.525833\pi$
$864$	−811.894	+	295.505i	−0.0319690	+	0.0116358i
$865$	2740.72	−	997.540i	0.107731	−	0.0392108i
$866$	−5339.70	−	9248.63i	−0.209527	−	0.362911i
$867$	163.621	−	283.400i	0.00640930	−	0.0111012i
$868$	717.389	−	4068.52i	0.0280527	−	0.159095i
$869$	22037.7	−	18491.8i	0.860273	−	0.721854i
$870$	−2277.28	−	1910.87i	−0.0887438	−	0.0744649i
$871$	−3515.13	−	19935.3i	−0.136746	−	0.775524i
$872$	−8415.88	−	3063.13i	−0.326832	−	0.118957i
$873$	9717.25			0.376723
$874$	−31591.7	+	3108.97i	−1.22266	+	0.120323i
$875$	−38553.5			−1.48954
$876$	7482.99	+	2723.59i	0.288615	+	0.105047i
$877$	−7113.37	−	40341.9i	−0.273890	−	1.55331i	−0.742466	−	0.669884i	$-0.766344\pi$
$877$	−7113.37	−	40341.9i	−0.273890	−	1.55331i	0.468576	−	0.883423i	$-0.344767\pi$
$878$	−10835.8	−	9092.28i	−0.416502	−	0.349487i
$879$	−5571.79	+	4675.29i	−0.213802	+	0.179401i
$880$	808.245	−	4583.79i	0.0309613	−	0.175590i
$881$	1354.47	−	2346.01i	0.0517971	−	0.0897153i	−0.838964	−	0.544186i	$-0.816838\pi$
$881$	1354.47	−	2346.01i	0.0517971	−	0.0897153i	0.890761	+	0.454471i	$0.150172\pi$
$882$	−7084.88	−	12271.4i	−0.270477	−	0.468479i
$883$	−16488.8	+	6001.42i	−0.628415	+	0.228725i	−0.636541	−	0.771242i	$-0.719636\pi$
$883$	−16488.8	+	6001.42i	−0.628415	+	0.228725i	0.00812602	+	0.999967i	$0.497413\pi$
$884$	−12098.8	+	4403.60i	−0.460324	+	0.167544i
$885$	−663.970	−	1150.03i	−0.0252193	−	0.0436811i
$886$	−13112.0	+	22710.7i	−0.497187	+	0.861153i
$887$	6501.36	−	36871.0i	0.246104	−	1.39573i	−0.571811	−	0.820386i	$-0.693759\pi$
$887$	6501.36	−	36871.0i	0.246104	−	1.39573i	0.817915	−	0.575340i	$-0.195130\pi$
$888$	6368.48	−	5343.79i	0.240667	−	0.201944i
$889$	57236.7	+	48027.3i	2.15934	+	1.81190i
$890$	−1881.34	−	10669.6i	−0.0708569	−	0.401849i
$891$	4319.71	+	1572.25i	0.162420	+	0.0591159i
$892$	−10457.4			−0.392535
$893$	−3351.47	+	43760.4i	−0.125591	+	1.63985i
$894$	9808.00			0.366922
$895$	−324.049	−	117.944i	−0.0121025	−	0.00440496i
$896$	−747.239	−	4237.80i	−0.0278611	−	0.158008i
$897$	−20454.0	−	17162.9i	−0.761359	−	0.638856i
$898$	−7890.81	+	6621.18i	−0.293229	+	0.246049i
$899$	−515.654	+	2924.42i	−0.0191302	+	0.108493i
$900$	1777.06	−	3077.95i	0.0658169	−	0.113998i
$901$	−10162.6	−	17602.2i	−0.375768	−	0.650849i
$902$	−31246.0	+	11372.6i	−1.15341	+	0.419808i
$903$	13027.3	−	4741.54i	0.480089	−	0.174738i
$904$	7681.96	+	13305.5i	0.282631	+	0.489531i
$905$	702.544	−	1216.84i	0.0258048	−	0.0446952i
$906$	−677.157	+	3840.35i	−0.0248312	+	0.140825i
$907$	−31918.9	+	26783.1i	−1.16852	+	0.980507i	−0.999987	−	0.00518845i	$-0.998348\pi$
$907$	−31918.9	+	26783.1i	−1.16852	+	0.980507i	−0.168536	+	0.985695i	$0.553904\pi$
$908$	7067.96	+	5930.73i	0.258324	+	0.216760i
$909$	297.764	+	1688.70i	0.0108649	+	0.0616180i
$910$	15040.5	+	5474.29i	0.547899	+	0.199419i
