LMFDB - Embedded newform 35.4.j.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,4,Mod(4,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("35.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	35.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.06506685020$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 55 x^{18} + 2018 x^{16} - 42095 x^{14} + 639938 x^{12} - 5744691 x^{10} + 35287093 x^{8} + \cdots + 9834496 $ x^20 - 55x^18 + 2018x^16 - 42095x^14 + 639938x^12 - 5744691x^10 + 35287093x^8 - 51070316x^6 + 53741776x^4 - 27082496*x^2 + 9834496
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.6
Root			$-0.736336 + 0.425124i$ of defining polynomial
Character	$\chi$	$=$	35.4
Dual form			35.4.j.a.9.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.736336 - 0.425124i) q^{2} +(3.23521 + 1.86785i) q^{3} +(-3.63854 + 6.30214i) q^{4} +(10.5026 + 3.83358i) q^{5} +3.17627 q^{6} +(3.68367 - 18.1502i) q^{7} +12.9893i q^{8} +(-6.52228 - 11.2969i) q^{9} +O(q^{10})$	\(q+(0.736336 - 0.425124i) q^{2} +(3.23521 + 1.86785i) q^{3} +(-3.63854 + 6.30214i) q^{4} +(10.5026 + 3.83358i) q^{5} +3.17627 q^{6} +(3.68367 - 18.1502i) q^{7} +12.9893i q^{8} +(-6.52228 - 11.2969i) q^{9} +(9.36316 - 1.64208i) q^{10} +(-4.34744 + 7.52998i) q^{11} +(-23.5429 + 13.5925i) q^{12} +0.148705i q^{13} +(-5.00368 - 14.9307i) q^{14} +(26.8174 + 32.0196i) q^{15} +(-23.5863 - 40.8526i) q^{16} +(-102.028 - 58.9060i) q^{17} +(-9.60518 - 5.54555i) q^{18} +(10.2669 + 17.7829i) q^{19} +(-62.3737 + 52.2399i) q^{20} +(45.8193 - 51.8392i) q^{21} +7.39279i q^{22} +(56.3669 - 32.5435i) q^{23} +(-24.2621 + 42.0231i) q^{24} +(95.6074 + 80.5247i) q^{25} +(0.0632181 + 0.109497i) q^{26} -149.594i q^{27} +(100.982 + 89.2553i) q^{28} +211.705 q^{29} +(33.3589 + 12.1765i) q^{30} +(-139.692 + 241.954i) q^{31} +(-124.727 - 72.0114i) q^{32} +(-28.1297 + 16.2407i) q^{33} -100.169 q^{34} +(108.268 - 176.502i) q^{35} +94.9262 q^{36} +(53.8473 - 31.0888i) q^{37} +(15.1198 + 8.72945i) q^{38} +(-0.277759 + 0.481092i) q^{39} +(-49.7955 + 136.421i) q^{40} +93.6108 q^{41} +(11.7003 - 57.6500i) q^{42} +346.387i q^{43} +(-31.6366 - 54.7963i) q^{44} +(-25.1930 - 143.650i) q^{45} +(27.6700 - 47.9259i) q^{46} +(-193.183 + 111.534i) q^{47} -176.222i q^{48} +(-315.861 - 133.719i) q^{49} +(104.632 + 18.6483i) q^{50} +(-220.055 - 381.146i) q^{51} +(-0.937159 - 0.541069i) q^{52} +(-418.474 - 241.606i) q^{53} +(-63.5961 - 110.152i) q^{54} +(-74.5259 + 62.4178i) q^{55} +(235.759 + 47.8483i) q^{56} +76.7084i q^{57} +(155.886 - 90.0007i) q^{58} +(-91.8863 + 159.152i) q^{59} +(-299.368 + 52.5024i) q^{60} +(185.020 + 320.463i) q^{61} +237.545i q^{62} +(-229.067 + 76.7667i) q^{63} +254.925 q^{64} +(-0.570072 + 1.56178i) q^{65} +(-13.8086 + 23.9172i) q^{66} +(903.793 + 521.805i) q^{67} +(742.467 - 428.663i) q^{68} +243.145 q^{69} +(4.68655 - 175.992i) q^{70} -478.256 q^{71} +(146.739 - 84.7198i) q^{72} +(-261.727 - 151.108i) q^{73} +(26.4332 - 45.7836i) q^{74} +(158.902 + 439.095i) q^{75} -149.427 q^{76} +(120.656 + 106.645i) q^{77} +0.472327i q^{78} +(387.695 + 671.507i) q^{79} +(-91.1043 - 519.476i) q^{80} +(103.318 - 178.953i) q^{81} +(68.9290 - 39.7962i) q^{82} +83.8379i q^{83} +(159.983 + 477.379i) q^{84} +(-845.736 - 1009.80i) q^{85} +(147.258 + 255.057i) q^{86} +(684.909 + 395.432i) q^{87} +(-97.8092 - 56.4701i) q^{88} +(-524.740 - 908.876i) q^{89} +(-79.6196 - 95.0646i) q^{90} +(2.69903 + 0.547780i) q^{91} +473.643i q^{92} +(-903.866 + 521.847i) q^{93} +(-94.8317 + 164.253i) q^{94} +(39.6571 + 226.125i) q^{95} +(-269.013 - 465.944i) q^{96} -164.959i q^{97} +(-289.427 + 35.8182i) q^{98} +113.421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 30 q^{4} + 3 q^{5} - 96 q^{6} + 82 q^{9}+O(q^{10}) $ 20 * q + 30 * q^4 + 3 * q^5 - 96 * q^6 + 82 * q^9	$ 20 q + 30 q^{4} + 3 q^{5} - 96 q^{6} + 82 q^{9} - 32 q^{10} + 36 q^{11} + 26 q^{14} - 146 q^{15} - 22 q^{16} - 192 q^{19} + 584 q^{20} - 404 q^{21} - 444 q^{24} - 187 q^{25} + 434 q^{26} + 260 q^{29} - 658 q^{30} + 834 q^{31} - 160 q^{34} + 661 q^{35} + 516 q^{36} + 868 q^{39} + 674 q^{40} - 1224 q^{41} + 542 q^{44} + 60 q^{45} - 1274 q^{46} - 326 q^{49} - 2556 q^{50} + 986 q^{51} - 2808 q^{54} - 742 q^{55} - 36 q^{56} - 2514 q^{59} - 204 q^{60} + 512 q^{61} + 6900 q^{64} - 946 q^{65} + 1396 q^{66} + 3064 q^{69} + 5190 q^{70} - 2944 q^{71} + 1590 q^{74} + 3003 q^{75} + 44 q^{76} + 46 q^{79} + 2304 q^{80} - 130 q^{81} - 12952 q^{84} - 5082 q^{85} - 1592 q^{86} - 5876 q^{89} - 3316 q^{90} + 4348 q^{91} - 3314 q^{94} - 2155 q^{95} + 3756 q^{96} + 13860 q^{99}+O(q^{100}) $ 20 * q + 30 * q^4 + 3 * q^5 - 96 * q^6 + 82 * q^9 - 32 * q^10 + 36 * q^11 + 26 * q^14 - 146 * q^15 - 22 * q^16 - 192 * q^19 + 584 * q^20 - 404 * q^21 - 444 * q^24 - 187 * q^25 + 434 * q^26 + 260 * q^29 - 658 * q^30 + 834 * q^31 - 160 * q^34 + 661 * q^35 + 516 * q^36 + 868 * q^39 + 674 * q^40 - 1224 * q^41 + 542 * q^44 + 60 * q^45 - 1274 * q^46 - 326 * q^49 - 2556 * q^50 + 986 * q^51 - 2808 * q^54 - 742 * q^55 - 36 * q^56 - 2514 * q^59 - 204 * q^60 + 512 * q^61 + 6900 * q^64 - 946 * q^65 + 1396 * q^66 + 3064 * q^69 + 5190 * q^70 - 2944 * q^71 + 1590 * q^74 + 3003 * q^75 + 44 * q^76 + 46 * q^79 + 2304 * q^80 - 130 * q^81 - 12952 * q^84 - 5082 * q^85 - 1592 * q^86 - 5876 * q^89 - 3316 * q^90 + 4348 * q^91 - 3314 * q^94 - 2155 * q^95 + 3756 * q^96 + 13860 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.736336	−	0.425124i	0.260334	−	0.150304i	−0.364153	−	0.931339i	$-0.618641\pi$
$2$	0.736336	−	0.425124i	0.260334	−	0.150304i	0.624487	+	0.781035i	$0.285308\pi$
$3$	3.23521	+	1.86785i	0.622616	+	0.359468i	0.777887	−	0.628404i	$-0.216292\pi$
$3$	3.23521	+	1.86785i	0.622616	+	0.359468i	−0.155271	+	0.987872i	$0.549625\pi$
$4$	−3.63854	+	6.30214i	−0.454817	+	0.787767i
$5$	10.5026	+	3.83358i	0.939377	+	0.342886i
$5$	10.5026	+	3.83358i	0.939377	+	0.342886i
$6$	3.17627			0.216118
$7$	3.68367	−	18.1502i	0.198899	−	0.980020i
$7$	3.68367	−	18.1502i	0.198899	−	0.980020i
$8$			12.9893i			0.574051i
$9$	−6.52228	−	11.2969i	−0.241566	−	0.418404i
$10$	9.36316	−	1.64208i	0.296089	−	0.0519273i
$11$	−4.34744	+	7.52998i	−0.119164	+	0.206398i	−0.919437	−	0.393238i	$-0.871355\pi$
$11$	−4.34744	+	7.52998i	−0.119164	+	0.206398i	0.800273	+	0.599636i	$0.204688\pi$
$12$	−23.5429	+	13.5925i	−0.566354	+	0.326984i
$13$			0.148705i			0.00317257i	0.999999	+	0.00158628i	$0.000504930\pi$
$13$			0.148705i			0.00317257i	−0.999999	+	0.00158628i	$0.999495\pi$
$14$	−5.00368	−	14.9307i	−0.0955206	−	0.285028i
$15$	26.8174	+	32.0196i	0.461615	+	0.551162i
$16$	−23.5863	−	40.8526i	−0.368535	−	0.638322i
$17$	−102.028	−	58.9060i	−1.45562	−	0.840400i	−0.456824	−	0.889557i	$-0.651013\pi$
$17$	−102.028	−	58.9060i	−1.45562	−	0.840400i	−0.998791	+	0.0491571i	$0.984346\pi$
$18$	−9.60518	−	5.54555i	−0.125776	−	0.0726166i
$19$	10.2669	+	17.7829i	0.123968	+	0.214719i	0.921329	−	0.388783i	$-0.127105\pi$
$19$	10.2669	+	17.7829i	0.123968	+	0.214719i	−0.797361	+	0.603503i	$0.793771\pi$
$20$	−62.3737	+	52.2399i	−0.697359	+	0.584060i
$21$	45.8193	−	51.8392i	0.476124	−	0.538679i
$22$			7.39279i			0.0716431i
$23$	56.3669	−	32.5435i	0.511014	−	0.295034i	−0.222236	−	0.974993i	$-0.571336\pi$
$23$	56.3669	−	32.5435i	0.511014	−	0.295034i	0.733250	+	0.679959i	$0.238002\pi$
$24$	−24.2621	+	42.0231i	−0.206353	+	0.357414i
$25$	95.6074	+	80.5247i	0.764859	+	0.644198i
$26$	0.0632181	+	0.109497i	0.000476849	+	0.000825927i
$27$		−	149.594i		−	1.06628i
$28$	100.982	+	89.2553i	0.681564	+	0.602416i
$29$	211.705			1.35561			0.677803	−	0.735244i	$-0.262932\pi$
$29$	211.705			1.35561			0.677803	+	0.735244i	$0.262932\pi$
$30$	33.3589	+	12.1765i	0.203016	+	0.0741037i
$31$	−139.692	+	241.954i	−0.809336	+	1.40181i	0.103989	+	0.994578i	$0.466839\pi$
$31$	−139.692	+	241.954i	−0.809336	+	1.40181i	−0.913325	+	0.407232i	$0.866494\pi$
$32$	−124.727	−	72.0114i	−0.689028	−	0.397810i
$33$	−28.1297	+	16.2407i	−0.148387	+	0.0856711i
$34$	−100.169			−0.505262
$35$	108.268	−	176.502i	0.522876	−	0.852409i
$36$	94.9262			0.439473
$37$	53.8473	−	31.0888i	0.239255	−	0.138134i	−0.375579	−	0.926790i	$-0.622556\pi$
$37$	53.8473	−	31.0888i	0.239255	−	0.138134i	0.614834	+	0.788656i	$0.289223\pi$
$38$	15.1198	+	8.72945i	0.0645464	+	0.0372659i
$39$	−0.277759	+	0.481092i	−0.00114044	+	0.00197529i
$40$	−49.7955	+	136.421i	−0.196834	+	0.539251i
$41$	93.6108			0.356574			0.178287	−	0.983979i	$-0.442944\pi$
$41$	93.6108			0.356574			0.178287	+	0.983979i	$0.442944\pi$
$42$	11.7003	−	57.6500i	0.0429857	−	0.211800i
$43$			346.387i			1.22846i	0.789129	+	0.614228i	$0.210532\pi$
$43$			346.387i			1.22846i	−0.789129	+	0.614228i	$0.789468\pi$
$44$	−31.6366	−	54.7963i	−0.108395	−	0.187746i
$45$	−25.1930	−	143.650i	−0.0834566	−	0.475869i
$46$	27.6700	−	47.9259i	0.0886896	−	0.153615i
$47$	−193.183	+	111.534i	−0.599545	+	0.346148i	−0.768863	−	0.639414i	$-0.779177\pi$
$47$	−193.183	+	111.534i	−0.599545	+	0.346148i	0.169317	+	0.985562i	$0.445844\pi$
$48$		−	176.222i		−	0.529906i
$49$	−315.861	−	133.719i	−0.920878	−	0.389851i
$50$	104.632	+	18.6483i	0.295944	+	0.0527454i
$51$	−220.055	−	381.146i	−0.604193	−	1.04649i
$52$	−0.937159	−	0.541069i	−0.00249924	−	0.00144294i
$53$	−418.474	−	241.606i	−1.08456	−	0.626173i	−0.152439	−	0.988313i	$-0.548713\pi$
