LMFDB - Embedded newform 114.4.h.b.65.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(65,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("114.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.h (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:	$6.72621774065$
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} - 5 x^{19} + 10 x^{18} - 183 x^{17} + 864 x^{16} - 495 x^{15} - 1530 x^{14} + \cdots + 205891132094649 $ x^20 - 5x^19 + 10x^18 - 183x^17 + 864x^16 - 495x^15 - 1530x^14 + 118935x^13 - 524961x^12 + 4026996x^11 - 36285408x^10 + 108728892x^9 - 382696569x^8 + 2340997605x^7 - 813104730x^6 - 7102708965x^5 + 334731302496x^4 - 1914244636149x^3 + 2824295364810x^2 - 38127987424935*x + 205891132094649
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.3
Root			$2.45275 + 4.58083i$ of defining polynomial
Character	$\chi$	$=$	114.65
Dual form			114.4.h.b.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.74074 - 4.41456i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.43899 - 0.830800i) q^{5} +(-10.3870 + 0.332533i) q^{6} -19.8418 q^{7} -8.00000 q^{8} +(-11.9767 + 24.1983i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.74074 - 4.41456i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.43899 - 0.830800i) q^{5} +(-10.3870 + 0.332533i) q^{6} -19.8418 q^{7} -8.00000 q^{8} +(-11.9767 + 24.1983i) q^{9} +(-2.87798 + 1.66160i) q^{10} +21.2986i q^{11} +(-9.81102 + 18.3233i) q^{12} +(48.9843 - 28.2811i) q^{13} +(-19.8418 + 34.3671i) q^{14} +(0.276268 + 8.62951i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-105.287 - 60.7878i) q^{17} +(29.9360 + 44.9426i) q^{18} +(8.99894 + 82.3287i) q^{19} +6.64640i q^{20} +(54.3812 + 87.5930i) q^{21} +(36.8902 + 21.2986i) q^{22} +(-136.041 + 78.5435i) q^{23} +(21.9259 + 35.3165i) q^{24} +(-61.1195 - 105.862i) q^{25} -113.125i q^{26} +(139.650 - 13.4492i) q^{27} +(39.6837 + 68.7341i) q^{28} +(-54.8266 - 94.9625i) q^{29} +(15.2230 + 8.15100i) q^{30} -44.3660i q^{31} +(16.0000 + 27.7128i) q^{32} +(94.0239 - 58.3738i) q^{33} +(-210.575 + 121.576i) q^{34} +(28.5522 + 16.4846i) q^{35} +(107.779 - 6.90803i) q^{36} -343.647i q^{37} +(151.596 + 66.7421i) q^{38} +(-259.102 - 138.733i) q^{39} +(11.5119 + 6.64640i) q^{40} +(-40.7078 + 70.5080i) q^{41} +(206.097 - 6.59806i) q^{42} +(206.392 - 357.482i) q^{43} +(73.7804 - 42.5971i) q^{44} +(37.3383 - 24.8708i) q^{45} +314.174i q^{46} +(-152.609 + 88.1087i) q^{47} +(83.0959 - 2.66026i) q^{48} +50.6984 q^{49} -244.478 q^{50} +(20.2139 + 631.401i) q^{51} +(-195.937 - 113.125i) q^{52} +(-152.058 - 263.372i) q^{53} +(116.355 - 255.330i) q^{54} +(17.6949 - 30.6484i) q^{55} +158.735 q^{56} +(338.782 - 265.368i) q^{57} -219.307 q^{58} +(135.032 - 233.882i) q^{59} +(29.3410 - 18.2160i) q^{60} +(104.925 + 181.735i) q^{61} +(-76.8441 - 44.3660i) q^{62} +(237.640 - 480.139i) q^{63} +64.0000 q^{64} -93.9839 q^{65} +(-7.08247 - 221.228i) q^{66} +(-479.257 + 276.699i) q^{67} +486.302i q^{68} +(719.589 + 385.296i) q^{69} +(57.1043 - 32.9692i) q^{70} +(220.629 - 382.141i) q^{71} +(95.8138 - 193.586i) q^{72} +(141.901 - 245.780i) q^{73} +(-595.213 - 343.647i) q^{74} +(-299.823 + 559.956i) q^{75} +(267.197 - 195.831i) q^{76} -422.603i q^{77} +(-499.395 + 310.044i) q^{78} +(929.490 + 536.641i) q^{79} +(23.0238 - 13.2928i) q^{80} +(-442.116 - 579.633i) q^{81} +(81.4156 + 141.016i) q^{82} +1164.34i q^{83} +(194.669 - 363.568i) q^{84} +(101.005 + 174.946i) q^{85} +(-412.785 - 714.964i) q^{86} +(-268.953 + 502.303i) q^{87} -170.389i q^{88} +(-32.4360 - 56.1808i) q^{89} +(-5.73919 - 89.5427i) q^{90} +(-971.939 + 561.149i) q^{91} +(544.165 + 314.174i) q^{92} +(-195.856 + 121.595i) q^{93} +352.435i q^{94} +(55.4494 - 125.946i) q^{95} +(78.4882 - 146.587i) q^{96} +(687.273 + 396.797i) q^{97} +(50.6984 - 87.8122i) q^{98} +(-515.389 - 255.087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9	\( 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9} - 20 q^{12} - 111 q^{13} - 10 q^{14} - 133 q^{15} - 160 q^{16} - 90 q^{17} - 10 q^{18} - 143 q^{19} + 191 q^{21} - 54 q^{22} - 8 q^{24} + 184 q^{25} - 524 q^{27} + 20 q^{28} - 96 q^{29} - 292 q^{30} + 320 q^{32} - 55 q^{33} - 180 q^{34} + 774 q^{35} + 128 q^{36} - 314 q^{38} + 1002 q^{39} + 537 q^{41} - 382 q^{42} + 571 q^{43} - 108 q^{44} + 1516 q^{45} - 126 q^{47} + 64 q^{48} + 558 q^{49} + 736 q^{50} - 757 q^{51} + 444 q^{52} + 126 q^{53} - 1388 q^{54} + 366 q^{55} + 80 q^{56} - 281 q^{57} - 384 q^{58} - 1383 q^{59} - 52 q^{60} + 149 q^{61} - 222 q^{62} + 1153 q^{63} + 1280 q^{64} + 3636 q^{65} + 32 q^{66} - 1626 q^{67} + 236 q^{69} + 1548 q^{70} - 1368 q^{71} + 296 q^{72} + 946 q^{73} + 474 q^{74} - 669 q^{75} - 56 q^{76} + 132 q^{78} - 2109 q^{79} + 311 q^{81} - 1074 q^{82} - 1528 q^{84} + 786 q^{85} - 1142 q^{86} - 816 q^{87} - 1938 q^{89} + 1234 q^{90} - 3459 q^{91} - 705 q^{93} + 2502 q^{95} + 160 q^{96} + 1791 q^{97} + 558 q^{98} - 2285 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9 - 20 * q^12 - 111 * q^13 - 10 * q^14 - 133 * q^15 - 160 * q^16 - 90 * q^17 - 10 * q^18 - 143 * q^19 + 191 * q^21 - 54 * q^22 - 8 * q^24 + 184 * q^25 - 524 * q^27 + 20 * q^28 - 96 * q^29 - 292 * q^30 + 320 * q^32 - 55 * q^33 - 180 * q^34 + 774 * q^35 + 128 * q^36 - 314 * q^38 + 1002 * q^39 + 537 * q^41 - 382 * q^42 + 571 * q^43 - 108 * q^44 + 1516 * q^45 - 126 * q^47 + 64 * q^48 + 558 * q^49 + 736 * q^50 - 757 * q^51 + 444 * q^52 + 126 * q^53 - 1388 * q^54 + 366 * q^55 + 80 * q^56 - 281 * q^57 - 384 * q^58 - 1383 * q^59 - 52 * q^60 + 149 * q^61 - 222 * q^62 + 1153 * q^63 + 1280 * q^64 + 3636 * q^65 + 32 * q^66 - 1626 * q^67 + 236 * q^69 + 1548 * q^70 - 1368 * q^71 + 296 * q^72 + 946 * q^73 + 474 * q^74 - 669 * q^75 - 56 * q^76 + 132 * q^78 - 2109 * q^79 + 311 * q^81 - 1074 * q^82 - 1528 * q^84 + 786 * q^85 - 1142 * q^86 - 816 * q^87 - 1938 * q^89 + 1234 * q^90 - 3459 * q^91 - 705 * q^93 + 2502 * q^95 + 160 * q^96 + 1791 * q^97 + 558 * q^98 - 2285 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	−2.74074	−	4.41456i	−0.527455	−	0.849583i
$3$	−2.74074	−	4.41456i	−0.527455	−	0.849583i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−1.43899	−	0.830800i	−0.128707	−	0.0743090i	0.434264	−	0.900786i	$-0.357008\pi$
$5$	−1.43899	−	0.830800i	−0.128707	−	0.0743090i	−0.562971	+	0.826477i	$0.690342\pi$
$6$	−10.3870	+	0.332533i	−0.706745	+	0.0226260i
$7$	−19.8418			−1.07136			−0.535679	−	0.844422i	$-0.679944\pi$
$7$	−19.8418			−1.07136			−0.535679	+	0.844422i	$0.679944\pi$
$8$	−8.00000			−0.353553
$9$	−11.9767	+	24.1983i	−0.443582	+	0.896234i
$10$	−2.87798	+	1.66160i	−0.0910096	+	0.0525444i
$11$			21.2986i			0.583796i	0.956449	+	0.291898i	$0.0942868\pi$
$11$			21.2986i			0.583796i	−0.956449	+	0.291898i	$0.905713\pi$
$12$	−9.81102	+	18.3233i	−0.236016	+	0.440790i
$13$	48.9843	−	28.2811i	1.04506	−	0.603367i	0.123800	−	0.992307i	$-0.460492\pi$
$13$	48.9843	−	28.2811i	1.04506	−	0.603367i	0.921263	+	0.388940i	$0.127159\pi$
$14$	−19.8418	+	34.3671i	−0.378782	+	0.656070i
$15$	0.276268	+	8.62951i	0.00475548	+	0.148542i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−105.287	−	60.7878i	−1.50212	−	0.867247i	−0.999997	−	0.00244806i	$-0.999221\pi$
$17$	−105.287	−	60.7878i	−1.50212	−	0.867247i	−0.502119	−	0.864799i	$-0.667446\pi$
$18$	29.9360	+	44.9426i	0.391999	+	0.588504i
$19$	8.99894	+	82.3287i	0.108658	+	0.994079i
$19$	8.99894	+	82.3287i	0.108658	+	0.994079i
$20$			6.64640i			0.0743090i
$21$	54.3812	+	87.5930i	0.565093	+	0.910208i
$22$	36.8902	+	21.2986i	0.357501	+	0.206403i
$23$	−136.041	+	78.5435i	−1.23333	+	0.712063i	−0.967722	−	0.252018i	$-0.918906\pi$
$23$	−136.041	+	78.5435i	−1.23333	+	0.712063i	−0.265607	+	0.964081i	$0.585572\pi$
$24$	21.9259	+	35.3165i	0.186484	+	0.300373i
$25$	−61.1195	−	105.862i	−0.488956	−	0.846897i
$26$		−	113.125i		−	0.853290i
$27$	139.650	−	13.4492i	0.995395	−	0.0958629i
$28$	39.6837	+	68.7341i	0.267840	+	0.463912i
$29$	−54.8266	−	94.9625i	−0.351071	−	0.608072i	0.635367	−	0.772211i	$-0.280849\pi$
$29$	−54.8266	−	94.9625i	−0.351071	−	0.608072i	−0.986437	+	0.164138i	$0.947516\pi$
$30$	15.2230	+	8.15100i	0.0926443	+	0.0496054i
$31$		−	44.3660i		−	0.257044i	−0.991707	−	0.128522i	$-0.958977\pi$
$31$		−	44.3660i		−	0.257044i	0.991707	−	0.128522i	$-0.0410233\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	94.0239	−	58.3738i	0.495983	−	0.307926i
$34$	−210.575	+	121.576i	−1.06216	+	0.613236i
$35$	28.5522	+	16.4846i	0.137891	+	0.0796116i
$36$	107.779	−	6.90803i	0.498976	−	0.0319816i
$37$		−	343.647i		−	1.52690i	−0.645869	−	0.763448i	$-0.723505\pi$
$37$		−	343.647i		−	1.52690i	0.645869	−	0.763448i	$-0.276495\pi$
$38$	151.596	+	66.7421i	0.647163	+	0.284921i
$39$	−259.102	−	138.733i	−1.06383	−	0.569618i
$40$	11.5119	+	6.64640i	0.0455048	+	0.0262722i
$41$	−40.7078	+	70.5080i	−0.155061	+	0.268573i	−0.933081	−	0.359666i	$-0.882891\pi$
$41$	−40.7078	+	70.5080i	−0.155061	+	0.268573i	0.778020	+	0.628239i	$0.216224\pi$
$42$	206.097	−	6.59806i	0.757177	−	0.0242405i
$43$	206.392	−	357.482i	0.731966	−	1.26780i	−0.224075	−	0.974572i	$-0.571936\pi$
$43$	206.392	−	357.482i	0.731966	−	1.26780i	0.956042	−	0.293231i	$-0.0947305\pi$
$44$	73.7804	−	42.5971i	0.252791	−	0.145949i
$45$	37.3383	−	24.8708i	0.123690	−	0.0823894i
$46$			314.174i			1.00701i
$47$	−152.609	+	88.1087i	−0.473623	+	0.273446i	−0.717755	−	0.696296i	$-0.754830\pi$
$47$	−152.609	+	88.1087i	−0.473623	+	0.273446i	0.244132	+	0.969742i	$0.421497\pi$
$48$	83.0959	−	2.66026i	0.249872	−	0.00799950i
$49$	50.6984			0.147809
$50$	−244.478			−0.691489
$51$	20.2139	+	631.401i	0.0555003	+	1.73361i
$52$	−195.937	−	113.125i	−0.522531	−	0.301684i
$53$	−152.058	−	263.372i	−0.394090	−	0.682583i	0.598895	−	0.800828i	$-0.295607\pi$
$53$	−152.058	−	263.372i	−0.394090	−	0.682583i	−0.992985	+	0.118244i	$0.962273\pi$
$54$	116.355	−	255.330i	0.293221	−	0.643445i
$55$	17.6949	−	30.6484i	0.0433813	−	0.0751387i
$56$	158.735			0.378782
$57$	338.782	−	265.368i	0.787241	−	0.616646i
$58$	−219.307			−0.496489
$59$	135.032	−	233.882i	0.297960	−	0.516082i	−0.677709	−	0.735330i	$-0.737027\pi$
$59$	135.032	−	233.882i	0.297960	−	0.516082i	0.975669	+	0.219248i	$0.0703605\pi$
$60$	29.3410	−	18.2160i	0.0631317	−	0.0391947i