$911$	38037.5			1.38336			0.691678	−	0.722206i	$-0.256872\pi$
$911$	38037.5			1.38336			0.691678	+	0.722206i	$0.256872\pi$
$912$	−303.568	+	3963.71i	−0.0110221	+	0.143916i
$913$	11742.8			0.425661
$914$	20267.4	+	7376.72i	0.733463	+	0.266959i
$915$	−2169.44	−	12303.5i	−0.0783820	−	0.444526i
$916$	−4416.89	−	3706.21i	−0.159321	−	0.133686i
$917$	20037.9	−	16813.8i	0.721602	−	0.605496i
$918$	−649.923	+	3685.90i	−0.0233667	+	0.132519i
$919$	−23758.5	+	41151.0i	−0.852798	+	1.47709i	0.0258744	+	0.999665i	$0.491763\pi$
$919$	−23758.5	+	41151.0i	−0.852798	+	1.47709i	−0.878673	+	0.477425i	$0.841570\pi$
$920$	3929.47	+	6806.04i	0.140816	+	0.243901i
$921$	−4204.90	+	1530.46i	−0.150441	+	0.0547560i
$922$	6638.19	−	2416.10i	0.237112	−	0.0863017i
$923$	964.161	+	1669.98i	0.0343832	+	0.0595535i
$924$	−11447.6	+	19827.8i	−0.407574	+	0.705939i
$925$	−5938.40	+	33678.3i	−0.211085	+	1.19712i
$926$	17591.0	−	14760.6i	0.624273	−	0.523827i
$927$	−8910.90	−	7477.13i	−0.315720	−	0.264921i
$928$	537.110	+	3046.10i	0.0189994	+	0.107751i
$929$	−50405.1	−	18346.0i	−1.78013	−	0.647913i	−0.999744	−	0.0226108i	$-0.992802\pi$
$929$	−50405.1	−	18346.0i	−1.78013	−	0.647913i	−0.780383	−	0.625302i	$-0.784976\pi$
$930$	944.855			0.0333151
$931$	−64882.5	+	6385.16i	−2.28404	+	0.224775i
$932$	7420.11			0.260787
$933$	20669.4	+	7523.03i	0.725278	+	0.263980i
$934$	3670.28	+	20815.2i	0.128582	+	0.729223i
$935$	−15445.6	−	12960.4i	−0.540241	−	0.453316i
$936$	−2561.44	+	2149.31i	−0.0894480	+	0.0750558i
$937$	562.487	−	3190.02i	0.0196112	−	0.111220i	−0.973431	−	0.228981i	$-0.926461\pi$
$937$	562.487	−	3190.02i	0.0196112	−	0.111220i	0.993042	+	0.117761i	$0.0375716\pi$
$938$	14653.9	−	25381.2i	0.510091	−	0.883504i
$939$	13813.8	+	23926.2i	0.480081	+	0.831524i
$940$	10210.2	−	3716.22i	0.354278	−	0.128947i
$941$	37002.9	−	13468.0i	1.28189	−	0.466571i	0.390835	−	0.920461i	$-0.372186\pi$
$941$	37002.9	−	13468.0i	1.28189	−	0.466571i	0.891058	+	0.453890i	$0.149964\pi$
$942$	691.665	+	1198.00i	0.0239232	+	0.0414362i
$943$	28071.8	−	48621.8i	0.969399	−	1.67905i
$944$	−239.926	+	1360.69i	−0.00827218	+	0.0469139i
$945$	3564.23	−	2990.75i	0.122693	−	0.102951i
$946$	−11951.9	−	10028.8i	−0.410770	−	0.344677i
$947$	6219.42	+	35272.1i	0.213415	+	1.21034i	0.883636	+	0.468175i	$0.155088\pi$
$947$	6219.42	+	35272.1i	0.213415	+	1.21034i	−0.670220	+	0.742162i	$0.733800\pi$
$948$	5716.03	+	2080.47i	0.195831	+	0.0712768i
$949$	30818.1			1.05416
$950$	−9524.01	−	13293.0i	−0.325263	−	0.453980i
$951$	8352.07			0.284789
$952$	−17516.7	−	6375.57i	−0.596345	−	0.217052i
$953$	806.431	+	4573.50i	0.0274112	+	0.155457i	0.995441	−	0.0953782i	$-0.0304060\pi$
$953$	806.431	+	4573.50i	0.0274112	+	0.155457i	−0.968030	+	0.250835i	$0.919295\pi$
$954$	−4043.58	−	3392.96i	−0.137228	−	0.115148i
$955$	11917.7	−	10000.2i	0.403820	−	0.338846i