$53$	−418.474	−	241.606i	−1.08456	−	0.626173i	−0.932124	+	0.362140i	$0.882046\pi$
$54$	−63.5961	−	110.152i	−0.160266	−	0.277588i
$55$	−74.5259	+	62.4178i	−0.182710	+	0.153026i
$56$	235.759	+	47.8483i	0.562582	+	0.114178i
$57$			76.7084i			0.178251i
$58$	155.886	−	90.0007i	0.352910	−	0.203753i
$59$	−91.8863	+	159.152i	−0.202756	+	0.351183i	−0.949415	−	0.314023i	$-0.898323\pi$
$59$	−91.8863	+	159.152i	−0.202756	+	0.351183i	0.746660	+	0.665206i	$0.231656\pi$
$60$	−299.368	+	52.5024i	−0.644138	+	0.112967i
$61$	185.020	+	320.463i	0.388350	+	0.672641i	0.992228	−	0.124436i	$-0.0397120\pi$
$61$	185.020	+	320.463i	0.388350	+	0.672641i	−0.603878	+	0.797077i	$0.706379\pi$
$62$			237.545i			0.486586i
$63$	−229.067	+	76.7667i	−0.458092	+	0.153519i
$64$	254.925			0.497901
$65$	−0.570072	+	1.56178i	−0.00108783	+	0.00298024i
$66$	−13.8086	+	23.9172i	−0.0257534	+	0.0446062i
$67$	903.793	+	521.805i	1.64800	+	0.951472i	0.977867	+	0.209229i	$0.0670955\pi$
$67$	903.793	+	521.805i	1.64800	+	0.951472i	0.670131	+	0.742243i	$0.266238\pi$
$68$	742.467	−	428.663i	1.32408	−	0.764457i
$69$	243.145			0.424221
$70$	4.68655	−	175.992i	0.00800214	−	0.300501i
$71$	−478.256			−0.799416			−0.399708	−	0.916642i	$-0.630888\pi$
$71$	−478.256			−0.799416			−0.399708	+	0.916642i	$0.630888\pi$
$72$	146.739	−	84.7198i	0.240186	−	0.138671i
$73$	−261.727	−	151.108i	−0.419627	−	0.242272i	0.275290	−	0.961361i	$-0.411226\pi$
$73$	−261.727	−	151.108i	−0.419627	−	0.242272i	−0.694918	+	0.719089i	$0.744559\pi$
$74$	26.4332	−	45.7836i	0.0415242	−	0.0719220i
$75$	158.902	+	439.095i	0.244645	+	0.676030i
$76$	−149.427			−0.225532
$77$	120.656	+	106.645i	0.178572	+	0.157835i
$78$			0.472327i			0.000685648i
$79$	387.695	+	671.507i	0.552140	+	0.956335i	0.998120	+	0.0612917i	$0.0195220\pi$
$79$	387.695	+	671.507i	0.552140	+	0.956335i	−0.445980	+	0.895043i	$0.647145\pi$
$80$	−91.1043	−	519.476i	−0.127322	−	0.725990i
$81$	103.318	−	178.953i	0.141726	−	0.245477i
$82$	68.9290	−	39.7962i	0.0928284	−	0.0535945i
$83$			83.8379i			0.110872i	0.998462	+	0.0554362i	$0.0176549\pi$
$83$			83.8379i			0.110872i	−0.998462	+	0.0554362i	$0.982345\pi$
$84$	159.983	+	477.379i	0.207804	+	0.620075i
$85$	−845.736	−	1009.80i	−1.07921	−	1.28856i
$86$	147.258	+	255.057i	0.184642	+	0.319809i
$87$	684.909	+	395.432i	0.844022	+	0.487296i
$88$	−97.8092	−	56.4701i	−0.118483	−	0.0684061i
$89$	−524.740	−	908.876i	−0.624970	−	1.08248i	−0.988547	−	0.150915i	$-0.951778\pi$
$89$	−524.740	−	908.876i	−0.624970	−	1.08248i	0.363577	−	0.931564i	$-0.381555\pi$
$90$	−79.6196	−	95.0646i	−0.0932516	−	0.111341i
$91$	2.69903	+	0.547780i	0.00310918	+	0.000631021i
$92$			473.643i			0.536746i
$93$	−903.866	+	521.847i	−1.00781	+	0.581860i
$94$	−94.8317	+	164.253i	−0.104055	+	0.180228i
$95$	39.6571	+	226.125i	0.0428288	+	0.244210i
$96$	−269.013	−	465.944i	−0.286000	−	0.495367i
$97$		−	164.959i		−	0.172670i	−0.996266	−	0.0863351i	$-0.972484\pi$
$97$		−	164.959i		−	0.172670i	0.996266	−	0.0863351i	$-0.0275156\pi$
$98$	−289.427	+	35.8182i	−0.298332	+	0.0369202i
$99$	113.421			0.115144
$100$	−855.349	+	309.538i	−0.855349	+	0.309538i
$101$	645.701	−	1118.39i	0.636135	−	1.10182i	−0.350138	−	0.936698i	$-0.613865\pi$
$101$	645.701	−	1118.39i	0.636135	−	1.10182i	0.986273	−	0.165121i	$-0.0528014\pi$
$102$	−324.069	−	187.101i	−0.314584	−	0.181625i
$103$	−603.084	+	348.191i	−0.576929	+	0.333090i	−0.759912	−	0.650026i	$-0.774758\pi$
$103$	−603.084	+	348.191i	−0.576929	+	0.333090i	0.182983	+	0.983116i	$0.441425\pi$
$104$	−1.93157			−0.00182122
$105$	679.950	−	368.793i	0.631965	−	0.342766i
$106$	−410.850			−0.376465
$107$	−196.567	+	113.488i	−0.177597	+	0.102536i	−0.586163	−	0.810193i	$-0.699362\pi$
$107$	−196.567	+	113.488i	−0.177597	+	0.102536i	0.408566	+	0.912729i	$0.366029\pi$
$108$	942.764	+	544.305i	0.839977	+	0.484961i
$109$	809.405	−	1401.93i	0.711256	−	1.23193i	−0.253129	−	0.967432i	$-0.581460\pi$
$109$	809.405	−	1401.93i	0.711256	−	1.23193i	0.964386	−	0.264500i	$-0.0852068\pi$
$110$	−28.3409	+	77.6432i	−0.0245654	+	0.0672999i
$111$	232.277			0.198619
$112$	−828.368	+	277.608i	−0.698869	+	0.234210i
$113$		−	1544.73i		−	1.28599i	−0.765872	−	0.642993i	$-0.777692\pi$
$113$		−	1544.73i		−	1.28599i	0.765872	−	0.642993i	$-0.222308\pi$
$114$	32.6106	+	56.4832i	0.0267918	+	0.0464047i
$115$	716.755	−	125.702i	0.581198	−	0.101929i
$116$	−770.295	+	1334.19i	−0.616553	+	1.06790i
$117$	1.67991	−	0.969896i	0.00132742	−	0.000766384i
$118$			156.252i			0.121900i
$119$	−1444.99	+	1634.84i	−1.11313	+	1.25938i
$120$	−415.913	+	348.340i	−0.316395	+	0.264991i
$121$	627.700	+	1087.21i	0.471600	+	0.816835i
$122$	272.473	+	157.312i	0.202201	+	0.116741i
$123$	302.850	+	174.851i	0.222009	+	0.128177i
$124$	−1016.55	−	1760.71i	−0.736200	−	1.27514i
$125$	695.424	+	1212.23i	0.497605	+	0.867404i
$126$	−136.035	+	153.908i	−0.0961824	+	0.108819i
$127$		−	1859.45i		−	1.29921i	−0.760273	−	0.649604i	$-0.774935\pi$
$127$		−	1859.45i		−	1.29921i	0.760273	−	0.649604i	$-0.225065\pi$
$128$	1185.53	−	684.466i	0.818648	−	0.472647i
$129$	−646.999	+	1120.64i	−0.441590	+	0.764856i
$130$	0.244186	+	1.39235i	0.000164743	+	0.000939362i
$131$	723.880	+	1253.80i	0.482791	+	0.836219i	0.999805	−	0.0197581i	$-0.00628962\pi$
$131$	723.880	+	1253.80i	0.482791	+	0.836219i	−0.517013	+	0.855977i	$0.672956\pi$
$132$		−	236.370i		−	0.155859i
$133$	360.583	−	120.841i	0.235087	−	0.0787839i
$134$	887.327			0.572040
$135$	573.482	−	1571.12i	0.365611	−	1.00164i
$136$	765.147	−	1325.27i	0.482433	−	0.835598i
$137$	284.651	+	164.343i	0.177514	+	0.102488i	0.586124	−	0.810221i	$-0.300653\pi$
$137$	284.651	+	164.343i	0.177514	+	0.102488i	−0.408610	+	0.912709i	$0.633986\pi$
$138$	179.037	−	103.367i	0.110439	−	0.0637621i
$139$	1175.96			0.717583			0.358791	−	0.933418i	$-0.383189\pi$
$139$	1175.96			0.717583			0.358791	+	0.933418i	$0.383189\pi$
$140$	718.402	+	1324.53i	0.433686	+	0.799595i
$141$	−833.317			−0.497716
$142$	−352.157	+	203.318i	−0.208115	+	0.120155i
$143$	−1.11975	−	0.646486i	−0.000654810	−	0.000378055i
$144$	−307.672	+	532.904i	−0.178051	+	0.308393i
$145$	2223.44	+	811.586i	1.27342	+	0.464818i
$146$	−256.958			−0.145658
$147$	−772.111	−	1022.59i	−0.433215	−	0.573753i
$148$			452.471i			0.251303i
$149$	343.064	+	594.204i	0.188623	+	0.326705i	0.944791	−	0.327672i	$-0.106264\pi$
$149$	343.064	+	594.204i	0.188623	+	0.326705i	−0.756168	+	0.654377i	$0.772931\pi$
$150$	303.675	+	255.768i	0.165300	+	0.139223i
$151$	419.185	−	726.049i	0.225912	−	0.391292i	−0.730680	−	0.682720i	$-0.760797\pi$
$151$	419.185	−	726.049i	0.225912	−	0.391292i	0.956593	+	0.291428i	$0.0941304\pi$
$152$	−230.987	+	133.360i	−0.123260	+	0.0711642i
$153$			1536.80i			0.812048i
$154$	134.181	+	27.2326i	0.0702117	+	0.0142498i
$155$	−2394.67	+	2005.61i	−1.24093	+	1.03932i
$156$	−2.02127	−	3.50095i	−0.00103738	−	0.00179679i
$157$	−2256.14	−	1302.58i	−1.14688	−	0.662150i	−0.198752	−	0.980050i	$-0.563689\pi$
$157$	−2256.14	−	1302.58i	−1.14688	−	0.662150i	−0.948124	+	0.317900i	$0.897022\pi$
$158$	570.947	+	329.637i	0.287482	+	0.165978i
$159$	−902.568	−	1563.29i	−0.450178	−	0.779731i
$160$	−1033.89	−	1234.46i	−0.510853	−	0.609952i
$161$	−383.034	−	1142.95i	−0.187499	−	0.559486i
$162$		−	175.692i		−	0.0852080i
$163$	−1334.40	+	770.415i	−0.641215	+	0.370206i	−0.785082	−	0.619391i	$-0.787379\pi$
$163$	−1334.40	+	770.415i	−0.641215	+	0.370206i	0.143867	+	0.989597i	$0.454046\pi$
$164$	−340.606	+	589.948i	−0.162176	+	0.280897i
$165$	−357.694	+	62.7314i	−0.168766	+	0.0295978i
$166$	35.6415	+	61.7329i	0.0166646	+	0.0288639i
$167$		−	1122.87i		−	0.520303i	−0.965568	−	0.260152i	$-0.916227\pi$
$167$		−	1122.87i		−	0.520303i	0.965568	−	0.260152i	$-0.0837725\pi$
$168$	673.356	+	595.161i	0.309229	+	0.273319i
$169$	2196.98			0.999990
$170$	−1052.03	−	384.007i	−0.474631	−	0.173247i
$171$	133.928	−	231.970i	0.0598930	−	0.103738i
$172$	−2182.98	−	1260.34i	−0.967736	−	0.558723i
$173$	−1078.16	+	622.476i	−0.473821	+	0.273561i	−0.717838	−	0.696210i	$-0.754868\pi$
$173$	−1078.16	+	622.476i	−0.473821	+	0.273561i	0.244017	+	0.969771i	$0.421535\pi$
$174$	672.431			0.292970
$175$	1813.73	−	1438.67i	0.783457	−	0.621446i
$176$	410.159			0.175664
$177$	−594.543	+	343.260i	−0.252478	+	0.145768i
$178$	−772.769	−	446.159i	−0.325402	−	0.187871i
$179$	1159.66	−	2008.58i	0.484228	−	0.838707i	−0.515608	−	0.856825i	$-0.672434\pi$
$179$	1159.66	−	2008.58i	0.484228	−	0.838707i	0.999836	+	0.0181175i	$0.00576728\pi$
$180$	996.968	+	363.907i	0.412831	+	0.150689i
$181$	−3256.27			−1.33722			−0.668609	−	0.743614i	$-0.733110\pi$
$181$	−3256.27			−1.33722			−0.668609	+	0.743614i	$0.733110\pi$
$182$	2.22027	−	0.744072i	0.000904270	−	0.000303045i
$183$			1382.35i			0.558397i
$184$	422.717	+	732.167i	0.169365	+	0.293348i
$185$	684.716	−	120.084i	0.272115	−	0.0477228i
$186$	−443.699	+	768.510i	−0.174912	+	0.302956i
$187$	887.122	−	512.180i	0.346913	−	0.200290i
$188$		−	1623.29i		−	0.629736i
$189$	−2715.17	−	551.056i	−1.04497	−	0.212082i
$190$	125.332	+	149.645i	0.0478555	+	0.0571387i
$191$	−1081.42	−	1873.08i	−0.409681	−	0.709589i	0.585173	−	0.810909i	$-0.301027\pi$
$191$	−1081.42	−	1873.08i	−0.409681	−	0.709589i	−0.994854	+	0.101320i	$0.967693\pi$
$192$	824.736	+	476.162i	0.310001	+	0.178979i
$193$	2232.98	+	1289.21i	0.832817	+	0.480827i	0.854816	−	0.518931i	$-0.173670\pi$