$61$	104.925	+	181.735i	0.220234	+	0.381456i	0.954879	−	0.296995i	$-0.0959846\pi$
$61$	104.925	+	181.735i	0.220234	+	0.381456i	−0.734645	+	0.678452i	$0.762651\pi$
$62$	−76.8441	−	44.3660i	−0.157407	−	0.0908788i
$63$	237.640	−	480.139i	0.475236	−	0.960187i
$64$	64.0000			0.125000
$65$	−93.9839			−0.179343
$66$	−7.08247	−	221.228i	−0.0132090	−	0.412595i
$67$	−479.257	+	276.699i	−0.873889	+	0.504540i	−0.868639	−	0.495446i	$-0.835005\pi$
$67$	−479.257	+	276.699i	−0.873889	+	0.504540i	−0.00525065	+	0.999986i	$0.501671\pi$
$68$			486.302i			0.867247i
$69$	719.589	+	385.296i	1.25548	+	0.672234i
$70$	57.1043	−	32.9692i	0.0975039	−	0.0562939i
$71$	220.629	−	382.141i	0.368787	−	0.638758i	−0.620589	−	0.784136i	$-0.713106\pi$
$71$	220.629	−	382.141i	0.368787	−	0.638758i	0.989376	+	0.145378i	$0.0464398\pi$
$72$	95.8138	−	193.586i	0.156830	−	0.316866i
$73$	141.901	−	245.780i	0.227510	−	0.394059i	−0.729559	−	0.683918i	$-0.760275\pi$
$73$	141.901	−	245.780i	0.227510	−	0.394059i	0.957070	+	0.289858i	$0.0936081\pi$
$74$	−595.213	−	343.647i	−0.935029	−	0.539839i
$75$	−299.823	+	559.956i	−0.461607	+	0.862109i
$76$	267.197	−	195.831i	0.403284	−	0.295570i
$77$		−	422.603i		−	0.625455i
$78$	−499.395	+	310.044i	−0.724941	+	0.450072i
$79$	929.490	+	536.641i	1.32374	+	0.764264i	0.984324	−	0.176371i	$-0.0564357\pi$
$79$	929.490	+	536.641i	1.32374	+	0.764264i	0.339421	+	0.940635i	$0.389769\pi$
$80$	23.0238	−	13.2928i	0.0321768	−	0.0185773i
$81$	−442.116	−	579.633i	−0.606469	−	0.795107i
$82$	81.4156	+	141.016i	0.109645	+	0.189910i
$83$			1164.34i			1.53979i	0.638168	+	0.769897i	$0.279693\pi$
$83$			1164.34i			1.53979i	−0.638168	+	0.769897i	$0.720307\pi$
$84$	194.669	−	363.568i	0.252858	−	0.472245i
$85$	101.005	+	174.946i	0.128889	+	0.223242i
$86$	−412.785	−	714.964i	−0.517578	−	0.896472i
$87$	−268.953	+	502.303i	−0.331434	+	0.618995i
$88$		−	170.389i		−	0.206403i
$89$	−32.4360	−	56.1808i	−0.0386316	−	0.0669118i	0.846063	−	0.533083i	$-0.178967\pi$
$89$	−32.4360	−	56.1808i	−0.0386316	−	0.0669118i	−0.884695	+	0.466171i	$0.845633\pi$
$90$	−5.73919	−	89.5427i	−0.00672182	−	0.104874i
$91$	−971.939	+	561.149i	−1.11964	+	0.646422i
$92$	544.165	+	314.174i	0.616665	+	0.356032i
$93$	−195.856	+	121.595i	−0.218380	+	0.135579i
$94$			352.435i			0.386711i
$95$	55.4494	−	125.946i	0.0598840	−	0.136019i
$96$	78.4882	−	146.587i	0.0834444	−	0.155843i
$97$	687.273	+	396.797i	0.719402	+	0.415347i	0.814533	−	0.580118i	$-0.196993\pi$
$97$	687.273	+	396.797i	0.719402	+	0.415347i	−0.0951302	+	0.995465i	$0.530327\pi$
$98$	50.6984	−	87.8122i	0.0522583	−	0.0905140i
$99$	−515.389	−	255.087i	−0.523218	−	0.258962i
$100$	−244.478	+	423.449i	−0.244478	+	0.423449i
$101$	−845.920	+	488.392i	−0.833388	+	0.481157i	−0.855011	−	0.518610i	$-0.826450\pi$
$101$	−845.920	+	488.392i	−0.833388	+	0.481157i	0.0216234	+	0.999766i	$0.493117\pi$
$102$	1113.83	+	596.390i	1.08123	+	0.578935i
$103$		−	413.122i		−	0.395205i	−0.980282	−	0.197603i	$-0.936684\pi$
$103$		−	413.122i		−	0.395205i	0.980282	−	0.197603i	$-0.0633156\pi$
$104$	−391.875	+	226.249i	−0.369485	+	0.213323i
$105$	−5.48167	−	171.225i	−0.00509482	−	0.159142i
$106$	−608.231			−0.557327
$107$	−893.126			−0.806933			−0.403466	−	0.914995i	$-0.632195\pi$
$107$	−893.126			−0.806933			−0.403466	+	0.914995i	$0.632195\pi$
$108$	−325.889	−	456.863i	−0.290358	−	0.407053i
$109$	441.720	+	255.027i	0.388156	+	0.224102i	0.681361	−	0.731947i	$-0.261388\pi$
$109$	441.720	+	255.027i	0.388156	+	0.224102i	−0.293205	+	0.956050i	$0.594722\pi$
$110$	−35.3897	−	61.2968i	−0.0306752	−	0.0531311i
$111$	−1517.05	+	941.845i	−1.29722	+	0.805369i
$112$	158.735	−	274.937i	0.133920	−	0.231956i
$113$	−351.785			−0.292860			−0.146430	−	0.989221i	$-0.546778\pi$
$113$	−351.785			−0.292860			−0.146430	+	0.989221i	$0.546778\pi$
$114$	−120.849	−	852.155i	−0.0992854	−	0.700102i
$115$	261.016			0.211651
$116$	−219.307	+	379.850i	−0.175535	+	0.304036i
$117$	97.6834	+	1524.05i	0.0771866	+	1.20426i
$118$	−270.064	−	467.764i	−0.210690	−	0.364925i
$119$	2089.10	+	1206.14i	1.60930	+	0.929132i
$120$	−2.21015	−	69.0361i	−0.00168132	−	0.0525175i
$121$	877.371			0.659182
$122$	419.700			0.311458
$123$	422.831	−	13.5367i	0.309963	−	0.00992326i
$124$	−153.688	+	88.7320i	−0.111303	+	0.0642610i
$125$			410.813i			0.293954i
$126$	−593.985	−	891.744i	−0.419971	−	0.630499i
$127$	−1081.55	+	624.432i	−0.755683	+	0.436294i	−0.827744	−	0.561106i	$-0.810376\pi$
$127$	−1081.55	+	624.432i	−0.755683	+	0.436294i	0.0720604	+	0.997400i	$0.477043\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−2143.79	+	68.6323i	−1.46318	+	0.0468429i
$130$	−93.9839	+	162.785i	−0.0634072	+	0.109824i
$131$	−1734.18	−	1001.23i	−1.15661	−	0.667769i	−0.206121	−	0.978526i	$-0.566084\pi$
$131$	−1734.18	−	1001.23i	−1.15661	−	0.667769i	−0.950489	+	0.310757i	$0.899417\pi$
$132$	−390.260	−	208.961i	−0.257332	−	0.137786i
$133$	−178.556	−	1633.55i	−0.116411	−	1.06502i
$134$			1106.80i			0.713528i
$135$	−212.128	−	96.6680i	−0.135238	−	0.0616286i
$136$	842.300	+	486.302i	0.531078	+	0.306618i
$137$	2296.22	−	1325.72i	1.43196	−	0.826745i	0.434693	−	0.900579i	$-0.356857\pi$