$956$	2330.16	−	13215.0i	0.0788314	−	0.447075i
$957$	8228.45	−	14252.1i	0.277939	−	0.481405i
$958$	−746.841	−	1293.57i	−0.0251872	−	0.0436255i
$959$	−11203.4	+	4077.71i	−0.377244	+	0.137306i
$960$	924.817	−	336.606i	0.0310920	−	0.0113166i
$961$	14423.6	+	24982.4i	0.484159	+	0.838588i
$962$	16086.8	−	27863.1i	0.539146	−	0.933828i
$963$	86.6578	−	491.461i	0.00289980	−	0.0164456i
$964$	12603.8	−	10575.8i	0.421100	−	0.353345i
$965$	−5716.08	−	4796.36i	−0.190681	−	0.160000i
$966$	−6712.83	−	38070.4i	−0.223584	−	1.26801i
$967$	10767.7	+	3919.14i	0.358084	+	0.130332i	0.514797	−	0.857312i	$-0.327867\pi$
$967$	10767.7	+	3919.14i	0.358084	+	0.130332i	−0.156713	+	0.987644i	$0.550090\pi$
$968$	15118.7			0.501996
$969$	14212.5	+	9724.03i	0.471176	+	0.322374i
$970$	−11068.8			−0.366389
$971$	−34110.2	−	12415.1i	−1.12734	−	0.410319i	−0.290015	−	0.957022i	$-0.593660\pi$
$971$	−34110.2	−	12415.1i	−1.12734	−	0.410319i	−0.837326	+	0.546703i	$0.815883\pi$
$972$	168.786	+	957.233i	0.00556977	+	0.0315877i
$973$	19509.0	+	16370.0i	0.642786	+	0.539362i
$974$	30528.8	−	25616.7i	1.00432	−	0.842723i
$975$	2388.46	−	13545.6i	0.0784533	−	0.444931i
$976$	−6499.46	+	11257.4i	−0.213159	+	0.369202i
$977$	−1914.80	−	3316.52i	−0.0627019	−	0.108603i	0.832970	−	0.553318i	$-0.186638\pi$
$977$	−1914.80	−	3316.52i	−0.0627019	−	0.108603i	−0.895672	+	0.444715i	$0.853305\pi$
$978$	−13689.0	+	4982.39i	−0.447572	+	0.162903i
$979$	56359.5	−	20513.2i	1.83990	−	0.669668i
$980$	8070.29	+	13978.2i	0.263057	+	0.455628i
$981$	−5037.74	+	8725.63i	−0.163958	+	0.283984i
$982$	−995.741	+	5647.13i	−0.0323578	+	0.183510i
$983$	17264.1	−	14486.3i	0.560164	−	0.470033i	−0.318202	−	0.948023i	$-0.603079\pi$
$983$	17264.1	−	14486.3i	0.560164	−	0.470033i	0.878365	+	0.477990i	$0.158634\pi$
$984$	−5385.92	−	4519.33i	−0.174489	−	0.146414i
$985$	1614.34	+	9155.38i	0.0522205	+	0.296157i
$986$	12590.9	+	4582.71i	0.406669	+	0.148015i
$987$	−53446.8			−1.72364
$988$	4142.53	+	14816.5i	0.133392	+	0.477100i
$989$	26343.4			0.846989
$990$	−4920.52	−	1790.92i	−0.157964	−	0.0574942i
$991$	4423.48	+	25086.8i	0.141793	+	0.804146i	0.969887	+	0.243556i	$0.0783141\pi$
$991$	4423.48	+	25086.8i	0.141793	+	0.804146i	−0.828094	+	0.560589i	$0.810575\pi$
$992$	−753.094	−	631.921i	−0.0241036	−	0.0202253i
$993$	24195.8	−	20302.7i	0.773245	−	0.648829i
$994$	−484.798	+	2749.43i	−0.0154697	+	0.0877329i
$995$	−3075.01	+	5326.07i	−0.0979742	+	0.169696i
$996$	1241.47	+	2150.29i	0.0394955	+	0.0684083i
$997$	44569.4	−	16221.9i	1.41577	−	0.515300i	0.482955	−	0.875645i	$-0.339563\pi$
$997$	44569.4	−	16221.9i	1.41577	−	0.515300i	0.932819	+	0.360346i	$0.117341\pi$
$998$	−25170.2	+	9161.19i	−0.798344	+	0.290574i
$999$	−4676.32	−	8099.63i	−0.148100	−	0.256518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.i.d.61.1	yes	18