$193$	2232.98	+	1289.21i	0.832817	+	0.480827i	−0.0219989	+	0.999758i	$0.507003\pi$
$194$	−70.1278	−	121.465i	−0.0259530	−	0.0449519i
$195$	−4.76148	+	3.98789i	−0.00174860	+	0.00146451i
$196$	1991.99	−	1504.06i	0.725943	−	0.548126i
$197$			3464.77i			1.25307i	0.779393	+	0.626535i	$0.215528\pi$
$197$			3464.77i			1.25307i	−0.779393	+	0.626535i	$0.784472\pi$
$198$	83.5158	−	48.2178i	0.0299758	−	0.0173065i
$199$	−2402.03	+	4160.44i	−0.855656	+	1.48204i	0.0203798	+	0.999792i	$0.493512\pi$
$199$	−2402.03	+	4160.44i	−0.855656	+	1.48204i	−0.876035	+	0.482247i	$0.839821\pi$
$200$	−1045.96	+	1241.87i	−0.369803	+	0.439068i
$201$	1949.31	+	3376.30i	0.684047	+	1.18480i
$202$		−	1098.01i		−	0.382455i
$203$	779.849	−	3842.49i	0.269629	−	1.32852i
$204$	3202.72			1.09919
$205$	983.152	+	358.864i	0.334958	+	0.122264i
$206$	−296.049	+	512.771i	−0.100130	+	0.173429i
$207$	−735.281	−	424.515i	−0.246887	−	0.142540i
$208$	6.07499	−	3.50740i	0.00202512	−	0.00116920i
$209$	−178.540			−0.0590901
$210$	343.889	−	560.618i	0.113003	−	0.184221i
$211$	652.820			0.212995			0.106498	−	0.994313i	$-0.466036\pi$
$211$	652.820			0.212995			0.106498	+	0.994313i	$0.466036\pi$
$212$	3045.27	−	1758.19i	0.986557	−	0.569589i
$213$	−1547.26	−	893.310i	−0.497730	−	0.287364i
$214$	−96.4929	+	167.131i	−0.0308230	+	0.0533870i
$215$	−1327.90	+	3637.95i	−0.421220	+	1.15398i
$216$	1943.13			0.612097
$217$	3876.93	+	3426.72i	1.21283	+	1.07198i
$218$		−	1376.39i		−	0.427619i
$219$	−564.494	−	977.732i	−0.174178	−	0.301685i
$220$	−122.200	−	696.782i	−0.0374487	−	0.213532i
$221$	8.75962	−	15.1721i	0.00266622	−	0.00461804i
$222$	171.034	−	98.7463i	0.0517073	−	0.0298532i
$223$			509.150i			0.152893i	0.997074	+	0.0764466i	$0.0243575\pi$
$223$			509.150i			0.152893i	−0.997074	+	0.0764466i	$0.975643\pi$
$224$	−1766.48	+	1998.56i	−0.526909	+	0.596137i
$225$	286.104	−	1605.27i	0.0847714	−	0.475636i
$226$	−656.703	−	1137.44i	−0.193289	−	0.334786i
$227$	388.392	+	224.238i	0.113562	+	0.0655648i	0.555705	−	0.831380i	$-0.312448\pi$
$227$	388.392	+	224.238i	0.113562	+	0.0655648i	−0.442143	+	0.896944i	$0.645782\pi$
$228$	−483.427	−	279.107i	−0.140420	−	0.0810714i
$229$	−2397.50	−	4152.59i	−0.691839	−	1.19830i	−0.971235	−	0.238124i	$-0.923468\pi$
$229$	−2397.50	−	4152.59i	−0.691839	−	1.19830i	0.279396	−	0.960176i	$-0.409866\pi$
$230$	474.333	−	397.269i	0.135985	−	0.113892i
$231$	191.152	+	570.386i	0.0544453	+	0.162462i
$232$			2749.89i			0.778187i
$233$	4238.98	−	2447.38i	1.19187	−	0.688125i	0.233137	−	0.972444i	$-0.425101\pi$
$233$	4238.98	−	2447.38i	1.19187	−	0.688125i	0.958730	+	0.284319i	$0.0917675\pi$
$234$	0.824651	−	1.42834i	0.000230381	−	0.000399032i
$235$	−2456.49	+	430.813i	−0.681888	+	0.119588i
$236$	−668.664	−	1158.16i	−0.184434	−	0.319448i
$237$			2896.62i			0.793906i
$238$	−368.990	+	1818.10i	−0.100496	+	0.495167i
$239$	4762.25			1.28889			0.644444	−	0.764651i	$-0.277089\pi$
$239$	4762.25			1.28889			0.644444	+	0.764651i	$0.277089\pi$
$240$	675.562	−	1850.78i	0.181697	−	0.497782i
$241$	−1780.18	+	3083.36i	−0.475815	+	0.824137i	−0.999616	−	0.0277043i	$-0.991180\pi$
$241$	−1780.18	+	3083.36i	−0.475815	+	0.824137i	0.523801	+	0.851841i	$0.324514\pi$
$242$	924.396	+	533.700i	0.245547	+	0.141767i
$243$	−2829.41	+	1633.56i	−0.746940	+	0.431246i
$244$	−2692.80			−0.706513
$245$	−2804.73	−	2615.27i	−0.731378	−	0.681973i
$246$	297.333			0.0770620
$247$	−2.64440	+	1.52675i	−0.000681212	+	0.000393298i
$248$	−3142.81	−	1814.50i	−0.804711	−	0.464600i
$249$	−156.597	+	271.233i	−0.0398550	+	0.0690310i
$250$	1027.42	+	596.970i	0.259918	+	0.151023i
$251$	2293.15			0.576662			0.288331	−	0.957531i	$-0.406900\pi$
$251$	2293.15			0.576662			0.288331	+	0.957531i	$0.406900\pi$
$252$	349.677	−	1722.93i	0.0874110	−	0.430693i
$253$			565.922i			0.140629i
$254$	−790.496	−	1369.18i	−0.195276	−	0.338228i
$255$	−849.985	−	4846.61i	−0.208738	−	1.19022i
$256$	−437.735	+	758.179i	−0.106869	+	0.185102i
$257$	−2049.65	+	1183.37i	−0.497486	+	0.287224i	−0.727675	−	0.685922i	$-0.759399\pi$
$257$	−2049.65	+	1183.37i	−0.497486	+	0.287224i	0.230189	+	0.973146i	$0.426066\pi$
$258$			1100.22i			0.265491i
$259$	−365.912	−	1091.86i	−0.0877865	−	0.261950i
$260$	−7.76834	−	9.27528i	−0.00185297	−	0.00221242i
$261$	−1380.80	−	2391.61i	−0.327468	−	0.567191i
$262$	1066.04	+	615.477i	0.251374	+	0.145131i
$263$	−2278.99	−	1315.78i	−0.534329	−	0.308495i	0.208448	−	0.978033i	$-0.433159\pi$
$263$	−2278.99	−	1315.78i	−0.534329	−	0.308495i	−0.742778	+	0.669538i	$0.766492\pi$
$264$	−210.955	−	365.386i	−0.0491796	−	0.0851815i
$265$	−3468.83	−	4141.74i	−0.804108	−	0.960094i
$266$	214.138	−	242.272i	0.0493595	−	0.0558446i
$267$		−	3920.54i		−	0.898626i
$268$	−6576.97	+	3797.22i	−1.49908	+	0.865492i
$269$	−404.946	+	701.388i	−0.0917844	+	0.158975i	−0.908262	−	0.418402i	$-0.862590\pi$
$269$	−404.946	+	701.388i	−0.0917844	+	0.158975i	0.816478	+	0.577377i	$0.195924\pi$
$270$	−245.647	−	1400.68i	−0.0553688	−	0.315713i
$271$	−315.657	−	546.734i	−0.0707558	−	0.122553i	0.828477	−	0.560023i	$-0.189208\pi$
$271$	−315.657	−	546.734i	−0.0707558	−	0.122553i	−0.899233	+	0.437471i	$0.855874\pi$
$272$			5557.49i			1.23887i
$273$	7.70876	+	6.81356i	0.00170899	+	0.00151053i
$274$	279.465			0.0616172
$275$	−1022.00	+	369.845i	−0.224104	+	0.0811000i
$276$	−884.693	+	1532.33i	−0.192943	+	0.334187i
$277$	4664.18	+	2692.86i	1.01171	+	0.584110i	0.911691	−	0.410876i	$-0.134777\pi$
$277$	4664.18	+	2692.86i	1.01171	+	0.584110i	0.100017	+	0.994986i	$0.468110\pi$
$278$	865.905	−	499.930i	0.186811	−	0.107856i
$279$	3644.44			0.782032
$280$	2292.64	+	1406.33i	0.489326	+	0.300158i
$281$	−2823.48			−0.599411			−0.299706	−	0.954032i	$-0.596888\pi$
$281$	−2823.48			−0.599411			−0.299706	+	0.954032i	$0.596888\pi$
$282$	−613.601	+	354.263i	−0.129572	+	0.0748087i
$283$	5003.38	+	2888.70i	1.05095	+	0.606769i	0.922917	−	0.385000i	$-0.125799\pi$
$283$	5003.38	+	2888.70i	1.05095	+	0.606769i	0.128038	+	0.991769i	$0.459132\pi$
$284$	1740.15	−	3014.03i	0.363588	−	0.629754i
$285$	−294.068	+	805.635i	−0.0611195	+	0.167444i
$286$	−1.09935			−0.000227293
$287$	344.831	−	1699.06i	0.0709224	−	0.349450i
$288$			1878.71i			0.384389i
$289$	4483.33	+	7765.35i	0.912544	+	1.58057i
$290$	1982.22	−	347.637i	0.401380	−	0.0703929i
$291$	308.118	−	533.676i	0.0620694	−	0.107507i
$292$	1904.61	−	1099.62i	0.381708	−	0.220379i
$293$		−	6132.13i		−	1.22267i	−0.791371	−	0.611336i	$-0.790632\pi$
$293$		−	6132.13i		−	1.22267i	0.791371	−	0.611336i	$-0.209368\pi$
$294$	−1003.26	−	424.727i	−0.199018	−	0.0842536i
$295$	−1575.16	+	1319.25i	−0.310880	+	0.260371i
$296$	403.821	+	699.439i	0.0792961	+	0.137345i
$297$	1126.44	+	650.352i	0.220077	+	0.127061i
$298$	505.220	+	291.689i	0.0982101	+	0.0567016i
$299$	4.83938	+	8.38205i	0.000936015	+	0.00162123i
$300$	−3345.40	−	596.242i	−0.643823	−	0.114747i
$301$	6287.01	+	1275.98i	1.20391	+	0.244339i
$302$		−	712.822i		−	0.135822i
$303$	4177.96	−	2412.15i	0.792137	−	0.457340i
$304$	484.318	−	838.863i	0.0913734	−	0.158263i
$305$	714.657	+	4074.97i	0.134168	+	0.765023i
$306$	653.332	+	1131.60i	0.122054	+	0.211404i
$307$		−	3159.64i		−	0.587394i	−0.955899	−	0.293697i	$-0.905114\pi$
$307$		−	3159.64i		−	0.587394i	0.955899	−	0.293697i	$-0.0948857\pi$
$308$	−1111.10	+	372.361i	−0.205555	+	0.0688871i
$309$	−2601.47			−0.478941
$310$	−910.649	+	2494.83i	−0.166843	+	0.457087i
$311$	2292.39	−	3970.53i	0.417972	−	0.723949i	−0.577763	−	0.816205i	$-0.696074\pi$
$311$	2292.39	−	3970.53i	0.417972	−	0.723949i	0.995735	+	0.0922552i	$0.0294076\pi$
$312$	−6.24905	−	3.60789i	−0.00113392	−	0.000654669i
$313$	5977.06	−	3450.86i	1.07937	−	0.623176i	0.148645	−	0.988891i	$-0.452509\pi$
$313$	5977.06	−	3450.86i	1.07937	−	0.623176i	0.930727	+	0.365715i	$0.119175\pi$
$314$	−2215.04			−0.398095
$315$	−2700.08	−	71.9013i	−0.482960	−	0.0128609i
$316$	−5642.57			−1.00449
$317$	−6977.23	+	4028.31i	−1.23622	+	0.713729i	−0.968319	−	0.249718i	$-0.919662\pi$
$317$	−6977.23	+	4028.31i	−1.23622	+	0.713729i	−0.267897	+	0.963448i	$0.586329\pi$
$318$	−1329.19	−	767.406i	−0.234393	−	0.135327i
$319$	−920.372	+	1594.13i	−0.161539	+	0.279794i
$320$	2677.36	+	977.275i	0.467716	+	0.170723i
$321$	−847.914			−0.147433
$322$	−767.938	−	678.760i	−0.132905	−	0.117471i
$323$		−	2419.14i		−	0.416732i
$324$	751.856	+	1302.25i	0.128919	+	0.223294i
$325$	−11.9744	+	14.2173i	−0.00204376	+	0.00242657i
$326$	−655.043	+	1134.57i	−0.111287	+	0.192754i
$327$	5237.19	−	3023.69i	0.885680	−	0.511347i
$328$			1215.94i			0.204692i
$329$	1312.75	+	3917.17i	0.219982	+	0.656415i
$330$	−236.714	+	198.256i	−0.0394870	+	0.0330716i
$331$	549.863	+	952.391i	0.0913088	+	0.158152i	0.908062	−	0.418836i	$-0.137562\pi$
$331$	549.863	+	952.391i	0.0913088	+	0.158152i	−0.816753	+	0.576987i	$0.804228\pi$
$332$	−528.358	−	305.048i	−0.0873416	−	0.0504267i
$333$	−702.414	−	405.539i	−0.115592	−	0.0667370i
$334$	−477.361	−	826.813i	−0.0782036	−	0.135453i
$335$	7491.75	+	8945.05i	1.22185	+	1.45887i
$336$	−3198.47	−	649.144i	−0.519319	−	0.105398i
$337$		−	1968.88i		−	0.318255i	−0.987258	−	0.159128i	$-0.949132\pi$
$337$		−	1968.88i		−	0.318255i	0.987258	−	0.159128i	$-0.0508681\pi$
$338$	1617.71	−	933.988i	0.260331	−	0.150302i
$339$	2885.33	−	4997.54i	0.462270	−	0.800676i
$340$	9441.11	−	1655.76i	1.50593	−	0.264106i
$341$	−1214.60	−	2103.75i	−0.192887	−	0.334090i