$137$	2296.22	−	1325.72i	1.43196	−	0.826745i	0.997271	+	0.0738338i	$0.0235234\pi$
$138$	1386.94	−	861.068i	0.855538	−	0.531152i
$139$	−1361.02	−	2357.36i	−0.830505	−	1.43848i	−0.897638	−	0.440733i	$-0.854718\pi$
$139$	−1361.02	−	2357.36i	−0.830505	−	1.43848i	0.0671330	−	0.997744i	$-0.478615\pi$
$140$		−	131.877i		−	0.0796116i
$141$	807.221	+	432.218i	0.482130	+	0.258151i
$142$	−441.259	−	764.283i	−0.260772	−	0.451670i
$143$	602.347	+	1043.30i	0.352244	+	0.610104i
$144$	−239.488	−	359.541i	−0.138592	−	0.208068i
$145$			182.200i			0.104351i
$146$	−283.802	−	491.559i	−0.160874	−	0.278642i
$147$	−138.951	−	223.811i	−0.0779625	−	0.125576i
$148$	−1190.43	+	687.293i	−0.661165	+	0.381724i
$149$	2420.81	+	1397.65i	1.33101	+	0.768458i	0.985454	−	0.169942i	$-0.0543579\pi$
$149$	2420.81	+	1397.65i	1.33101	+	0.768458i	0.345553	+	0.938399i	$0.387691\pi$
$150$	670.050	+	1079.26i	0.364729	+	0.587477i
$151$			5.86693i			0.00316188i	0.999999	+	0.00158094i	$0.000503229\pi$
$151$			5.86693i			0.00316188i	−0.999999	+	0.00158094i	$0.999497\pi$
$152$	−71.9915	−	658.630i	−0.0384163	−	0.351460i
$153$	2731.96	−	1819.74i	1.44357	−	0.961551i
$154$	−731.969	−	422.603i	−0.383011	−	0.221132i
$155$	−36.8593	+	63.8421i	−0.0191007	+	0.0330834i
$156$	37.6176	+	1175.02i	0.0193065	+	0.603058i
$157$	1156.20	−	2002.59i	0.587736	−	1.01799i	−0.406792	−	0.913521i	$-0.633353\pi$
$157$	1156.20	−	2002.59i	0.587736	−	1.01799i	0.994528	−	0.104468i	$-0.0333141\pi$
$158$	1858.98	−	1073.28i	0.936029	−	0.540416i
$159$	−745.921	+	1393.10i	−0.372046	+	0.694844i
$160$		−	53.1712i		−	0.0262722i
$161$	2699.31	−	1558.45i	1.32134	−	0.762875i
$162$	−1446.07	+	186.135i	−0.701321	+	0.0902724i
$163$	1070.79			0.514543			0.257271	−	0.966339i	$-0.417177\pi$
$163$	1070.79			0.514543			0.257271	+	0.966339i	$0.417177\pi$
$164$	325.662			0.155061
$165$	−183.796	+	5.88412i	−0.0867183	+	0.00277623i
$166$	2016.70	+	1164.34i	0.942928	+	0.544400i
$167$	−1584.24	−	2743.99i	−0.734086	−	1.27147i	−0.955123	−	0.296208i	$-0.904278\pi$
$167$	−1584.24	−	2743.99i	−0.734086	−	1.27147i	0.221038	−	0.975265i	$-0.429056\pi$
$168$	−435.050	−	700.744i	−0.199791	−	0.321807i
$169$	501.144	−	868.007i	0.228104	−	0.395087i
$170$	404.020			0.182276
$171$	−2099.99	−	768.269i	−0.939126	−	0.343573i
$172$	−1651.14			−0.731966
$173$	−78.9259	+	136.704i	−0.0346857	+	0.0600774i	−0.882847	−	0.469660i	$-0.844376\pi$
$173$	−78.9259	+	136.704i	−0.0346857	+	0.0600774i	0.848161	+	0.529738i	$0.177710\pi$
$174$	601.062	+	968.142i	0.261876	+	0.421809i
$175$	1212.72	+	2100.50i	0.523847	+	0.907330i
$176$	−295.122	−	170.389i	−0.126396	−	0.0729745i
$177$	−1402.57	+	44.9025i	−0.595615	+	0.0190682i
$178$	−129.744			−0.0546333
$179$	4596.07			1.91914			0.959571	−	0.281465i	$-0.0908205\pi$
$179$	4596.07			1.91914			0.959571	+	0.281465i	$0.0908205\pi$
$180$	−160.832	−	79.6021i	−0.0665983	−	0.0329622i
$181$	−2033.24	+	1173.89i	−0.834970	+	0.482070i	−0.855551	−	0.517718i	$-0.826782\pi$
$181$	−2033.24	+	1173.89i	−0.834970	+	0.482070i	0.0205812	+	0.999788i	$0.493448\pi$
$182$			2244.60i			0.914179i
$183$	514.710	−	961.287i	0.207915	−	0.388308i
$184$	1088.33	−	628.348i	0.436048	−	0.251752i
$185$	−285.502	+	494.503i	−0.113462	+	0.196522i
$186$	14.7531	+	460.829i	0.00581588	+	0.181665i
$187$	1294.69	−	2242.47i	0.506296	−	0.876930i
$188$	610.435	+	352.435i	0.236811	+	0.136723i
$189$	−2770.91	+	266.857i	−1.06642	+	0.102704i
$190$	−162.696	−	221.988i	−0.0621222	−	0.0847614i
$191$			730.904i			0.276892i	0.990370	+	0.138446i	$0.0442107\pi$
$191$			730.904i			0.276892i	−0.990370	+	0.138446i	$0.955789\pi$
$192$	−175.407	−	282.532i	−0.0659319	−	0.106198i
$193$	−394.732	−	227.898i	−0.147220	−	0.0849973i	0.424581	−	0.905390i	$-0.360422\pi$
$193$	−394.732	−	227.898i	−0.147220	−	0.0849973i	−0.571800	+	0.820393i	$0.693755\pi$
$194$	1374.55	−	793.595i	0.508694	−	0.293695i
$195$	257.585	+	414.898i	0.0945951	+	0.152366i
$196$	−101.397	−	175.624i	−0.0369522	−	0.0640031i
$197$			196.846i			0.0711914i	0.999366	+	0.0355957i	$0.0113329\pi$
$197$			196.846i			0.0711914i	−0.999366	+	0.0355957i	$0.988667\pi$
$198$	−957.213	+	637.593i	−0.343567	+	0.228847i
$199$	390.887	+	677.036i	0.139242	+	0.241175i	0.927210	−	0.374542i	$-0.122200\pi$
$199$	390.887	+	677.036i	0.139242	+	0.241175i	−0.787968	+	0.615717i	$0.788867\pi$
$200$	488.956	+	846.897i	0.172872	+	0.299423i
$201$	2535.02	+	1357.35i	0.889586	+	0.476319i
$202$			1953.57i			0.680458i
$203$	1087.86	+	1884.23i	0.376123	+	0.651463i
$204$	2146.81	−	1332.83i	0.736798	−	0.457434i
$205$	117.156	−	67.6401i	0.0399148	−	0.0230448i
$206$	−715.549	−	413.122i	−0.242013	−	0.139726i
$207$	−271.290	−	4232.66i	−0.0910917	−	1.42121i
$208$			904.996i			0.301684i
$209$	−1753.48	+	191.665i	−0.580340	+	0.0634340i
$210$	−302.053	−	161.731i	−0.0992553	−	0.0531452i
$211$	−4060.61	−	2344.39i	−1.32485	−	0.764904i	−0.340354	−	0.940297i	$-0.610547\pi$
$211$	−4060.61	−	2344.39i	−1.32485	−	0.764904i	−0.984498	+	0.175394i	$0.943880\pi$
$212$	−608.231	+	1053.49i	−0.197045	+	0.341292i
$213$	−2291.67	+	73.3665i	−0.737197	+	0.0236009i
$214$	−893.126	+	1546.94i	−0.285294	+	0.494143i