19.5	even	9	inner	114.4.i.d.43.1	✓	18
19.9	even	9		2166.4.a.bm.1.3		9
19.10	odd	18		2166.4.a.bj.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.d.43.1	✓	18	19.5	even	9	inner
114.4.i.d.61.1	yes	18	1.1	even	1	trivial
2166.4.a.bj.1.3		9	19.10	odd	18
2166.4.a.bm.1.3		9	19.9	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87939 - 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-3.92666 + 3.29486i) q^{5} +(1.04189 - 5.90885i) q^{6} +(16.8093 - 29.1145i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +O(q^{10})\)	\(q+(-1.87939 - 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-3.92666 + 3.29486i) q^{5} +(1.04189 - 5.90885i) q^{6} +(16.8093 - 29.1145i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +(9.63351 - 3.50631i) q^{10} +(28.3762 + 49.1490i) q^{11} +(-6.00000 + 10.3923i) q^{12} +(-8.06433 + 45.7351i) q^{13} +(-51.5067 + 43.2192i) q^{14} +(-11.7800 - 9.88457i) q^{15} +(2.77837 + 15.7569i) q^{16} +(65.1304 + 23.7055i) q^{17} +18.0000 q^{18} +(34.1860 - 75.4342i) q^{19} -20.5035 q^{20} +(94.7734 + 34.4947i) q^{21} +(-19.7099 - 111.780i) q^{22} +(146.811 + 123.189i) q^{23} +(18.3851 - 15.4269i) q^{24} +(-17.1435 + 97.2254i) q^{25} +(46.4406 - 80.4375i) q^{26} +(-13.5000 - 23.3827i) q^{27} +(126.365 - 45.9929i) q^{28} +(-90.8298 + 33.0594i) q^{29} +(15.3777 + 26.6349i) q^{30} +(15.3608 - 26.6058i) q^{31} +(5.55674 - 31.5138i) q^{32} +(-130.425 + 109.439i) q^{33} +(-106.190 - 89.1036i) q^{34} +(29.9239 + 169.707i) q^{35} +(-33.8289 - 12.3127i) q^{36} +346.394 q^{37} +(-115.849 + 118.385i) q^{38} -139.322 q^{39} +(38.5341 + 14.0253i) q^{40} +(-50.8704 - 288.500i) q^{41} +(-154.520 - 129.658i) q^{42} +(105.298 - 88.3557i) q^{43} +(-39.4198 + 223.561i) q^{44} +(23.0665 - 39.9523i) q^{45} +(-191.648 - 331.945i) q^{46} +(-497.974 + 181.248i) q^{47} +(-45.1052 + 16.4170i) q^{48} +(-393.605 - 681.743i) q^{49} +(98.7253 - 170.997i) q^{50} +(-36.1068 + 204.772i) q^{51} +(-142.302 + 119.406i) q^{52} +(-224.643 - 188.498i) q^{53} +(9.37700 + 53.1796i) q^{54} +(-273.362 - 99.4958i) q^{55} -268.949 q^{56} +(240.674 + 61.7029i) q^{57} +193.318 q^{58} +(81.1472 + 29.5352i) q^{59} +(-10.6812 - 60.5761i) q^{60} +(622.360 + 522.222i) q^{61} +(-47.0684 + 39.4950i) q^{62} +(-52.5403 + 297.971i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-119.025 - 206.157i) q^{65} +(319.979 - 116.463i) q^{66} +(-409.599 + 149.082i) q^{67} +(138.621 + 240.098i) q^{68} +(-287.472 + 497.917i) q^{69} +(59.8479 - 339.414i) q^{70} +(31.8079 - 26.6900i) q^{71} +(55.1552 + 46.2807i) q^{72} +(-115.233 - 653.521i) q^{73} +(-651.009 - 236.948i) q^{74} -296.176 q^{75} +(298.705 - 143.246i) q^{76} +1907.93 q^{77} +(261.840 + 95.3018i) q^{78} +(-88.0234 - 499.205i) q^{79} +(-62.8265 - 52.7177i) q^{80} +(62.0496 - 52.0658i) q^{81} +(-101.741 + 