$342$		−	227.743i		−	0.0360086i
$343$	−3590.55	+	5240.38i	−0.565223	+	0.824938i
$344$	−4499.33			−0.705196
$345$	2553.65	+	932.116i	0.398503	+	0.145459i
$346$	−529.259	+	916.704i	−0.0822345	+	0.142434i
$347$	−9516.70	−	5494.47i	−1.47229	−	0.850025i	−0.472772	−	0.881185i	$-0.656746\pi$
$347$	−9516.70	−	5494.47i	−1.47229	−	0.850025i	−0.999514	+	0.0311604i	$0.990080\pi$
$348$	−4984.14	+	2877.59i	−0.767752	+	0.443262i
$349$	−1425.64			−0.218661			−0.109330	−	0.994005i	$-0.534871\pi$
$349$	−1425.64			−0.218661			−0.109330	+	0.994005i	$0.534871\pi$
$350$	723.901	−	1830.40i	0.110555	−	0.279540i
$351$	22.2454			0.00338283
$352$	1084.49	−	626.129i	0.164214	−	0.0948091i
$353$	7209.93	+	4162.66i	1.08710	+	0.627637i	0.932803	−	0.360388i	$-0.117356\pi$
$353$	7209.93	+	4162.66i	1.08710	+	0.627637i	0.154296	+	0.988025i	$0.450689\pi$
$354$	−291.856	+	505.509i	−0.0438191	+	0.0758969i
$355$	−5022.91	−	1833.43i	−0.750953	−	0.274108i
$356$	7637.14			1.13699
$357$	−7728.50	+	2590.03i	−1.14576	+	0.383975i
$358$		−	1971.99i		−	0.291125i
$359$	−4172.77	−	7227.45i	−0.613455	−	1.06254i	−0.990653	−	0.136403i	$-0.956446\pi$
$359$	−4172.77	−	7227.45i	−0.613455	−	1.06254i	0.377198	−	0.926133i	$-0.376888\pi$
$360$	1865.91	−	327.239i	0.273173	−	0.0479084i
$361$	3218.68	−	5574.92i	0.469264	−	0.812789i
$362$	−2397.71	+	1384.32i	−0.348123	+	0.200989i
$363$			4689.79i			0.678100i
$364$	−13.2727	+	15.0165i	−0.00191121	+	0.00216231i
$365$	−2169.52	−	2590.37i	−0.311117	−	0.371469i
$366$	587.672	+	1017.88i	0.0839292	+	0.145370i
$367$	−6481.88	−	3742.31i	−0.921938	−	0.532281i	−0.0376853	−	0.999290i	$-0.511998\pi$
$367$	−6481.88	−	3742.31i	−0.921938	−	0.532281i	−0.884253	+	0.467008i	$0.845332\pi$
$368$	−2658.97	−	1535.16i	−0.376653	−	0.217461i
$369$	−610.555	−	1057.51i	−0.0861361	−	0.149192i
$370$	453.131	−	379.511i	0.0636679	−	0.0533239i
$371$	−5926.73	+	6705.40i	−0.829381	+	0.938348i
$372$		−	7595.04i		−	1.05856i
$373$	−5569.81	+	3215.73i	−0.773173	+	0.446392i	−0.834005	−	0.551756i	$-0.813958\pi$
$373$	−5569.81	+	3215.73i	−0.773173	+	0.446392i	0.0608321	+	0.998148i	$0.480625\pi$
$374$	435.480	−	754.273i	0.0602089	−	0.104285i
$375$	−14.4287	+	5220.78i	−0.00198692	+	0.718933i
$376$	−1448.75	−	2509.31i	−0.198707	−	0.344170i
$377$			31.4815i			0.00430075i
$378$	−2233.55	+	748.522i	−0.303919	+	0.101851i
$379$	−5857.64			−0.793896			−0.396948	−	0.917841i	$-0.629931\pi$
$379$	−5857.64			−0.793896			−0.396948	+	0.917841i	$0.629931\pi$
$380$	−1569.36	−	572.839i	−0.211859	−	0.0773316i
$381$	3473.17	−	6015.71i	0.467023	−	0.808908i
$382$	−1592.58	−	919.479i	−0.213308	−	0.123153i
$383$	7965.82	−	4599.07i	1.06275	−	0.613581i	0.136561	−	0.990632i	$-0.456395\pi$
$383$	7965.82	−	4599.07i	1.06275	−	0.613581i	0.926193	+	0.377051i	$0.123062\pi$
$384$	5113.91			0.679605
$385$	858.368	+	1582.59i	0.113627	+	0.209497i
$386$	2192.30			0.289081
$387$	3913.11	−	2259.23i	0.513991	−	0.296753i
$388$	1039.59	+	600.208i	0.136024	+	0.0785334i
$389$	−397.308	+	688.158i	−0.0517849	+	0.0896940i	−0.890756	−	0.454482i	$-0.849824\pi$
$389$	−397.308	+	688.158i	−0.0517849	+	0.0896940i	0.838971	+	0.544176i	$0.183158\pi$
$390$	−1.81070	+	4.96064i	−0.000235099	+	0.000644082i
$391$	−7668.02			−0.991786
$392$	1736.91	−	4102.82i	0.223794	−	0.528631i
$393$			5408.39i			0.694192i
$394$	1472.96	+	2551.24i	0.188342	+	0.326217i
$395$	1497.51	+	8538.80i	0.190754	+	1.08768i
$396$	−412.686	+	714.793i	−0.0523693	+	0.0907063i
$397$	−4195.20	+	2422.10i	−0.530356	+	0.306201i	−0.741161	−	0.671327i	$-0.765725\pi$
$397$	−4195.20	+	2422.10i	−0.530356	+	0.306201i	0.210806	+	0.977528i	$0.432391\pi$
$398$			4084.64i			0.514434i
$399$	1392.28	+	282.568i	0.174689	+	0.0354539i
$400$	1034.62	−	5805.09i	0.129328	−	0.725636i
$401$	2429.80	+	4208.53i	0.302589	+	0.524100i	0.976722	−	0.214511i	$-0.0688157\pi$
$401$	2429.80	+	4208.53i	0.302589	+	0.524100i	−0.674133	+	0.738610i	$0.735482\pi$
$402$	2870.69	+	1657.39i	0.356162	+	0.205630i
$403$	−35.9797	−	20.7729i	−0.00444734	−	0.00256767i
$404$	4698.82	+	8138.59i	0.578651	+	1.00225i
$405$	1771.14	−	1483.38i	0.217305	−	0.181999i
$406$	−1059.30	−	3160.89i	−0.129488	−	0.386385i
$407$			540.626i			0.0658423i
$408$	4950.83	−	2858.36i	0.600741	−	0.346838i
$409$	25.1554	−	43.5705i	0.00304121	−	0.00526753i	−0.864501	−	0.502631i	$-0.832365\pi$
$409$	25.1554	−	43.5705i	0.00304121	−	0.00526753i	0.867542	+	0.497364i	$0.165699\pi$
$410$	876.492	−	153.717i	0.105578	−	0.0185159i
$411$	613.938	+	1063.37i	0.0736820	+	0.127621i
$412$		−	5067.63i		−	0.605981i
$413$	2550.16	+	2254.02i	0.303838	+	0.268555i
$414$	−721.886			−0.0856975
$415$	−321.399	+	880.512i	−0.0380165	+	0.104151i
$416$	10.7085	−	18.5476i	0.00126208	−	0.00218599i
$417$	3804.49	+	2196.52i	0.446779	+	0.257948i
$418$	−131.465	+	75.9014i	−0.0153832	+	0.00888148i
$419$	1114.91			0.129993			0.0649965	−	0.997885i	$-0.479296\pi$
$419$	1114.91			0.129993			0.0649965	+	0.997885i	$0.479296\pi$
$420$	−149.843	+	5627.00i	−0.0174086	+	0.653737i
$421$	6534.99			0.756522			0.378261	−	0.925699i	$-0.376522\pi$
$421$	6534.99			0.756522			0.378261	+	0.925699i	$0.376522\pi$
$422$	480.695	−	277.529i	0.0554499	−	0.0320140i
$423$	2519.99	+	1454.91i	0.289659	+	0.167235i
$424$	3138.30	−	5435.69i	0.359455	−	0.622595i
$425$	−5011.25	−	13847.6i	−0.571956	−	1.58049i
$426$	−1519.07			−0.172768
$427$	6498.03	−	2177.67i	0.736444	−	0.246802i
$428$		−	1651.72i		−	0.186540i
$429$	−2.41508	−	4.18303i	−0.000271797	−	0.000470766i
$430$	568.797	+	3243.28i	0.0637903	+	0.363732i
$431$	−3693.03	+	6396.51i	−0.412730	+	0.714870i	−0.995187	−	0.0979917i	$-0.968758\pi$
$431$	−3693.03	+	6396.51i	−0.412730	+	0.714870i	0.582457	+	0.812862i	$0.302091\pi$
$432$	−6111.32	+	3528.37i	−0.680627	+	0.392960i
$433$		−	13486.9i		−	1.49686i	−0.663213	−	0.748431i	$-0.730808\pi$
$433$		−	13486.9i		−	1.49686i	0.663213	−	0.748431i	$-0.269192\pi$
$434$	4311.50	+	875.038i	0.476864	+	0.0967815i
$435$	5677.37	+	6778.70i	0.625768	+	0.747158i
$436$	5890.10	+	10202.0i	0.646984	+	1.12061i
$437$	1157.43	+	668.244i	0.126699	+	0.0731498i
$438$	−831.315	−	479.960i	−0.0906889	−	0.0523593i
$439$	1492.30	+	2584.74i	0.162240	+	0.281009i	0.935672	−	0.352871i	$-0.114795\pi$
$439$	1492.30	+	2584.74i	0.162240	+	0.281009i	−0.773431	+	0.633880i	$0.781461\pi$
$440$	−810.763	−	968.040i	−0.0878446	−	0.104885i
$441$	549.525	+	4440.41i	0.0593375	+	0.479474i
$442$		−	14.8957i		−	0.00160298i
$443$	−5232.62	+	3021.06i	−0.561195	+	0.324006i	−0.753625	−	0.657305i	$-0.771697\pi$
$443$	−5232.62	+	3021.06i	−0.561195	+	0.324006i	0.192430	+	0.981311i	$0.438363\pi$
$444$	−845.148	+	1463.84i	−0.0903354	+	0.156466i
$445$	−2026.86	−	11557.1i	−0.215916	−	1.23115i
$446$	216.452	+	374.905i	0.0229805	+	0.0398033i
$447$			2563.16i			0.271216i
$448$	939.059	−	4626.95i	0.0990321	−	0.487952i
$449$	−37.9318			−0.00398689			−0.00199344	−	0.999998i	$-0.500635\pi$
$449$	−37.9318			−0.00398689			−0.00199344	+	0.999998i	$0.500635\pi$
$450$	−471.771	−	1303.65i	−0.0494211	−	0.136566i
$451$	−406.967	+	704.887i	−0.0424907	+	0.0735961i
$452$	9735.12	+	5620.58i	1.01306	+	0.584889i
$453$	2712.30	−	1565.95i	0.281314	−	0.162416i
$454$	381.316			0.0394186
$455$	26.2468	+	16.1000i	0.00270432	+	0.00165886i
$456$	−996.389			−0.102325
$457$	−6391.22	+	3689.97i	−0.654199	+	0.377702i	−0.790063	−	0.613026i	$-0.789952\pi$
$457$	−6391.22	+	3689.97i	−0.654199	+	0.377702i	0.135864	+	0.990727i	$0.456619\pi$
$458$	−3530.73	−	2038.47i	−0.360219	−	0.207972i
$459$	−8812.00	+	15262.8i	−0.896098	+	1.55209i
$460$	−1815.75	+	4974.46i	−0.184043	+	0.504207i
$461$	−14713.8			−1.48653			−0.743263	−	0.668999i	$-0.766723\pi$
$461$	−14713.8			−1.48653			−0.743263	+	0.668999i	$0.766723\pi$
$462$	383.237	+	338.733i	0.0385926	+	0.0341110i
$463$			5039.14i			0.505807i	0.967491	+	0.252904i	$0.0813856\pi$
$463$			5039.14i			0.505807i	−0.967491	+	0.252904i	$0.918614\pi$
$464$	−4993.32	−	8648.68i	−0.499588	−	0.865312i
$465$	−11493.4	+	2015.69i	−1.14623	+	0.201022i
$466$	2080.88	−	3604.19i	0.206856	−	0.358285i
$467$	3018.55	−	1742.76i	0.299104	−	0.172688i	−0.342936	−	0.939359i	$-0.611421\pi$
$467$	3018.55	−	1742.76i	0.299104	−	0.172688i	0.642040	+	0.766671i	$0.278088\pi$
$468$			14.1160i			0.00139426i
$469$	12800.1	−	14481.9i	1.26025	−	1.42582i
$470$	−1625.65	+	1361.54i	−0.159544	+	0.133623i
$471$	−4866.06	−	8428.26i	−0.476043	−	0.824530i
$472$	−2067.27	−	1193.54i	−0.201597	−	0.116392i
$473$	−2608.29	−	1505.90i	−0.253550	−	0.146387i
$474$	1231.42	+	2132.89i	0.119327	+	0.206681i
$475$	−450.366	+	2526.92i	−0.0435036	+	0.244090i
$476$	−5045.34	−	15055.0i	−0.485825	−	1.44967i
$477$			6303.29i			0.605048i
$478$	3506.62	−	2024.55i	0.335542	−	0.193725i
$479$	3966.64	−	6870.42i	0.378372	−	0.655360i	−0.612453	−	0.790507i	$-0.709817\pi$
$479$	3966.64	−	6870.42i	0.378372	−	0.655360i	0.990826	+	0.135147i	$0.0431507\pi$
$480$	−1039.09	−	5924.88i	−0.0988078	−	0.563401i
$481$	4.62306	+	8.00737i	0.000438240	+	0.000759053i
$482$			3027.19i			0.286068i
$483$	895.666	−	4413.14i	0.0843772	−	0.415745i
$484$	−9135.64			−0.857968
$485$	632.382	−	1732.49i	0.0592061	−	0.162202i
$486$	−1388.93	+	2405.70i	−0.129636	+	0.224536i
$487$	3545.42	+	2046.95i	0.329894	+	0.190464i	0.655794	−	0.754940i	$-0.272334\pi$
$487$	3545.42	+	2046.95i	0.329894	+	0.190464i	−0.325900	+	0.945404i	$0.605667\pi$