$215$	−593.993	+	342.942i	−0.188418	+	0.108783i
$216$	−1117.20	+	107.594i	−0.351925	+	0.0338927i
$217$			880.302i			0.275386i
$218$	883.439	−	510.054i	0.274468	−	0.158464i
$219$	−1473.92	+	47.1867i	−0.454788	+	0.0145597i
$220$	−141.559			−0.0433813
$221$	−6876.58			−2.09307
$222$	114.274	+	3569.45i	0.0345475	+	1.07913i
$223$	557.865	+	322.084i	0.167522	+	0.0967189i	0.581417	−	0.813606i	$-0.302499\pi$
$223$	557.865	+	322.084i	0.167522	+	0.0967189i	−0.413895	+	0.910325i	$0.635832\pi$
$224$	−317.469	−	549.873i	−0.0946956	−	0.164018i
$225$	3293.70	−	211.108i	0.975910	−	0.0625504i
$226$	−351.785	+	609.310i	−0.103542	+	0.179339i
$227$	−2236.62			−0.653963			−0.326982	−	0.945031i	$-0.606032\pi$
$227$	−2236.62			−0.653963			−0.326982	+	0.945031i	$0.606032\pi$
$228$	−1596.82	−	642.838i	−0.463826	−	0.186724i
$229$	−1464.94			−0.422733			−0.211366	−	0.977407i	$-0.567791\pi$
$229$	−1464.94			−0.422733			−0.211366	+	0.977407i	$0.567791\pi$
$230$	261.016	−	452.093i	0.0748299	−	0.129609i
$231$	−1865.61	+	1158.24i	−0.531376	+	0.329899i
$232$	438.613	+	759.700i	0.124122	+	0.214986i
$233$	−3737.46	−	2157.82i	−1.05085	−	0.606711i	−0.127966	−	0.991779i	$-0.540845\pi$
$233$	−3737.46	−	2157.82i	−1.05085	−	0.606711i	−0.922888	+	0.385068i	$0.874178\pi$
$234$	2737.42	+	1354.86i	0.764747	+	0.378504i
$235$	292.803			0.0812781
$236$	−1080.25			−0.297960
$237$	−178.451	−	5574.09i	−0.0489098	−	1.52775i
$238$	4178.19	−	2412.28i	1.13795	−	0.656996i
$239$		−	629.940i		−	0.170491i	−0.996360	−	0.0852457i	$-0.972832\pi$
$239$		−	629.940i		−	0.170491i	0.996360	−	0.0852457i	$-0.0271675\pi$
$240$	−121.784	−	65.2080i	−0.0327547	−	0.0175382i
$241$	640.846	−	369.993i	0.171289	−	0.0988935i	−0.411905	−	0.911227i	$-0.635136\pi$
$241$	640.846	−	369.993i	0.171289	−	0.0988935i	0.583193	+	0.812333i	$0.301803\pi$
$242$	877.371	−	1519.65i	0.233056	−	0.403665i
$243$	−1347.10	+	3540.37i	−0.355624	+	0.934629i
$244$	419.700	−	726.941i	0.110117	−	0.190728i
$245$	−72.9544	−	42.1202i	−0.0190240	−	0.0109835i
$246$	399.385	−	745.902i	0.103512	−	0.193321i
$247$	2769.16	+	3778.32i	0.713349	+	0.973314i
$248$			354.928i			0.0908788i
$249$	5140.05	−	3191.15i	1.30818	−	0.812173i
$250$	711.548	+	410.813i	0.180009	+	0.103928i
$251$	−6236.06	+	3600.39i	−1.56819	+	0.905397i	−0.571813	+	0.820384i	$0.693760\pi$
$251$	−6236.06	+	3600.39i	−1.56819	+	0.905397i	−0.996380	+	0.0850128i	$0.972907\pi$
$252$	−2138.53	+	137.068i	−0.534582	+	0.0342638i
$253$	−1672.86	−	2897.49i	−0.415700	−	0.720013i
$254$			2497.73i			0.617013i
$255$	495.481	−	925.373i	0.121679	−	0.227251i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−1680.50	−	2910.72i	−0.407887	−	0.706481i	0.586766	−	0.809757i	$-0.300401\pi$
$257$	−1680.50	−	2910.72i	−0.407887	−	0.706481i	−0.994653	+	0.103276i	$0.967068\pi$
$258$	−2024.92	+	3781.79i	−0.488628	+	0.912574i
$259$			6818.58i			1.63585i
$260$	187.968	+	325.570i	0.0448356	+	0.0776576i
$261$	2954.58	−	189.372i	0.700704	−	0.0449112i
$262$	−3468.36	+	2002.46i	−0.817847	+	0.472184i
$263$	5190.58	+	2996.78i	1.21698	+	0.702621i	0.964270	−	0.264922i	$-0.0853462\pi$
$263$	5190.58	+	2996.78i	1.21698	+	0.702621i	0.252706	+	0.967543i	$0.418680\pi$
$264$	−752.191	+	466.990i	−0.175357	+	0.108868i
$265$			505.319i			0.117138i
$266$	−3007.95	−	1324.29i	−0.693344	−	0.305253i
$267$	−159.115	+	297.168i	−0.0364707	+	0.0681137i
$268$	1917.03	+	1106.80i	0.436945	+	0.252270i
$269$	−1726.55	+	2990.47i	−0.391336	+	0.677815i	−0.992626	−	0.121217i	$-0.961320\pi$
$269$	−1726.55	+	2990.47i	−0.391336	+	0.677815i	0.601290	+	0.799031i	$0.294654\pi$
$270$	−379.562	+	270.749i	−0.0855534	+	0.0610269i
$271$	−2218.63	+	3842.77i	−0.497313	+	0.861372i	−0.999995	−	0.00309958i	$-0.999013\pi$
$271$	−2218.63	+	3842.77i	−0.497313	+	0.861372i	0.502682	+	0.864471i	$0.332347\pi$
$272$	1684.60	−	972.604i	0.375529	−	0.216812i
$273$	5141.06	+	2752.72i	1.13975	+	0.610265i
$274$		−	5302.89i		−	1.16919i
$275$	2254.71	−	1301.76i	0.494415	−	0.285451i
$276$	−104.473	−	3263.32i	−0.0227846	−	0.711698i
$277$	2854.66			0.619206			0.309603	−	0.950866i	$-0.399804\pi$
$277$	2854.66			0.619206			0.309603	+	0.950866i	$0.399804\pi$
$278$	−5444.08			−1.17451
$279$	1073.58	+	531.359i	0.230372	+	0.114020i
$280$	−228.417	−	131.877i	−0.0487520	−	0.0281470i
$281$	−2479.52	−	4294.66i	−0.526392	−	0.911737i	−0.999527	−	0.0307474i	$-0.990211\pi$
$281$	−2479.52	−	4294.66i	−0.526392	−	0.911737i	0.473136	−	0.880990i	$-0.343122\pi$
$282$	1555.84	−	965.931i	0.328543	−	0.203973i
$283$	1595.31	−	2763.15i	0.335092	−	0.580397i	−0.648410	−	0.761291i	$-0.724566\pi$
$283$	1595.31	−	2763.15i	0.335092	−	0.580397i	0.983503	+	0.180894i	$0.0578992\pi$
$284$	−1765.03			−0.368787
$285$	−707.970	+	100.401i	−0.147146	+	0.0208676i
$286$	2409.39			0.498148
$287$	807.718	−	1399.01i	0.166126	−	0.287738i
$288$	−862.231	+	55.2642i	−0.176415	+	0.0113072i
$289$	4933.80	+	8545.60i	1.00423	+	1.73938i
$290$	315.580	+	182.200i	0.0639016	+	0.0368936i
$291$	−131.948	−	4121.53i	−0.0265805	−	0.830269i
$292$	−1135.21			−0.227510
$293$	9391.88			1.87263			0.936313	−	0.351167i	$-0.114215\pi$