577.001i) q^{82} +(103.456 - 179.191i) q^{83} +(201.712 + 349.375i) q^{84} +(-333.851 + 121.512i) q^{85} +(-258.335 + 94.0262i) q^{86} +(-144.989 - 251.128i) q^{87} +(227.009 - 393.192i) q^{88} +(183.513 - 1040.76i) q^{89} +(-70.6798 + 59.3074i) q^{90} +(1196.00 + 1003.56i) q^{91} +(133.118 + 754.947i) q^{92} +(86.6068 + 31.5223i) q^{93} +1059.87 q^{94} +(114.308 + 408.842i) q^{95} +96.0000 q^{96} +(-1014.58 - 369.277i) q^{97} +(273.395 + 1550.50i) q^{98} +(-391.274 - 328.317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 15 q^{5} - 72 q^{8}+O(q^{10}) \) 18 * q + 15 * q^5 - 72 * q^8	\( 18 q + 15 q^{5} - 72 q^{8} - 6 q^{10} - 39 q^{11} - 108 q^{12} - 42 q^{14} + 45 q^{15} + 159 q^{17} + 324 q^{18} + 159 q^{19} + 216 q^{20} + 99 q^{21} - 246 q^{22} + 300 q^{23} - 267 q^{25} - 198 q^{26} - 243 q^{27} + 132 q^{28} - 231 q^{29} - 162 q^{30} - 243 q^{31} - 126 q^{33} - 618 q^{34} + 774 q^{35} + 1422 q^{37} - 270 q^{38} + 594 q^{39} - 24 q^{40} - 69 q^{41} - 126 q^{42} - 60 q^{43} - 492 q^{44} - 243 q^{45} - 456 q^{46} + 540 q^{47} - 2229 q^{49} - 348 q^{50} + 450 q^{51} - 180 q^{52} - 750 q^{53} - 450 q^{55} + 297 q^{57} + 1836 q^{58} + 1263 q^{59} - 144 q^{60} + 1518 q^{61} - 390 q^{62} - 108 q^{63} - 576 q^{64} + 237 q^{65} + 990 q^{66} - 4812 q^{67} - 228 q^{68} - 684 q^{69} + 1548 q^{70} - 1371 q^{71} + 672 q^{73} + 186 q^{74} + 1044 q^{75} - 84 q^{76} - 270 q^{77} + 270 q^{78} - 2301 q^{79} + 240 q^{80} - 138 q^{82} - 2490 q^{83} + 5757 q^{85} + 96 q^{86} - 1377 q^{87} - 312 q^{88} + 7203 q^{89} + 270 q^{90} + 1284 q^{91} + 156 q^{92} - 207 q^{93} - 264 q^{94} + 3270 q^{95} + 1728 q^{96} - 1977 q^{97} + 498 q^{98} - 378 q^{99}+O(q^{100}) \) 18 * q + 15 * q^5 - 72 * q^8 - 6 * q^10 - 39 * q^11 - 108 * q^12 - 42 * q^14 + 45 * q^15 + 159 * q^17 + 324 * q^18 + 159 * q^19 + 216 * q^20 + 99 * q^21 - 246 * q^22 + 300 * q^23 - 267 * q^25 - 198 * q^26 - 243 * q^27 + 132 * q^28 - 231 * q^29 - 162 * q^30 - 243 * q^31 - 126 * q^33 - 618 * q^34 + 774 * q^35 + 1422 * q^37 - 270 * q^38 + 594 * q^39 - 24 * q^40 - 69 * q^41 - 126 * q^42 - 60 * q^43 - 492 * q^44 - 243 * q^45 - 456 * q^46 + 540 * q^47 - 2229 * q^49 - 348 * q^50 + 450 * q^51 - 180 * q^52 - 750 * q^53 - 450 * q^55 + 297 * q^57 + 1836 * q^58 + 1263 * q^59 - 144 * q^60 + 1518 * q^61 - 390 * q^62 - 108 * q^63 - 576 * q^64 + 237 * q^65 + 990 * q^66 - 4812 * q^67 - 228 * q^68 - 684 * q^69 + 1548 * q^70 - 1371 * q^71 + 672 * q^73 + 186 * q^74 + 1044 * q^75 - 84 * q^76 - 270 * q^77 + 270 * q^78 - 2301 * q^79 + 240 * q^80 - 138 * q^82 - 2490 * q^83 + 5757 * q^85 + 96 * q^86 - 1377 * q^87 - 312 * q^88 + 7203 * q^89 + 270 * q^90 + 1284 * q^91 + 156 * q^92 - 207 * q^93 - 264 * q^94 + 3270 * q^95 + 1728 * q^96 - 1977 * q^97 + 498 * q^98 - 378 * q^99

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