$488$	−4162.59	+	2403.27i	−0.386131	+	0.222933i
$489$	−5756.07			−0.532308
$490$	−3177.04	−	733.359i	−0.292906	−	0.0676118i
$491$	18968.8			1.74349			0.871743	−	0.489963i	$-0.162990\pi$
$491$	18968.8			1.74349			0.871743	+	0.489963i	$0.162990\pi$
$492$	−2203.87	+	1272.40i	−0.201947	+	0.116594i
$493$	−21599.8	−	12470.7i	−1.97324	−	1.13925i
$494$	−1.29811	+	2.24840i	−0.000118228	+	0.000204778i
$495$	1191.21	+	434.807i	0.108163	+	0.0394811i
$496$	13179.2			1.19308
$497$	−1761.74	+	8680.45i	−0.159003	+	0.783444i
$498$			266.292i			0.0239615i
$499$	−5228.23	−	9055.57i	−0.469034	−	0.812390i	0.530340	−	0.847785i	$-0.322064\pi$
$499$	−5228.23	−	9055.57i	−0.469034	−	0.812390i	−0.999373	+	0.0353949i	$0.988731\pi$
$500$	−10170.0	−	28.1068i	−0.909631	−	0.00251395i
$501$	2097.36	−	3632.73i	0.187032	−	0.323949i
$502$	1688.53	−	974.872i	0.150125	−	0.0866746i
$503$			12719.0i			1.12746i	0.825960	+	0.563729i	$0.190634\pi$
$503$			12719.0i			1.12746i	−0.825960	+	0.563729i	$0.809366\pi$
$504$	−997.146	−	2975.43i	−0.0881278	−	0.262968i
$505$	11068.9	−	9270.58i	0.975369	−	0.816902i
$506$	240.587	+	416.709i	0.0211372	+	0.0366106i
$507$	7107.69	+	4103.62i	0.622610	+	0.359464i
$508$	11718.5	+	6765.68i	1.02347	+	0.590902i
$509$	8386.16	+	14525.3i	0.730275	+	1.26487i	0.956766	+	0.290860i	$0.0939414\pi$
$509$	8386.16	+	14525.3i	0.730275	+	1.26487i	−0.226491	+	0.974013i	$0.572725\pi$
$510$	−2686.28	−	3207.38i	−0.233237	−	0.278481i
$511$	−3706.76	+	4193.77i	−0.320895	+	0.363055i
$512$			11695.8i			1.00954i
$513$	2660.22	−	1535.88i	0.228950	−	0.132184i
$514$	−1006.16	+	1742.71i	−0.0863417	+	0.149548i
$515$	−7668.74	+	1344.92i	−0.656166	+	0.115077i
$516$	−4708.27	−	8154.96i	−0.401686	−	0.695740i
$517$		−	1939.55i		−	0.164993i
$518$	−733.611	−	648.419i	−0.0622259	−	0.0549998i
$519$	−4650.77			−0.393345
$520$	−20.2865	−	7.40484i	−0.00171081	−	0.000624469i
$521$	−2170.69	+	3759.74i	−0.182533	+	0.316156i	−0.942742	−	0.333522i	$-0.891763\pi$
$521$	−2170.69	+	3759.74i	−0.182533	+	0.316156i	0.760210	+	0.649678i	$0.225096\pi$
$522$	−2033.46	−	1174.02i	−0.170502	−	0.0984395i
$523$	−9905.69	+	5719.05i	−0.828194	+	0.478158i	−0.853234	−	0.521528i	$-0.825362\pi$
$523$	−9905.69	+	5719.05i	−0.828194	+	0.478158i	0.0250400	+	0.999686i	$0.492029\pi$
$524$	−10535.5			−0.878328
$525$	8555.01	−	1266.62i	0.711183	−	0.105295i
$526$	−2237.47			−0.185472
$527$	28505.0	−	16457.4i	2.35616	−	1.36033i
$528$	1326.95	+	766.115i	0.109371	+	0.0631456i
$529$	−3965.35	+	6868.18i	−0.325910	+	0.564493i
$530$	−4314.98	−	1575.03i	−0.353643	−	0.129084i
$531$	2397.23			0.195915
$532$	−550.438	+	2712.13i	−0.0448581	+	0.221026i
$533$			13.9204i			0.00113126i
$534$	−1666.71	−	2886.83i	−0.135067	−	0.233943i
$535$	−2499.52	+	438.359i	−0.201988	+	0.0354241i
$536$	−6777.88	+	11739.6i	−0.546194	+	0.946035i
$537$	7503.46	−	4332.13i	0.602976	−	0.348129i
$538$			688.609i			0.0551823i
$539$	2380.09	−	1797.09i	0.190200	−	0.143611i
$540$	7814.80	+	9330.75i	0.622769	+	0.743577i
$541$	−1856.91	−	3216.26i	−0.147569	−	0.255597i	0.782760	−	0.622324i	$-0.213811\pi$
$541$	−1856.91	−	3216.26i	−0.147569	−	0.255597i	−0.930328	+	0.366728i	$0.880478\pi$
$542$	−464.860	−	268.387i	−0.0368403	−	0.0212697i
$543$	−10534.7	−	6082.22i	−0.832574	−	0.480687i
$544$	8483.80	+	14694.4i	0.668639	+	1.15812i
$545$	13875.2	−	11620.9i	1.09055	−	0.913369i
$546$	8.57285	+	1.73990i	0.000671949	+	0.000136375i
$547$			14861.2i			1.16164i	0.814030	+	0.580822i	$0.197269\pi$
$547$			14861.2i			1.16164i	−0.814030	+	0.580822i	$0.802731\pi$
$548$	−2071.43	+	1195.94i	−0.161473	+	0.0932264i
$549$	2413.50	−	4180.30i	0.187624	−	0.324974i
$550$	−595.303	+	706.805i	−0.0461524	+	0.0547969i
$551$	2173.56	+	3764.72i	0.168052	+	0.291075i
$552$			3158.29i			0.243525i
$553$	13616.1	−	4563.14i	1.04705	−	0.350894i
$554$	4579.20			0.351176
$555$	2439.50	+	890.450i	0.186578	+	0.0681036i
$556$	−4278.79	+	7411.09i	−0.326369	+	0.565288i
$557$	−3280.94	−	1894.25i	−0.249583	−	0.144097i	0.369990	−	0.929036i	$-0.379361\pi$
$557$	−3280.94	−	1894.25i	−0.249583	−	0.144097i	−0.619573	+	0.784939i	$0.712694\pi$
$558$	2683.53	−	1549.34i	0.203589	−	0.117542i
$559$	−51.5096			−0.00389736
$560$	−9764.21	−	260.014i	−0.736809	−	0.0196207i
$561$	3826.70			0.287992
$562$	−2079.03	+	1200.33i	−0.156047	+	0.0900939i
$563$	9307.44	+	5373.65i	0.696735	+	0.402260i	0.806130	−	0.591738i	$-0.201558\pi$
$563$	9307.44	+	5373.65i	0.696735	+	0.402260i	−0.109395	+	0.993998i	$0.534891\pi$
$564$	3032.06	−	5251.67i	0.226370	−	0.392084i
$565$	5921.86	−	16223.7i	0.440946	−	1.20803i
$566$	4912.23			0.364799
$567$	−2867.44	−	2534.45i	−0.212383	−	0.187720i
$568$		−	6212.21i		−	0.458906i
$569$	−259.548	−	449.550i	−0.0191227	−	0.0331215i	0.856306	−	0.516469i	$-0.172754\pi$
$569$	−259.548	−	449.550i	−0.0191227	−	0.0331215i	−0.875428	+	0.483348i	$0.839421\pi$
$570$	125.962	+	718.233i	0.00925606	+	0.0527780i
$571$	4878.00	−	8448.95i	0.357510	−	0.619225i	−0.630034	−	0.776567i	$-0.716959\pi$
$571$	4878.00	−	8448.95i	0.357510	−	0.619225i	0.987544	+	0.157342i	$0.0502925\pi$
$572$	8.14848	−	4.70453i	0.000595638	−	0.000343892i
$573$		−	8079.75i		−	0.589069i
$574$	−468.398	−	1397.67i	−0.0340602	−	0.101634i
$575$	8009.65	+	1427.54i	0.580914	+	0.103535i
$576$	−1662.69	−	2879.87i	−0.120276	−	0.208324i
$577$	9730.30	+	5617.79i	0.702041	+	0.405323i	0.808107	−	0.589036i	$-0.200492\pi$
$577$	9730.30	+	5617.79i	0.702041	+	0.405323i	−0.106066	+	0.994359i	$0.533826\pi$
$578$	6602.47	+	3811.94i	0.475133	+	0.274318i
$579$	4816.12	+	8341.76i	0.345684	+	0.598742i
$580$	−13204.8	+	11059.4i	−0.945344	+	0.791755i
$581$	1521.68	+	308.831i	0.108657	+	0.0220524i
$582$		−	523.953i		−	0.0373171i
$583$	3638.58	−	2100.73i	0.258481	−	0.149234i
$584$	1962.79	−	3399.65i	0.139077	−	0.240888i
$585$	21.3615	−	3.74632i	0.00150973	−	0.000264772i
$586$	−2606.92	−	4515.31i	−0.183773	−	0.318303i
$587$		−	16873.7i		−	1.18646i	−0.805034	−	0.593229i	$-0.797853\pi$
$587$		−	16873.7i		−	1.18646i	0.805034	−	0.593229i	$-0.202147\pi$
$588$	9253.85	−	1145.21i	0.649018	−	0.0803195i
$589$	−5736.84			−0.401328
$590$	−599.005	+	1641.05i	−0.0417977	+	0.114510i
$591$	−6471.68	+	11209.3i	−0.450439	+	0.780183i
$592$	−2540.11	−	1466.54i	−0.176348	−	0.101815i
$593$	−20740.4	+	11974.5i	−1.43627	+	0.829229i	−0.997588	−	0.0694150i	$-0.977887\pi$
$593$	−20740.4	+	11974.5i	−1.43627	+	0.829229i	−0.438679	+	0.898644i	$0.644553\pi$
$594$	1105.92			0.0763914
$595$	−21443.4	+	11630.5i	−1.47747	+	0.801354i
$596$	−4993.00			−0.343157
$597$	−15542.2	+	8973.26i	−1.06549	+	0.615161i
$598$	7.12682	+	4.11467i	0.000487353	+	0.000281373i
$599$	−1161.71	+	2012.15i	−0.0792427	+	0.137252i	−0.902923	−	0.429801i	$-0.858584\pi$
$599$	−1161.71	+	2012.15i	−0.0792427	+	0.137252i	0.823681	+	0.567054i	$0.191917\pi$
$600$	−5703.53	+	2064.02i	−0.388076	+	0.140439i
$601$	−6094.01			−0.413611			−0.206805	−	0.978382i	$-0.566307\pi$
$601$	−6094.01			−0.413611			−0.206805	+	0.978382i	$0.566307\pi$
$602$	5171.80	−	1733.21i	0.350144	−	0.117343i
$603$		−	13613.4i		−	0.919372i
$604$	3050.44	+	5283.52i	0.205498	+	0.355933i
$605$	2424.55	+	13824.8i	0.162929	+	0.929021i
$606$	2050.92	−	3552.30i	0.137480	−	0.238123i
$607$	−15875.2	+	9165.55i	−1.06154	+	0.612880i	−0.925858	−	0.377872i	$-0.876656\pi$
$607$	−15875.2	+	9165.55i	−1.06154	+	0.612880i	−0.135682	+	0.990752i	$0.543323\pi$
$608$		−	2957.35i		−	0.197264i
$609$	9700.16	−	10974.6i	0.645436	−	0.730236i
$610$	2258.59	+	2696.73i	0.149914	+	0.178996i
$611$	−16.5857	−	28.7273i	−0.00109818	−	0.00190210i
$612$	−9685.15	−	5591.72i	−0.639704	−	0.369333i
$613$	−1896.80	−	1095.12i	−0.124977	−	0.0721557i	0.436208	−	0.899846i	$-0.356321\pi$
$613$	−1896.80	−	1095.12i	−0.124977	−	0.0721557i	−0.561185	+	0.827690i	$0.689655\pi$
$614$	−1343.24	−	2326.55i	−0.0882877	−	0.152919i
$615$	2510.40	+	2997.38i	0.164600	+	0.196530i
$616$	−1385.24	+	1567.24i	−0.0906055	+	0.102510i
$617$		−	9759.14i		−	0.636772i	−0.947961	−	0.318386i	$-0.896859\pi$
$617$		−	9759.14i		−	0.636772i	0.947961	−	0.318386i	$-0.103141\pi$
$618$	−1915.56	+	1105.95i	−0.124685	+	0.0719867i
$619$	7612.84	−	13185.8i	0.494323	−	0.856192i	−0.505656	−	0.862735i	$-0.668749\pi$
$619$	7612.84	−	13185.8i	0.494323	−	0.856192i	0.999979	+	0.00654301i	$0.00208272\pi$
$620$	−3926.53	−	22389.0i	−0.254344	−	1.45027i
$621$	−4868.32	−	8432.18i	−0.314588	−	0.544882i
$622$		−	3898.20i		−	0.251292i
$623$	−18429.3	+	6176.15i	−1.18516	+	0.397178i
$624$	26.2051			0.00168116
$625$	2656.53	+	15397.5i	0.170018	+	0.985441i
$626$	2934.08	−	5081.98i	0.187332	−	0.324468i
$627$	−577.613	−	333.485i	−0.0367905	−	0.0212410i
$628$	16418.1	−	9479.00i	1.04324	−	0.602314i
$629$	−7325.26			−0.464352
$630$	−2018.74	+	1094.93i	−0.127664	+	0.0692427i
$631$	75.5019			0.00476337			0.00238168	−	0.999997i	$-0.499242\pi$
$631$	75.5019			0.00476337			0.00238168	+	0.999997i	$0.499242\pi$
$632$	−8722.41	+	5035.88i	−0.548985	+	0.316957i
$633$	2112.01	+	1219.37i	0.132614	+	0.0765649i
$634$	−3425.06	+	5932.37i	−0.214553	+	0.371616i
$635$	7128.34	−	19529.0i	0.445480	−	1.22045i
$636$	13136.1			0.818995
$637$	19.8847	−	46.9702i	0.00123683	−	0.00292155i
$638$			1565.09i			0.0971198i
$639$	3119.32	+	5402.82i	0.193112	+	0.334479i
$640$	15075.0	−	2643.82i	0.931083	−	0.163291i
$641$	11208.5	−	19413.7i	0.690654	−	1.19625i	−0.280969	−	0.959717i	$-0.590656\pi$