$293$	9391.88			1.87263			0.936313	+	0.351167i	$0.114215\pi$
$294$	−526.603	+	16.8589i	−0.104463	+	0.00334432i
$295$	−388.618	+	224.369i	−0.0766991	+	0.0442822i
$296$			2749.17i			0.539839i
$297$	286.449	+	2974.34i	0.0559644	+	0.581108i
$298$	4841.61	−	2795.31i	0.941164	−	0.543382i
$299$	−4442.60	+	7694.80i	−0.859271	+	1.48830i
$300$	2539.39	−	81.2970i	0.488706	−	0.0156456i
$301$	−4095.20	+	7093.10i	−0.784198	+	1.35827i
$302$	10.1618	+	5.86693i	0.00193625	+	0.00111789i
$303$	4474.48	+	2395.81i	0.848357	+	0.454244i
$304$	−1212.77	−	533.937i	−0.228807	−	0.100735i
$305$		−	348.687i		−	0.0654615i
$306$	−419.923	−	6551.63i	−0.0784491	−	1.22396i
$307$	1863.53	+	1075.91i	0.346440	+	0.200017i	0.663116	−	0.748516i	$-0.269234\pi$
$307$	1863.53	+	1075.91i	0.346440	+	0.200017i	−0.316676	+	0.948534i	$0.602567\pi$
$308$	−1463.94	+	845.205i	−0.270830	+	0.156364i
$309$	−1823.75	+	1132.26i	−0.335760	+	0.208453i
$310$	73.7185	+	127.684i	0.0135062	+	0.0233935i
$311$		−	8834.65i		−	1.61083i	−0.592713	−	0.805414i	$-0.701943\pi$
$311$		−	8834.65i		−	1.61083i	0.592713	−	0.805414i	$-0.298057\pi$
$312$	2072.82	+	1109.87i	0.376122	+	0.201390i
$313$	−4668.60	−	8086.26i	−0.843083	−	1.46026i	−0.887276	−	0.461240i	$-0.847405\pi$
$313$	−4668.60	−	8086.26i	−0.843083	−	1.46026i	0.0441927	−	0.999023i	$-0.485928\pi$
$314$	−2312.39	−	4005.18i	−0.415592	−	0.719827i
$315$	−740.861	+	493.483i	−0.132517	+	0.0882686i
$316$		−	4293.13i		−	0.764264i
$317$	2202.74	+	3815.26i	0.390279	+	0.675983i	0.992486	−	0.122357i	$-0.0390453\pi$
$317$	2202.74	+	3815.26i	0.390279	+	0.675983i	−0.602207	+	0.798340i	$0.705712\pi$
$318$	1667.00	+	2685.07i	0.293965	+	0.473495i
$319$	2022.57	−	1167.73i	0.354990	−	0.204954i
$320$	−92.0953	−	53.1712i	−0.0160884	−	0.00928863i
$321$	2447.82	+	3942.76i	0.425621	+	0.685556i
$322$		−	6233.79i		−	1.07887i
$323$	4057.10	−	9215.21i	0.698895	−	1.58746i
$324$	−1123.67	+	2690.80i	−0.192674	+	0.461386i
$325$	−5987.80	−	3457.06i	−1.02198	−	0.590040i
$326$	1070.79	−	1854.66i	0.181918	−	0.315092i
$327$	−84.8048	−	2648.96i	−0.0143416	−	0.447975i
$328$	325.662	−	564.064i	0.0548223	−	0.0949549i
$329$	3028.04	−	1748.24i	0.507420	−	0.292959i
$330$	−173.605	+	324.228i	−0.0289594	+	0.0540854i
$331$		−	6219.09i		−	1.03273i	−0.856370	−	0.516363i	$-0.827286\pi$
$331$		−	6219.09i		−	1.03273i	0.856370	−	0.516363i	$-0.172714\pi$
$332$	4033.39	−	2328.68i	0.666751	−	0.384949i
$333$	8315.66	+	4115.76i	1.36846	+	0.677304i
$334$	−6336.97			−1.03815
$335$	919.527			0.149968
$336$	−1648.77	+	52.7845i	−0.267702	+	0.00857033i
$337$	−10453.5	−	6035.32i	−1.68973	−	0.975564i	−0.954721	−	0.297502i	$-0.903847\pi$
$337$	−10453.5	−	6035.32i	−1.68973	−	0.975564i	−0.735005	−	0.678062i	$-0.762820\pi$
$338$	−1002.29	−	1736.01i	−0.161294	−	0.279369i
$339$	964.150	+	1552.98i	0.154470	+	0.248809i
$340$	404.020	−	699.783i	0.0644443	−	0.111621i
$341$	944.932			0.150061
$342$	−3430.68	+	2869.03i	−0.542426	+	0.453623i
$343$	5799.80			0.913002
$344$	−1651.14	+	2859.86i	−0.258789	+	0.448236i
$345$	−715.376	−	1152.27i	−0.111636	−	0.179815i
$346$	157.852	+	273.407i	0.0245265	+	0.0424811i
$347$	−3626.43	−	2093.72i	−0.561029	−	0.323910i	0.192529	−	0.981291i	$-0.438331\pi$
$347$	−3626.43	−	2093.72i	−0.561029	−	0.323910i	−0.753559	+	0.657381i	$0.771664\pi$
$348$	2277.93	−	72.9266i	0.350891	−	0.0112336i
$349$	−8340.81			−1.27929			−0.639647	−	0.768669i	$-0.720919\pi$
$349$	−8340.81			−1.27929			−0.639647	+	0.768669i	$0.720919\pi$
$350$	4850.90			0.740832
$351$	6460.31	−	4608.26i	0.982409	−	0.700771i
$352$	−590.243	+	340.777i	−0.0893752	+	0.0516008i
$353$			11746.7i			1.77114i	0.464508	+	0.885569i	$0.346231\pi$
$353$			11746.7i			1.77114i	−0.464508	+	0.885569i	$0.653769\pi$
$354$	−1324.80	+	2474.23i	−0.198905	+	0.371480i
$355$	−634.966	+	366.598i	−0.0949310	+	0.0548084i
$356$	−129.744	+	224.723i	−0.0193158	+	0.0334559i
$357$	−401.081	−	12528.2i	−0.0594607	−	1.85731i
$358$	4596.07	−	7960.63i	0.678519	−	1.17523i
$359$	−8792.64	−	5076.43i	−1.29264	−	0.746306i	−0.313518	−	0.949582i	$-0.601508\pi$
$359$	−8792.64	−	5076.43i	−1.29264	−	0.746306i	−0.979121	+	0.203276i	$0.934841\pi$
$360$	−298.707	+	198.967i	−0.0437312	+	0.0291290i
$361$	−6697.04	+	1481.74i	−0.976387	+	0.216029i
$362$			4695.57i			0.681750i
$363$	−2404.64	−	3873.21i	−0.347689	−	0.560030i
$364$	3887.76	+	2244.60i	0.559818	+	0.323211i
$365$	−408.388	+	235.783i	−0.0585644	+	0.0338121i
$366$	−1150.29	−	1852.79i	−0.164280	−	0.264609i
$367$	4448.57	+	7705.15i	0.632734	+	1.09593i	0.986990	+	0.160779i	$0.0514006\pi$
$367$	4448.57	+	7705.15i	0.632734	+	1.09593i	−0.354257	+	0.935148i	$0.615266\pi$
$368$		−	2513.39i		−	0.356032i
$369$	−1218.63	−	1829.51i	−0.171922	−	0.258105i
$370$	571.003	+	989.007i	0.0802299	+	0.138962i
$371$	3017.11	+	5225.78i	0.422211	+	0.731291i
$372$	812.932	+	435.275i	0.113303	+	0.0606666i
$373$			9681.90i			1.34399i	0.740554	+	0.671997i	$0.234563\pi$
$373$			9681.90i			1.34399i	−0.740554	+	0.671997i	$0.765437\pi$
$374$	−2589.38	−	4484.95i	−0.358005	−	0.620083i
$375$	1813.56	−	1125.93i	0.249738	−	0.155047i
$376$	1220.87	−	704.869i	0.167451	−	0.0966778i
$377$	−5371.29	−	3101.12i	−0.733782	−	0.423649i
$378$	−2308.70	+	5066.22i	−0.314145	+	0.689360i
$379$		−	5571.36i		−	0.755097i	−0.925990	−	0.377548i	$-0.876767\pi$
$379$		−	5571.36i		−	0.755097i	0.925990	−	0.377548i	$-0.123233\pi$
$380$	−547.190	+	59.8106i	−0.0738691	+	0.00807426i
$381$	5720.83	+	3063.16i	0.769257	+	0.411890i
$382$	1265.96	+	730.904i	0.169561	+	0.0978960i
$383$	−3239.79	+	5611.48i	−0.432234	+	0.748651i	−0.997065	−	0.0765554i	$-0.975608\pi$
$383$	−3239.79	+	5611.48i	−0.432234	+	0.748651i	0.564832	+	0.825206i	$0.308941\pi$
$384$	−664.767	+	21.2821i	−0.0883431	+	0.00282825i
$385$	−351.098	+	608.120i	−0.0464770	+	0.0805005i
$386$	−789.463	+	455.797i	−0.104100	+	0.0601022i
$387$	6178.56	+	9275.81i	0.811560	+	1.21839i
$388$		−	3174.38i		−	0.415347i
$389$	2835.38	−	1637.01i	0.369562	−	0.213367i	−0.303705	−	0.952766i	$-0.598224\pi$
$389$	2835.38	−	1637.01i	0.369562	−	0.213367i	0.673267	+	0.739399i	$0.264890\pi$
$390$	976.209	−	31.2527i	0.126749	−	0.00405780i
$391$	19097.9			2.47014
$392$	−405.587			−0.0522583
$393$	332.942	+	10399.8i	0.0427346	+	1.33486i
$394$	340.947	+	196.846i	0.0435956	+	0.0251700i
$395$	−891.684	−	1544.44i	−0.113583	−	0.196732i
$396$	147.131	+	2295.53i	0.0186707	+	0.291300i
$397$	−3635.25	+	6296.45i	−0.459567	+	0.795994i	−0.998938	−	0.0460745i	$-0.985329\pi$
$397$	−3635.25	+	6296.45i	−0.459567	+	0.795994i	0.539371	+	0.842068i	$0.318662\pi$
$398$	1563.55			0.196918
$399$	−6722.05	+	5265.38i	−0.843417	+	0.660649i
$400$	1955.83			0.244478
$401$	1342.46	−	2325.20i	0.167180	−	0.289564i	−0.770247	−	0.637745i	$-0.779867\pi$
$401$	1342.46	−	2325.20i	0.167180	−	0.289564i	0.937427	+	0.348181i	$0.113201\pi$
$402$	4886.03	−	3033.44i	0.606201	−	0.376354i
$403$	−1254.72	−	2173.24i	−0.155092	−	0.268627i
$404$	3383.68	+	1953.57i	0.416694	+	0.240578i
$405$	154.641	+	1201.40i	0.0189732	+	0.147402i
$406$	4351.44			0.531918
$407$	7319.18			0.891396
$408$	−161.711	−	5051.21i	−0.0196223	−	0.612922i
$409$	−3609.09	+	2083.71i	−0.436327	+	0.251914i	−0.702039	−	0.712139i	$-0.747727\pi$
$409$	−3609.09	+	2083.71i	−0.436327	+	0.251914i	0.265711	+	0.964053i	$0.414393\pi$
$410$		−	270.560i		−	0.0325903i
$411$	−12145.8	−	6503.34i	−1.45768	−	0.780501i
$412$	−1431.10	+	826.245i	−0.171129	+	0.0988014i
$413$	−2679.28	+	4640.65i	−0.319222	+	0.552909i
$414$	−7602.48	−	3762.77i	−0.902515	−	0.446692i
$415$	967.334	−	1675.47i	0.114421	−	0.198182i
$416$	1567.50	+	904.996i	0.184743	+	0.106661i
$417$	−6676.50	+	12469.2i	−0.784052	+	1.46432i
$418$	−1421.51	+	3228.79i	−0.166336	+	0.377811i
$419$		−	1735.82i		−	0.202388i	−0.994867	−	0.101194i	$-0.967734\pi$
$419$		−	1735.82i		−	0.202388i	0.994867	−	0.101194i	$-0.0322662\pi$
$420$	−582.178	+	361.440i	−0.0676367	+	0.0419915i
$421$	−5008.32	−	2891.56i	−0.579788	−	0.334741i	0.181261	−	0.983435i	$-0.441982\pi$
$421$	−5008.32	−	2891.56i	−0.579788	−	0.334741i	−0.761049	+	0.648694i	$0.775315\pi$
$422$	−8121.22	+	4688.79i	−0.936812	+	0.540869i
$423$	−304.328	−	4748.12i	−0.0349810	−	0.545772i
$424$	1216.46	+	2106.97i	0.139332	+	0.241330i
$425$			14861.3i			1.69618i
$426$	−2164.60	+	4042.66i	−0.246186	+	0.459783i
$427$	−2081.90	−	3605.96i	−0.235949	−	0.408676i
$428$	1786.25	+	3093.88i	0.201733	+	0.349412i
$429$	2954.82	−	5518.50i	0.332541	−	0.621062i
$430$			1371.77i			0.153843i
$431$	−5067.18	−	8776.61i	−0.566305	−	0.980868i	−0.996927	−	0.0783361i	$-0.975039\pi$
$431$	−5067.18	−	8776.61i	−0.566305	−	0.980868i	0.430622	−	0.902532i	$-0.358294\pi$
$432$	−930.842	+	2042.64i	−0.103669	+	0.227492i
$433$	1693.44	−	977.706i	0.187948	−	0.108512i	−0.403074	−	0.915168i	$-0.632058\pi$
$433$	1693.44	−	977.706i	0.187948	−	0.108512i	0.591021	+	0.806656i	$0.298725\pi$
$434$	1524.73	+	880.302i	0.168639	+	0.0973638i
$435$	804.333	−	499.362i	0.0886548	−	0.0550404i
$436$		−	2040.22i		−	0.224102i
$437$	−7690.61	−	10493.3i	−0.841858	−	1.14866i
$438$	−1392.19	+	2600.10i	−0.151876	+	0.283647i
$439$	13617.7	+	7862.21i	1.48050	+	0.854767i	0.999756	−	0.0220937i	$-0.00703320\pi$
$439$	13617.7	+	7862.21i	1.48050	+	0.854767i	0.480744	+	0.876861i	$0.340367\pi$
$440$	−141.559	+	245.187i	−0.0153376	+	0.0265655i
$441$	−607.201	+	1226.82i	−0.0655653	+	0.132471i
$442$	−6876.58	+	11910.6i	−0.740013	+	1.28174i
$443$	−316.066	+	182.481i	−0.0338979	+	0.0195710i	−0.516853	−	0.856074i	$-0.672897\pi$
$443$	−316.066	+	182.481i	−0.0338979	+	0.0195710i	0.482955	+	0.875645i	$0.339563\pi$
$444$	6296.74	+	3371.52i	0.673041	+	0.360373i
$445$			107.791i			0.0114827i
$446$	1115.73	−	644.167i	0.118456	−	0.0683906i
$447$	−464.765	−	14517.4i	−0.0491782	−	1.53613i
$448$	−1269.88			−0.133920
$449$	7524.39			0.790864			0.395432	−	0.918495i	$-0.370595\pi$
$449$	7524.39			0.790864			0.395432	+	0.918495i	$0.370595\pi$
$450$	2928.05	−	5915.96i	0.306732	−	0.619735i
$451$	−1501.72	−	867.018i	−0.156792	−	0.0905239i
$452$	703.570	+	1218.62i	0.0732149	+	0.126812i
$453$	25.8999	−	16.0797i	0.00268628	−	0.00166775i
$454$	−2236.62	+	3873.94i	−0.231211	+	0.400469i
$455$	1864.81			0.192140
$456$	−2710.25	+	2122.94i	−0.278332	+	0.218017i
$457$	−8316.45			−0.851263			−0.425631	−	0.904897i	$-0.639948\pi$