$641$	11208.5	−	19413.7i	0.690654	−	1.19625i	0.971624	−	0.236532i	$-0.0760107\pi$
$642$	−624.350	+	360.468i	−0.0383818	+	0.0221597i
$643$			16435.4i			1.00801i	0.863702	+	0.504003i	$0.168140\pi$
$643$			16435.4i			1.00801i	−0.863702	+	0.504003i	$0.831860\pi$
$644$	8596.72	+	1744.74i	0.526022	+	0.106758i
$645$	−11091.2	+	9289.22i	−0.677078	+	0.567074i
$646$	−1028.43	−	1781.30i	−0.0626365	−	0.108490i
$647$	−19522.6	−	11271.4i	−1.18626	−	0.684889i	−0.228808	−	0.973472i	$-0.573483\pi$
$647$	−19522.6	−	11271.4i	−1.18626	−	0.684889i	−0.957455	+	0.288582i	$0.906816\pi$
$648$	2324.47	+	1342.03i	0.140916	+	0.0813581i
$649$	−798.940	−	1383.80i	−0.0483222	−	0.0836966i
$650$	−2.77310	+	15.5593i	−0.000167338	+	0.000938903i
$651$	6142.10	+	18327.7i	0.369782	+	1.10341i
$652$		−	11212.7i		−	0.673504i
$653$	−13238.6	+	7643.29i	−0.793361	+	0.458047i	−0.841145	−	0.540810i	$-0.818118\pi$
$653$	−13238.6	+	7643.29i	−0.793361	+	0.458047i	0.0477832	+	0.998858i	$0.484784\pi$
$654$	2570.89	−	4452.91i	0.153715	−	0.266242i
$655$	2796.06	+	15943.1i	0.166796	+	0.951067i
$656$	−2207.93	−	3824.24i	−0.131410	−	0.227609i
$657$			3942.27i			0.234099i
$658$	2631.91	+	2326.27i	0.155931	+	0.137823i
$659$	−27936.7			−1.65138			−0.825690	−	0.564125i	$-0.809214\pi$
$659$	−27936.7			−1.65138			−0.825690	+	0.564125i	$0.809214\pi$
$660$	906.142	−	2482.49i	0.0534417	−	0.146410i
$661$	−7368.72	+	12763.0i	−0.433600	+	0.751018i	−0.997180	−	0.0750437i	$-0.976090\pi$
$661$	−7368.72	+	12763.0i	−0.433600	+	0.751018i	0.563580	+	0.826062i	$0.309424\pi$
$662$	809.768	+	467.520i	0.0475416	+	0.0274482i
$663$	56.6784	−	32.7233i	0.00332007	−	0.00191684i
$664$	−1089.00			−0.0636464
$665$	4250.30	+	113.182i	0.247849	+	0.00660004i
$666$	−689.617			−0.0401233
$667$	11933.1	−	6889.60i	0.692733	−	0.399950i
$668$	7076.50	+	4085.62i	0.409878	+	0.236643i
$669$	−951.015	+	1647.21i	−0.0549602	+	0.0951938i
$670$	9319.20	+	3401.64i	0.537361	+	0.196144i
$671$	−3217.44			−0.185109
$672$	−9447.94	+	3166.26i	−0.542354	+	0.181758i
$673$			4686.20i			0.268410i	0.990954	+	0.134205i	$0.0428480\pi$
$673$			4686.20i			0.268410i	−0.990954	+	0.134205i	$0.957152\pi$
$674$	−837.019	−	1449.76i	−0.0478350	−	0.0828526i
$675$	12046.0	−	14302.3i	0.686893	−	0.815551i
$676$	−7993.79	+	13845.7i	−0.454813	+	0.787759i
$677$	7735.29	−	4465.97i	0.439131	−	0.253532i	−0.264098	−	0.964496i	$-0.585074\pi$
$677$	7735.29	−	4465.97i	0.439131	−	0.253532i	0.703229	+	0.710964i	$0.251741\pi$
$678$		−	4906.49i		−	0.277924i
$679$	−2994.03	−	607.652i	−0.169220	−	0.0343440i
$680$	13116.5	−	10985.5i	0.739701	−	0.619522i
$681$	837.687	+	1450.92i	0.0471369	+	0.0816435i
$682$	−1788.71	−	1032.71i	−0.100430	−	0.0579834i
$683$	21786.6	+	12578.5i	1.22056	+	0.704691i	0.965037	−	0.262112i	$-0.0844190\pi$
$683$	21786.6	+	12578.5i	1.22056	+	0.704691i	0.255523	+	0.966803i	$0.417752\pi$
$684$	974.603	+	1688.06i	0.0544808	+	0.0943635i
$685$	2359.54	+	2817.26i	0.131611	+	0.157142i
$686$	−416.045	+	5385.11i	−0.0231555	+	0.299715i
$687$		−	17912.7i		−	0.994775i
$688$	14150.8	−	8169.98i	0.784150	−	0.452729i
$689$	35.9281	−	62.2292i	0.00198657	−	0.00344085i
$690$	2276.61	−	399.265i	0.125607	−	0.0220286i
$691$	1547.06	+	2679.58i	0.0851706	+	0.147520i	0.905464	−	0.424423i	$-0.139523\pi$
$691$	1547.06	+	2679.58i	0.0851706	+	0.147520i	−0.820293	+	0.571943i	$0.806190\pi$
$692$		−	9059.62i		−	0.497681i
$693$	417.804	−	2058.61i	0.0229020	−	0.112843i
$694$	−9343.32			−0.511048
$695$	12350.6	+	4508.15i	0.674081	+	0.246049i
$696$	−5136.39	+	8896.49i	−0.279733	+	0.484512i
$697$	−9550.93	−	5514.23i	−0.519035	−	0.299665i
$698$	−1049.75	+	606.072i	−0.0569248	+	0.0328656i
$699$	18285.3			0.989435
$700$	2467.36	+	16665.0i	0.133225	+	0.899826i
$701$	−9365.19			−0.504591			−0.252296	−	0.967650i	$-0.581186\pi$
$701$	−9365.19			−0.504591			−0.252296	+	0.967650i	$0.581186\pi$
$702$	16.3801	−	9.45707i	0.000880666	−	0.000508453i
$703$	1105.70	+	638.373i	0.0593202	+	0.0342485i
$704$	−1108.27	+	1919.58i	−0.0593317	+	0.102766i
$705$	−8751.95	−	3194.58i	−0.467543	−	0.170660i
$706$	7078.58			0.377345
$707$	−17920.4	−	15839.4i	−0.953277	−	0.842576i
$708$		−	4995.86i		−	0.265192i
$709$	3277.65	+	5677.06i	0.173617	+	0.300714i	0.939682	−	0.342049i	$-0.111121\pi$
$709$	3277.65	+	5677.06i	0.173617	+	0.300714i	−0.766065	+	0.642764i	$0.777788\pi$
$710$	−4477.99	+	785.337i	−0.236698	+	0.0415115i
$711$	5057.31	−	8759.51i	0.266756	−	0.462036i
$712$	11805.7	−	6816.00i	0.621399	−	0.358765i
$713$			18184.2i			0.955126i
$714$	−4589.69	+	5192.70i	−0.240567	+	0.272174i
$715$	−9.28184	−	11.0824i	−0.000485484	−	0.000579661i
$716$	8438.91	+	14616.6i	0.440470	+	0.762917i
$717$	15406.9	+	8895.17i	0.802483	+	0.463314i
$718$	−6145.13	−	3547.89i	−0.319407	−	0.184410i
$719$	4294.75	+	7438.72i	0.222764	+	0.385838i	0.955646	−	0.294517i	$-0.0951589\pi$
$719$	4294.75	+	7438.72i	0.222764	+	0.385838i	−0.732883	+	0.680355i	$0.761826\pi$
$720$	−5274.27	+	4417.37i	−0.273001	+	0.228647i
$721$	4098.18	+	12228.7i	0.211684	+	0.631653i
$722$		−	5473.35i		−	0.282129i
$723$	−11518.5	+	6650.22i	−0.592501	+	0.342081i
$724$	11848.1	−	20521.4i	0.608190	−	1.05342i
$725$	20240.5	+	17047.5i	1.03685	+	0.873278i
$726$	1993.74	+	3453.26i	0.101921	+	0.176533i
$727$			17607.5i			0.898246i	0.893470	+	0.449123i	$0.148264\pi$
$727$			17607.5i			0.898246i	−0.893470	+	0.449123i	$0.851736\pi$
$728$	−7.11528	+	35.0585i	−0.000362239	+	0.00178483i
$729$	−17784.2			−0.903529
$730$	−2698.72	−	985.070i	−0.136828	−	0.0499440i
$731$	20404.3	−	35341.3i	1.03239	−	1.78816i
$732$	−8711.78	−	5029.75i	−0.439886	−	0.253968i
$733$	17807.4	−	10281.1i	0.897313	−	0.518064i	0.0209856	−	0.999780i	$-0.493320\pi$
$733$	17807.4	−	10281.1i	0.897313	−	0.518064i	0.876327	+	0.481716i	$0.159986\pi$
$734$	−6363.79			−0.320016
$735$	−4188.96	−	13699.7i	−0.210221	−	0.687514i
$736$	−9374.00			−0.469470
$737$	−7858.36	+	4537.03i	−0.392763	+	0.226762i
$738$	−899.148	−	519.123i	−0.0448484	−	0.0258932i
$739$	−6081.28	+	10533.1i	−0.302711	+	0.524311i	−0.976749	−	0.214386i	$-0.931225\pi$
$739$	−6081.28	+	10533.1i	−0.302711	+	0.524311i	0.674038	+	0.738697i	$0.264558\pi$
$740$	−1734.58	+	4752.10i	−0.0861683	+	0.236069i
$741$	−11.4069			−0.000565512
$742$	−1513.44	+	7457.02i	−0.0748787	+	0.368943i
$743$			3411.65i			0.168454i	0.996447	+	0.0842270i	$0.0268421\pi$
$743$			3411.65i			0.168454i	−0.996447	+	0.0842270i	$0.973158\pi$
$744$	−6778.43	−	11740.6i	−0.334018	−	0.578536i
$745$	1325.12	+	7555.82i	0.0651659	+	0.371575i
$746$	−2734.17	+	4735.72i	−0.134189	+	0.232422i
$747$	947.110	−	546.814i	0.0463895	−	0.0267830i
$748$			7454.35i			0.364382i
$749$	1335.75	+	3985.79i	0.0651630	+	0.194443i
$750$	2208.85	+	3850.38i	0.107541	+	0.187461i
$751$	−13872.7	−	24028.2i	−0.674064	−	1.16751i	−0.976742	−	0.214420i	$-0.931214\pi$
$751$	−13872.7	−	24028.2i	−0.674064	−	1.16751i	0.302678	−	0.953093i	$-0.402119\pi$
$752$	9112.93	+	5261.35i	0.441907	+	0.255135i
$753$	7418.82	+	4283.25i	0.359039	+	0.207291i
$754$	13.3836	+	23.1810i	0.000646419	+	0.00111963i
$755$	7185.88	−	6018.39i	0.346385	−	0.290108i
$756$	13352.1	−	15106.3i	0.642342	−	0.726736i
$757$			7942.09i			0.381321i	0.981656	+	0.190661i	$0.0610630\pi$
$757$			7942.09i			0.381321i	−0.981656	+	0.190661i	$0.938937\pi$
$758$	−4313.19	+	2490.22i	−0.206678	+	0.119326i
$759$	−1057.06	+	1830.88i	−0.0505517	+	0.0875582i
$760$	−2937.20	+	515.118i	−0.140189	+	0.0245859i
$761$	923.069	+	1598.80i	0.0439701	+	0.0761584i	0.887173	−	0.461437i	$-0.152666\pi$
$761$	923.069	+	1598.80i	0.0439701	+	0.0761584i	−0.843203	+	0.537596i	$0.819333\pi$
$762$		−	5906.11i		−	0.280782i
$763$	−22463.8	−	19855.1i	−1.06585	−	0.942076i
$764$	15739.2			0.745321
$765$	−5891.46	+	16140.4i	−0.278439	+	0.762819i
$766$	3910.35	−	6772.92i	0.184447	−	0.319472i
$767$	−23.6667	−	13.6640i	−0.00111415	−	0.000643256i
$768$	−2832.33	+	1635.25i	−0.133077	+	0.0768319i
$769$	5797.73			0.271874			0.135937	−	0.990717i	$-0.456595\pi$
$769$	5797.73			0.271874			0.135937	+	0.990717i	$0.456595\pi$
$770$	1304.84	+	800.405i	0.0610692	+	0.0374605i
$771$	−8841.41			−0.412990
$772$	−16249.6	+	9381.72i	−0.757560	+	0.437377i
$773$	−6785.24	−	3917.46i	−0.315716	−	0.182279i	0.333766	−	0.942656i	$-0.391681\pi$
$773$	−6785.24	−	3917.46i	−0.315716	−	0.182279i	−0.649481	+	0.760378i	$0.725014\pi$
$774$	1920.91	−	3327.11i	0.0892062	−	0.154510i
$775$	−32838.8	+	11883.9i	−1.52207	+	0.550815i
$776$	2142.70			0.0991215
$777$	855.630	−	4215.87i	0.0395052	−	0.194651i
$778$			675.620i			0.0311339i
$779$	961.096	+	1664.67i	0.0442039	+	0.0765634i
$780$	−7.80737	−	44.5176i	−0.000358396	−	0.00204357i
$781$	2079.19	−	3601.26i	0.0952614	−	0.164998i
$782$	−5646.24	+	3259.86i	−0.258196	+	0.149069i
$783$		−	31669.8i		−	1.44545i
$784$	1987.22	+	16057.7i	0.0905259	+	0.731490i
$785$	−18701.7	−	22329.5i	−0.850308	−	1.01526i
$786$	2299.24	+	3982.40i	0.104340	+	0.180722i
$787$	14009.5	+	8088.41i	0.634544	+	0.366354i	0.782510	−	0.622638i	$-0.213939\pi$
$787$	14009.5	+	8088.41i	0.634544	+	0.366354i	−0.147966	+	0.988992i	$0.547273\pi$
$788$	−21835.5	−	12606.7i	−0.987128	−	0.569918i
$789$	−4915.34	−	8513.63i	−0.221788	−	0.384148i
$790$	4732.72	+	5650.80i	0.213142	+	0.254489i
$791$	−28037.3	−	5690.29i	−1.26029	−	0.255782i
$792$			1473.26i			0.0660983i
$793$	−47.6545	+	27.5133i	−0.00213400	+	0.00123206i
$794$	−2059.39	+	3566.96i	−0.0920465	+	0.159429i
$795$	−3486.26	−	19878.6i	−0.155528	−	0.886821i
$796$	−17479.8	−	30275.8i	−0.778334	−	1.34811i
$797$			14662.9i			0.651677i	0.945425	+	0.325838i	$0.105647\pi$
$797$			14662.9i			0.651677i	−0.945425	+	0.325838i	$0.894353\pi$
$798$	1145.31	−	383.824i	0.0508064	−	0.0170266i
$799$	26280.1			1.16361
$800$	−6126.15	−	16928.5i	−0.270740	−	0.748139i
$801$	−6844.99	+	11855.9i	−0.301943	+	0.522980i
$802$	3578.29	+	2065.93i	0.157549	+	0.0909607i
$803$	2275.68	−	1313.86i	0.100009	−	0.0577401i
$804$	−28370.5			−1.24447
$805$	358.758	−	13472.3i	0.0157075	−	0.589859i
$806$	−35.3242			−0.00154372
$807$	−2620.17	+	1512.76i	−0.114293	+	0.0659871i
$808$	14527.1	+	8387.21i	0.632501	+	0.365174i
$809$	10591.4	−	18344.8i	0.460289	−	0.797244i	−0.538686	−	0.842507i	$-0.681079\pi$
$809$	10591.4	−	18344.8i	0.460289	−	0.797244i	0.998975	+	0.0452624i	$0.0144124\pi$
$810$	673.530	−	1845.22i	0.0292166	−	0.0800424i
$811$	−4297.33			−0.186066			−0.0930331	−	0.995663i	$-0.529656\pi$
$811$	−4297.33			−0.186066			−0.0930331	+	0.995663i	$0.529656\pi$
$812$	21378.4	+	18895.8i	0.923932	+	0.816639i
$813$		−	2358.40i		−	0.101738i
$814$	229.833	+	398.082i	0.00989636	+	0.0171410i
$815$	−16968.0	+	2975.81i	−0.729281	+	0.127899i
$816$	−10380.5	+	17979.6i	−0.445333	+	0.771340i
$817$	−6159.76	+	3556.34i	−0.263773	+	0.152290i
$818$		−	42.7767i		−	0.00182842i
$819$	−11.4156	−	34.0635i	−0.000487049	−	0.00145333i
$820$	−5838.85	+	4890.22i	−0.248660	+	0.208261i
$821$	18524.1	+	32084.7i	0.787449	+	1.36390i	0.927525	+	0.373760i	$0.121932\pi$
$821$	18524.1	+	32084.7i	0.787449	+	1.36390i	−0.140077	+	0.990141i	$0.544735\pi$
$822$	904.129	+	521.999i	0.0383639	+	0.0221494i
$823$	−15134.4	−	8737.85i	−0.641011	−	0.370088i	0.143993	−	0.989579i	$-0.454006\pi$
$823$	−15134.4	−	8737.85i	−0.641011	−	0.370088i	−0.785004	+	0.619491i	$0.787339\pi$
$824$	−4522.76	−	7833.64i	−0.191211	−	0.331187i
$825$	−3997.19	−	712.408i	−0.168684	−	0.0300641i
$826$	2836.01	+	575.581i	0.119464	+	0.0242458i
$827$		−	6228.20i		−	0.261881i	−0.991390	−	0.130941i	$-0.958200\pi$
$827$		−	6228.20i		−	0.261881i	0.991390	−	0.130941i	$-0.0417997\pi$
$828$	5350.70	−	3089.23i	0.224577	−	0.129660i
$829$	−1480.42	+	2564.16i	−0.0620229	+	0.107427i	−0.895370	−	0.445324i	$-0.853089\pi$
$829$	−1480.42	+	2564.16i	−0.0620229	+	0.107427i	0.833347	+	0.552751i	$0.186422\pi$
$830$	137.669	+	784.987i	0.00575730	+	0.0328281i
$831$	10059.7	+	17424.0i	0.419937	+	0.727353i
$832$			37.9087i			0.00157962i
$833$	24349.9	+	32249.2i	1.01281	+	1.34138i
$834$	3735.18			0.155082
$835$	4304.63	−	11793.0i	0.178404	−	0.488761i
$836$	649.623	−	1125.18i	0.0268752	−	0.0465492i
$837$	36194.9	+	20897.1i	1.49472	+	0.862975i
$838$	820.951	−	473.976i	0.0338416	−	0.0195385i
$839$	35151.5			1.44644			0.723220	−	0.690617i	$-0.242661\pi$
$839$	35151.5			1.44644			0.723220	+	0.690617i	$0.242661\pi$
$840$	4790.36	+	8832.07i	0.196766	+	0.362780i
$841$	20429.8			0.837666
$842$	4811.95	−	2778.18i	0.196949	−	0.113708i
$843$	−9134.55	−	5273.83i	−0.373203	−	0.215469i
$844$	−2375.31	+	4114.16i	−0.0968739	+	0.167791i
$845$	23073.9	+	8422.29i	0.939368	+	0.342882i
$846$	2474.08			0.100544
$847$	22045.3	−	7387.98i	0.894316	−	0.299709i
$848$			22794.3i			0.923067i
$849$	10791.3	+	18691.1i	0.436228	+	0.755569i
$850$	−9576.93	−	8066.11i	−0.386454	−	0.325489i
$851$	2023.47	−	3504.76i	0.0815085	−	0.141177i
$852$	11259.5	−	6500.69i	0.452752	−	0.261397i
$853$		−	25120.0i		−	1.00832i	−0.863612	−	0.504158i	$-0.831803\pi$
$853$		−	25120.0i		−	1.00832i	0.863612	−	0.504158i	$-0.168197\pi$
$854$	3858.96	−	4365.96i	0.154626	−	0.174942i
$855$	2295.86	−	1922.85i	0.0918323	−	0.0769124i
$856$	−1474.13	−	2553.27i	−0.0588607	−	0.101950i
$857$	−21007.0	−	12128.4i	−0.837323	−	0.483428i	0.0190306	−	0.999819i	$-0.493942\pi$
$857$	−21007.0	−	12128.4i	−0.837323	−	0.483428i	−0.856353	+	0.516390i	$0.827275\pi$
$858$	−3.55661	−	2.05341i	−0.000141516	−	8.17044e-5i
$859$	−825.252	−	1429.38i	−0.0327791	−	0.0567750i	0.849170	−	0.528119i	$-0.177102\pi$
$859$	−825.252	−	1429.38i	−0.0327791	−	0.0567750i	−0.881950	+	0.471344i	$0.843769\pi$
$860$	−18095.2	−	21605.5i	−0.717491	−	0.856674i
$861$	4289.18	−	4852.71i	0.169773	−	0.192079i
$862$			6279.97i			0.248140i
$863$	12781.7	−	7379.54i	0.504166	−	0.291080i	−0.226266	−	0.974065i	$-0.572652\pi$
$863$	12781.7	−	7379.54i	0.504166	−	0.291080i	0.730432	+	0.682985i	$0.239319\pi$
$864$	−10772.5	+	18658.5i	−0.424176	+	0.734694i
$865$	−13709.8	+	2404.38i	−0.538897	+	0.0945102i
$866$	−5733.62	−	9930.92i	−0.224984	−	0.389684i
$867$			33496.7i			1.31212i
$868$	−35702.0	+	11964.7i	−1.39609	+	0.467867i
$869$	−6741.91			−0.263180
$870$	7062.24	+	2577.82i	0.275210	+	0.100455i
$871$	−77.5950	+	134.399i	−0.00301861	+	0.00522838i
$872$	18210.1	+	10513.6i	0.707192	+	0.408298i
$873$	−1863.52	+	1075.91i	−0.0722459	+	0.0417112i
$874$	1136.35			0.0439788
$875$	24564.0	−	8156.63i	0.949046	−	0.315136i
$876$	8215.73			0.316877
$877$	37213.2	−	21485.0i	1.43284	−	0.827250i	0.435502	−	0.900188i	$-0.356571\pi$
$877$	37213.2	−	21485.0i	1.43284	−	0.827250i	0.997336	+	0.0729378i	$0.0232375\pi$
$878$	2197.67	+	1268.82i	0.0844735	+	0.0487708i
$879$	11453.9	−	19838.7i	0.439511	−	0.761256i
$880$	4307.72	+	1572.38i	0.165015	+	0.0602327i
$881$	−43642.7			−1.66897			−0.834483	−	0.551034i	$-0.814234\pi$
$881$	−43642.7			−1.66897			−0.834483	+	0.551034i	$0.814234\pi$
$882$	2292.36	+	3036.02i	0.0875144	+	0.115905i
$883$		−	13662.5i		−	0.520703i	−0.965514	−	0.260352i	$-0.916162\pi$
$883$		−	13662.5i		−	0.520703i	0.965514	−	0.260352i	$-0.0838385\pi$
$884$	63.7444	+	110.409i	0.00242529	+	0.00420073i
$885$	−7560.14	+	1325.88i	−0.287154	+	0.0503603i
$886$	−2568.65	+	4449.03i	−0.0973988	+	0.168700i
$887$	−8490.73	+	4902.12i	−0.321410	+	0.185566i	−0.652021	−	0.758201i	$-0.726079\pi$
$887$	−8490.73	+	4902.12i	−0.321410	+	0.185566i	0.330611	+	0.943767i	$0.392745\pi$
$888$			3017.11i			0.114018i
$889$	−33749.4	−	6849.59i	−1.27325	−	0.258412i
$890$	−6405.67	−	7648.28i	−0.241257	−	0.288057i
$891$	898.340	+	1555.97i	0.0337772	+	0.0585039i
$892$	−3208.73	−	1852.56i	−0.120444	−	0.0695385i
$893$	−3966.80	−	2290.23i	−0.148649	−	0.0858227i
$894$	1089.66	+	1887.35i	0.0407648	+	0.0706068i
$895$	19879.4	−	16649.6i	0.742453	−	0.621827i
$896$	−8056.11	−	24039.0i	−0.300375	−	0.896301i
$897$			36.1569i			0.00134587i
$898$	−27.9306	+	16.1257i	−0.00103792	+	0.000599245i
$899$	−29573.4	+	51222.7i	−1.09714	+	1.90030i
$900$	9075.65	+	7643.91i	0.336135	+	0.283108i
$901$	28464.1	+	49301.3i	1.05247	+	1.82293i
$902$			692.045i			0.0255461i
$903$	17956.5	+	15871.2i	0.661743	+	0.584897i
$904$	20065.0			0.738222
$905$	−34199.1	−	12483.2i	−1.25615	−	0.458513i
$906$	1331.44	−	2306.13i	0.0488237	−	0.0845651i
$907$	−20448.3	−	11805.8i	−0.748595	−	0.432202i	0.0765910	−	0.997063i	$-0.475596\pi$
$907$	−20448.3	−	11805.8i	−0.748595	−	0.432202i	−0.825186	+	0.564861i	$0.808930\pi$
$908$	−2826.36	+	1631.80i	−0.103300	+	0.0596401i
$909$	−16845.8			−0.614674
$910$	26.1709	+	0.696913i	0.000953361	+	2.53873e-5i
$911$	18257.4			0.663991			0.331995	−	0.943281i	$-0.392278\pi$
$911$	18257.4			0.663991			0.331995	+	0.943281i	$0.392278\pi$
$912$	3133.74	−	1809.26i	0.113781	−	0.0656916i
$913$	−631.298	−	364.480i	−0.0228838	−	0.0132120i
$914$	−3137.39	+	5434.12i	−0.113540	+	0.196657i
$915$	−5299.36	+	14518.3i	−0.191466	+	0.524545i
$916$	34893.6			1.25864
$917$	25423.2	−	8520.01i	0.915538	−	0.306822i
$918$			14984.8i			0.538749i
$919$	−24141.6	−	41814.5i	−0.866549	−	1.50091i	−0.865501	−	0.500907i	$-0.833000\pi$
$919$	−24141.6	−	41814.5i	−0.866549	−	1.50091i	−0.00104747	−	0.999999i	$-0.500333\pi$
$920$	1632.79	+	9310.14i	0.0585124	+	0.333637i
$921$	5901.73	−	10222.1i	0.211149	−	0.365721i
$922$	−10834.3	+	6255.18i	−0.386994	+	0.223431i
$923$		−	71.1191i		−	0.00253620i
$924$	−4290.17	−	870.708i	−0.152745	−	0.0310002i
$925$	7651.62	+	1363.73i	0.271982	+	0.0484747i
$926$	2142.26	+	3710.50i	0.0760248	+	0.131679i
$927$	7866.97	+	4542.00i	0.278733	+	0.160926i
$928$	−26405.3	−	15245.1i	−0.934050	−	0.539274i
$929$	−17815.6	−	30857.5i	−0.629182	−	1.08978i	−0.987716	−	0.156259i	$-0.950057\pi$
$929$	−17815.6	−	30857.5i	−0.629182	−	1.08978i	0.358534	−	0.933517i	$-0.383277\pi$
$930$	−7606.12	+	6370.36i	−0.268188	+	0.224615i
$931$	−865.026	−	6989.80i	−0.0304512	−	0.246060i
$932$			35619.5i			1.25188i
$933$	14832.7	−	8563.67i	0.520473	−	0.300495i
$934$	1481.78	−	2566.51i	0.0519114	−	0.0899131i
$935$	11280.5	−	1978.35i	0.394559	−	0.0691967i
$936$	12.5983	+	21.8208i	0.000439944	+	0.000762005i
$937$		−	3099.28i		−	0.108057i	−0.998539	−	0.0540283i	$-0.982794\pi$
$937$		−	3099.28i		−	0.108057i	0.998539	−	0.0540283i	$-0.0172061\pi$
$938$	3268.62	−	16105.2i	0.113778	−	0.560611i
$939$	25782.7			0.896046
$940$	6223.00	−	17048.7i	0.215927	−	0.591560i
$941$	6447.31	−	11167.1i	0.223354	−	0.386861i	−0.732470	−	0.680799i	$-0.761633\pi$
$941$	6447.31	−	11167.1i	0.223354	−	0.386861i	0.955824	+	0.293938i	$0.0949660\pi$
$942$	−7166.11	−	4137.36i	−0.247860	−	0.143102i
$943$	5276.55	−	3046.42i	0.182214	−	0.105202i
$944$	8669.02			0.298890
$945$	−26403.7	−	16196.3i	−0.908903	−	0.557530i
$946$	−2560.77			−0.0880104
$947$	−30461.6	+	17587.0i	−1.04527	+	0.603485i	−0.921321	−	0.388803i	$-0.872889\pi$
$947$	−30461.6	+	17587.0i	−1.04527	+	0.603485i	−0.123947	+	0.992289i	$0.539555\pi$
$948$	−18254.9	−	10539.5i	−0.625413	−	0.361082i
$949$	22.4705	−	38.9201i	0.000768624	−	0.00133130i
$950$	742.632	+	2052.12i	0.0253623	+	0.0700838i
$951$	−30097.1			−1.02625
$952$	−21235.5	−	18769.5i	−0.722947	−	0.638994i
$953$			20597.5i			0.700124i	0.936727	+	0.350062i	$0.113839\pi$
$953$			20597.5i			0.700124i	−0.936727	+	0.350062i	$0.886161\pi$
$954$	2679.68	+	4641.34i	0.0909411	+	0.157515i
$955$	−4177.11	−	23817.9i	−0.141537	−	0.807046i
$956$	−17327.6	+	30012.3i	−0.586209	+	1.01534i
$957$	−5955.19	+	3438.23i	−0.201154	+	0.116136i
$958$		−	6745.25i		−	0.227483i
$959$	4031.43	−	4561.10i	0.135747	−	0.153582i
$960$	6836.44	+	8162.61i	0.229839	+	0.274424i
$961$	−24132.2	−	41798.1i	−0.810049	−	1.40305i
$962$	6.80825	+	3.93074i	0.000228177	+	0.000131738i
$963$	2564.13	+	1480.40i	0.0858026	+	0.0495382i
$964$	−12954.5	−	22437.9i	−0.432818	−	0.749663i
$965$	18509.7	+	22100.4i	0.617461	+	0.737239i
$966$	−1216.62	−	3630.32i	−0.0405218	−	0.120915i
$967$			33222.2i			1.10481i	0.833575	+	0.552406i	$0.186290\pi$
$967$			33222.2i			1.10481i	−0.833575	+	0.552406i	$0.813710\pi$
$968$	−14122.1	+	8153.38i	−0.468905	+	0.270723i
$969$	4518.58	−	7826.42i	0.149802	−	0.259464i
$970$	−270.876	−	1544.53i	−0.00896629	−	0.0511257i
$971$	18530.7	+	32096.1i	0.612440	+	1.06078i	0.990828	+	0.135129i	$0.0431450\pi$
$971$	18530.7	+	32096.1i	0.612440	+	1.06078i	−0.378388	+	0.925647i	$0.623522\pi$
$972$		−	23775.1i		−	0.784553i
$973$	4331.86	−	21344.0i	0.142727	−	0.703245i
$974$	3480.83			0.114510
$975$	−65.2956	+	23.6295i	−0.00214475	+	0.000776153i
$976$	8727.83	−	15117.1i	0.286241	−	0.495784i
$977$	−32163.5	−	18569.6i	−1.05323	−	0.608080i	−0.129675	−	0.991557i	$-0.541393\pi$
$977$	−32163.5	−	18569.6i	−1.05323	−	0.608080i	−0.923551	+	0.383477i	$0.874727\pi$
$978$	−4238.41	+	2447.04i	−0.138578	+	0.0800080i
$979$	9125.09			0.297895
$980$	26686.9	−	8160.02i	0.869879	−	0.265982i
$981$	−21116.7			−0.687261
$982$	13967.4	−	8064.10i	0.453889	−	0.262053i
$983$	8918.42	+	5149.05i	0.289373	+	0.167069i	0.637659	−	0.770319i	$-0.279903\pi$
$983$	8918.42	+	5149.05i	0.289373	+	0.167069i	−0.348286	+	0.937388i	$0.613236\pi$
$984$	−2271.19	+	3933.82i	−0.0735802	+	0.127445i
$985$	−13282.5	+	36389.0i	−0.429660	+	1.17711i
$986$	−21206.3			−0.684936
$987$	−3069.66	+	15124.9i	−0.0989953	+	0.487771i
$988$		−	22.2205i		−	0.000715515i
$989$	11272.6	+	19524.8i	0.362436	+	0.627758i
$990$	1061.98	−	186.246i	0.0340927	−	0.00597909i
$991$	−2190.93	+	3794.80i	−0.0702293	+	0.121641i	−0.899002	−	0.437945i	$-0.855706\pi$
$991$	−2190.93	+	3794.80i	−0.0702293	+	0.121641i	0.828772	+	0.559586i	$0.189040\pi$
$992$	34846.8	−	20118.8i	1.11531	−	0.643924i
$993$			4108.25i			0.131290i
$994$	2393.04	+	7140.69i	0.0763607	+	0.227856i
$995$	−41176.8	+	34486.9i	−1.31195	+	1.09880i
$996$	−1139.57	−	1973.79i	−0.0362535	−	0.0627930i
$997$	−25384.9	−	14656.0i	−0.806366	−	0.465555i	0.0393265	−	0.999226i	$-0.487479\pi$
$997$	−25384.9	−	14656.0i	−0.806366	−	0.465555i	−0.845692	+	0.533671i	$0.820812\pi$
$998$	−7699.47	−	4445.29i	−0.244211	−	0.140995i
$999$	−4650.71	−	8055.26i	−0.147289	−	0.255112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.4.j.a.4.6	yes	20
5.2	odd	4		175.4.e.g.151.6		20
5.3	odd	4		175.4.e.g.151.5		20
5.4	even	2	inner	35.4.j.a.4.5	✓	20
7.2	even	3	inner	35.4.j.a.9.5	yes	20
7.3	odd	6		245.4.b.f.99.6		10
7.4	even	3		245.4.b.e.99.6		10
7.5	odd	6		245.4.j.d.79.5		20
7.6	odd	2		245.4.j.d.214.6		20
35.2	odd	12		175.4.e.g.51.6		20
35.3	even	12		1225.4.a.bq.1.6		10
35.4	even	6		245.4.b.e.99.5		10
35.9	even	6	inner	35.4.j.a.9.6	yes	20
35.17	even	12		1225.4.a.bq.1.5		10
35.18	odd	12		1225.4.a.bp.1.6		10
35.19	odd	6		245.4.j.d.79.6		20
35.23	odd	12		175.4.e.g.51.5		20
35.24	odd	6		245.4.b.f.99.5		10
35.32	odd	12		1225.4.a.bp.1.5		10
35.34	odd	2		245.4.j.d.214.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.j.a.4.5	✓	20	5.4	even	2	inner
35.4.j.a.4.6	yes	20	1.1	even	1	trivial
35.4.j.a.9.5	yes	20	7.2	even	3	inner
35.4.j.a.9.6	yes	20	35.9	even	6	inner
175.4.e.g.51.5		20	35.23	odd	12
175.4.e.g.51.6		20	35.2	odd	12
175.4.e.g.151.5		20	5.3	odd	4
175.4.e.g.151.6		20	5.2	odd	4
245.4.b.e.99.5		10	35.4	even	6
245.4.b.e.99.6		10	7.4	even	3
245.4.b.f.99.5		10	35.24	odd	6
245.4.b.f.99.6		10	7.3	odd	6
245.4.j.d.79.5		20	7.5	odd	6
245.4.j.d.79.6		20	35.19	odd	6
245.4.j.d.214.5		20	35.34	odd	2
245.4.j.d.214.6		20	7.6	odd	2
1225.4.a.bp.1.5		10	35.32	odd	12
1225.4.a.bp.1.6		10	35.18	odd	12
1225.4.a.bq.1.5		10	35.17	even	12
1225.4.a.bq.1.6		10	35.3	even	12

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.736336 - 0.425124i) q^{2} +(3.23521 + 1.86785i) q^{3} +(-3.63854 + 6.30214i) q^{4} +(10.5026 + 3.83358i) q^{5} +3.17627 q^{6} +(3.68367 - 18.1502i) q^{7} +12.9893i q^{8} +(-6.52228 - 11.2969i) q^{9} +O(q^{10})\)	\(q+(0.736336 - 0.425124i) q^{2} +(3.23521 + 1.86785i) q^{3} +(-3.63854 + 6.30214i) q^{4} +(10.5026 + 3.83358i) q^{5} +3.17627 q^{6} +(3.68367 - 18.1502i) q^{7} +12.9893i q^{8} +(-6.52228 - 11.2969i) q^{9} +(9.36316 - 1.64208i) q^{10} +(-4.34744 + 7.52998i) q^{11} +(-23.5429 + 13.5925i) q^{12} +0.148705i q^{13} +(-5.00368 - 14.9307i) q^{14} +(26.8174 + 32.0196i) q^{15} +(-23.5863 - 40.8526i) q^{16} +(-102.028 - 58.9060i) q^{17} +(-9.60518 - 5.54555i) q^{18} +(10.2669 + 17.7829i) q^{19} +(-62.3737 + 52.2399i) q^{20} +(45.8193 - 51.8392i) q^{21} +7.39279i q^{22} +(56.3669 - 32.5435i) q^{23} +(-24.2621 + 42.0231i) q^{24} +(95.6074 + 80.5247i) q^{25} +(0.0632181 + 0.109497i) q^{26} -149.594i q^{27} +(100.982 + 89.2553i) q^{28} +211.705 q^{29} +(33.3589 + 12.1765i) q^{30} +(-139.692 + 241.954i) q^{31} +(-124.727 - 72.0114i) q^{32} +(-28.1297 + 16.2407i) q^{33} -100.169 q^{34} +(108.268 - 176.502i) q^{35} +94.9262 q^{36} +(53.8473 - 31.0888i) q^{37} +(15.1198 + 8.72945i) q^{38} +(-0.277759 + 0.481092i) q^{39} +(-49.7955 + 136.421i) q^{40} +93.6108 q^{41} +(11.7003 - 57.6500i) q^{42} +346.387i q^{43} +(-31.6366 - 54.7963i) q^{44} +(-25.1930 - 143.650i) q^{45} +(27.6700 - 47.9259i) q^{46} +(-193.183 + 111.534i) q^{47} -176.222i q^{48} +(-315.861 - 133.719i) q^{49} +(104.632 + 18.6483i) q^{50} +(-220.055 - 381.146i) q^{51} +(-0.937159 - 0.541069i) q^{52} +(-418.474 - 241.606i) q^{53} +(-63.5961 - 110.152i) q^{54} +(-74.5259 + 62.4178i) q^{55} +(235.759 + 47.8483i) q^{56} +76.7084i q^{57} +(155.886 - 90.0007i) q^{58} +(-91.8863 + 159.152i) q^{59} +(-299.368 + 52.5024i) q^{60} +(185.020 + 320.463i) q^{61} +237.545i q^{62} +(-229.067 + 76.7667i) q^{63} +254.925 q^{64} +(-0.570072 + 1.56178i) q^{65} +(-13.8086 + 23.9172i) q^{66} +(903.793 + 521.805i) q^{67} +(742.467 - 428.663i) q^{68} +243.145 q^{69} +(4.68655 - 175.992i) q^{70} -478.256 q^{71} +(146.739 - 84.7198i) q^{72} +(-261.727 - 151.108i) q^{73} +(26.4332 - 45.7836i) q^{74} +(158.902 + 439.095i) q^{75} -149.427 q^{76} +(120.656 + 106.645i) q^{77} +0.472327i q^{78} +(387.695 + 671.507i) q^{79} +(-91.1043 - 519.476i) q^{80} +(103.318 - 178.953i) q^{81} +(68.9290 - 39.7962i) q^{82} +83.8379i q^{83} +(159.983 + 477.379i) q^{84} +(-845.736 - 1009.80i) q^{85} +(147.258 + 255.057i) q^{86} +(684.909 + 395.432i) q^{87} +(-97.8092 - 56.4701i) q^{88} +(-524.740 - 908.876i) q^{89} +(-79.6196 - 95.0646i) q^{90} +(2.69903 + 0.547780i) q^{91} +473.643i q^{92} +(-903.866 + 521.847i) q^{93} +(-94.8317 + 164.253i) q^{94} +(39.6571 + 226.125i) q^{95} +(-269.013 - 465.944i) q^{96} -164.959i q^{97} +(-289.427 + 35.8182i) q^{98} +113.421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 30 q^{4} + 3 q^{5} - 96 q^{6} + 82 q^{9}+O(q^{10}) \) 20 * q + 30 * q^4 + 3 * q^5 - 96 * q^6 + 82 * q^9	\( 20 q + 30 q^{4} + 3 q^{5} - 96 q^{6} + 82 q^{9} - 32 q^{10} + 36 q^{11} + 26 q^{14} - 146 q^{15} - 22 q^{16} - 192 q^{19} + 584 q^{20} - 404 q^{21} - 444 q^{24} - 187 q^{25} + 434 q^{26} + 260 q^{29} - 658 q^{30} + 834 q^{31} - 160 q^{34} + 661 q^{35} + 516 q^{36} + 868 q^{39} + 674 q^{40} - 1224 q^{41} + 542 q^{44} + 60 q^{45} - 1274 q^{46} - 326 q^{49} - 2556 q^{50} + 986 q^{51} - 2808 q^{54} - 742 q^{55} - 36 q^{56} - 2514 q^{59} - 204 q^{60} + 512 q^{61} + 6900 q^{64} - 946 q^{65} + 1396 q^{66} + 3064 q^{69} + 5190 q^{70} - 2944 q^{71} + 1590 q^{74} + 3003 q^{75} + 44 q^{76} + 46 q^{79} + 2304 q^{80} - 130 q^{81} - 12952 q^{84} - 5082 q^{85} - 1592 q^{86} - 5876 q^{89} - 3316 q^{90} + 4348 q^{91} - 3314 q^{94} - 2155 q^{95} + 3756 q^{96} + 13860 q^{99}+O(q^{100}) \) 20 * q + 30 * q^4 + 3 * q^5 - 96 * q^6 + 82 * q^9 - 32 * q^10 + 36 * q^11 + 26 * q^14 - 146 * q^15 - 22 * q^16 - 192 * q^19 + 584 * q^20 - 404 * q^21 - 444 * q^24 - 187 * q^25 + 434 * q^26 + 260 * q^29 - 658 * q^30 + 834 * q^31 - 160 * q^34 + 661 * q^35 + 516 * q^36 + 868 * q^39 + 674 * q^40 - 1224 * q^41 + 542 * q^44 + 60 * q^45 - 1274 * q^46 - 326 * q^49 - 2556 * q^50 + 986 * q^51 - 2808 * q^54 - 742 * q^55 - 36 * q^56 - 2514 * q^59 - 204 * q^60 + 512 * q^61 + 6900 * q^64 - 946 * q^65 + 1396 * q^66 + 3064 * q^69 + 5190 * q^70 - 2944 * q^71 + 1590 * q^74 + 3003 * q^75 + 44 * q^76 + 46 * q^79 + 2304 * q^80 - 130 * q^81 - 12952 * q^84 - 5082 * q^85 - 1592 * q^86 - 5876 * q^89 - 3316 * q^90 + 4348 * q^91 - 3314 * q^94 - 2155 * q^95 + 3756 * q^96 + 13860 * q^99

Introduction

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