$457$	−8316.45			−0.851263			−0.425631	+	0.904897i	$0.639948\pi$
$458$	−1464.94	+	2537.35i	−0.149459	+	0.258870i
$459$	−15520.9	−	7072.98i	−1.57833	−	0.719256i
$460$	−522.032	−	904.185i	−0.0529127	−	0.0916475i
$461$	8970.62	+	5179.19i	0.906298	+	0.523251i	0.879238	−	0.476382i	$-0.158052\pi$
$461$	8970.62	+	5179.19i	0.906298	+	0.523251i	0.0270598	+	0.999634i	$0.491386\pi$
$462$	140.529	+	4389.57i	0.0141515	+	0.442037i
$463$	3365.82			0.337847			0.168923	−	0.985629i	$-0.445971\pi$
$463$	3365.82			0.337847			0.168923	+	0.985629i	$0.445971\pi$
$464$	1754.45			0.175535
$465$	382.857	−	12.2569i	0.0381818	−	0.00122237i
$466$	−7474.92	+	4315.65i	−0.743066	+	0.429009i
$467$		−	2275.51i		−	0.225477i	−0.993625	−	0.112739i	$-0.964038\pi$
$467$		−	2275.51i		−	0.225477i	0.993625	−	0.112739i	$-0.0359623\pi$
$468$	5084.11	−	3386.49i	0.502165	−	0.334489i
$469$	9509.34	−	5490.22i	0.936249	−	0.540543i
$470$	292.803	−	507.149i	0.0287361	−	0.0497725i
$471$	−12009.4	+	384.474i	−1.17487	+	0.0376128i
$472$	−1080.25	+	1871.06i	−0.105345	+	0.182462i
$473$	7613.86	+	4395.86i	0.740139	+	0.427319i
$474$	−9833.05	−	5265.00i	−0.952842	−	0.510189i
$475$	8165.48	−	5984.54i	0.788754	−	0.578083i
$476$		−	9649.12i		−	0.929132i
$477$	8194.31	−	525.210i	0.786565	−	0.0504145i
$478$	−1091.09	−	629.940i	−0.104404	−	0.0602778i
$479$	−7635.00	+	4408.07i	−0.728292	+	0.420480i	−0.817797	−	0.575507i	$-0.804805\pi$
$479$	−7635.00	+	4408.07i	−0.728292	+	0.420480i	0.0895048	+	0.995986i	$0.471472\pi$
$480$	−234.728	+	145.728i	−0.0223204	+	0.0138574i
$481$	−9718.71	−	16833.3i	−0.921279	−	1.59570i
$482$		−	1479.97i		−	0.139856i
$483$	−14278.0	−	7644.98i	−1.34507	−	0.720204i
$484$	−1754.74	−	3039.30i	−0.164795	−	0.285434i
$485$	−659.319	−	1141.97i	−0.0617281	−	0.106916i
$486$	4785.00	+	5873.62i	0.446609	+	0.548216i
$487$			5023.60i			0.467435i	0.972304	+	0.233718i	$0.0750892\pi$
$487$			5023.60i			0.467435i	−0.972304	+	0.233718i	$0.924911\pi$
$488$	−839.400	−	1453.88i	−0.0778644	−	0.134865i
$489$	−2934.74	−	4727.05i	−0.271398	−	0.437147i
$490$	−145.909	+	84.2405i	−0.0134520	+	0.00776652i
$491$	4955.92	+	2861.30i	0.455514	+	0.262991i	0.710156	−	0.704044i	$-0.248624\pi$
$491$	4955.92	+	2861.30i	0.455514	+	0.262991i	−0.254642	+	0.967035i	$0.581958\pi$
$492$	−892.555	−	1437.66i	−0.0817876	−	0.131737i
$493$			13331.2i			1.21786i
$494$	9313.40	−	1018.00i	0.848238	−	0.0927166i
$495$	529.713	+	795.253i	0.0480986	+	0.0722100i
$496$	614.753	+	354.928i	0.0556517	+	0.0321305i
$497$	−4377.69	+	7582.38i	−0.395103	+	0.684339i
$498$	−387.181	−	12094.0i	−0.0348394	−	1.08824i
$499$	1611.36	−	2790.96i	0.144558	−	0.250382i	−0.784650	−	0.619939i	$-0.787157\pi$
$499$	1611.36	−	2790.96i	0.144558	−	0.250382i	0.929208	+	0.369557i	$0.120491\pi$
$500$	1423.10	−	821.625i	0.127286	−	0.0734884i
$501$	−7771.51	+	14514.3i	−0.693025	+	1.29431i
$502$			14401.6i			1.28042i
$503$	12177.6	−	7030.74i	1.07947	−	0.623231i	0.148715	−	0.988880i	$-0.452486\pi$
$503$	12177.6	−	7030.74i	1.07947	−	0.623231i	0.930753	+	0.365649i	$0.119153\pi$
$504$	−1901.12	+	3841.11i	−0.168021	+	0.339477i
$505$	1623.03			0.143017
$506$	−6691.46			−0.587888
$507$	−5205.38	+	166.647i	−0.455974	+	0.0145977i
$508$	4326.19	+	2497.73i	0.377842	+	0.218147i
$509$	−3746.26	−	6488.70i	−0.326228	−	0.565043i	0.655532	−	0.755167i	$-0.272444\pi$
$509$	−3746.26	−	6488.70i	−0.326228	−	0.565043i	−0.981760	+	0.190124i	$0.939111\pi$
$510$	−1107.31	−	1783.57i	−0.0961424	−	0.154859i
$511$	−2815.58	+	4876.72i	−0.243745	+	0.422179i
$512$	−512.000			−0.0441942
$513$	2363.96	+	11376.2i	0.203453	+	0.979085i
$514$	−6722.02			−0.576839
$515$	−343.222	+	594.478i	−0.0293673	+	0.0508657i
$516$	4525.34	+	7289.06i	0.386079	+	0.621866i
$517$	−1876.59	−	3250.35i	−0.159637	−	0.276499i
$518$	11810.1	+	6818.58i	1.00175	+	0.578361i
$519$	819.802	−	26.2455i	0.0693359	−	0.00221974i
$520$	751.871			0.0634072
$521$	−8702.80			−0.731817			−0.365908	−	0.930651i	$-0.619242\pi$
$521$	−8702.80			−0.731817			−0.365908	+	0.930651i	$0.619242\pi$
$522$	2626.57	−	5306.85i	0.220234	−	0.444970i
$523$	7102.18	−	4100.44i	0.593798	−	0.342830i	−0.172800	−	0.984957i	$-0.555281\pi$
$523$	7102.18	−	4100.44i	0.593798	−	0.342830i	0.766598	+	0.642127i	$0.221948\pi$
$524$			8009.83i			0.667769i
$525$	5949.03	−	11110.6i	0.494546	−	0.923628i
$526$	10381.2	−	5993.56i	0.860532	−	0.496828i
$527$	−2696.91	+	4671.18i	−0.222921	+	0.386110i
$528$	56.6598	+	1769.82i	0.00467008	+	0.145874i
$529$	6254.66	−	10833.4i	0.514067	−	0.890391i
$530$	875.238	+	505.319i	0.0717319	+	0.0414144i
$531$	4042.31	+	6068.68i	0.330360	+	0.495967i
$532$	−5301.68	+	3885.64i	−0.432062	+	0.316661i
$533$			4605.05i			0.374234i
$534$	355.594	+	572.763i	0.0288166	+	0.0464155i
$535$	1285.20	+	742.010i	0.103858	+	0.0599624i
$536$	3834.06	−	2213.59i	0.308967	−	0.178382i
$537$	−12596.6	−	20289.6i	−1.01226	−	1.63047i
$538$	3453.10	+	5980.94i	0.276717	+	0.479287i
$539$			1079.80i			0.0862902i
$540$	89.3888	+	928.170i	0.00712348	+	0.0739668i
$541$	9894.92	+	17138.5i	0.786351	+	1.36200i	0.928189	+	0.372110i	$0.121366\pi$
$541$	9894.92	+	17138.5i	0.786351	+	1.36200i	−0.141838	+	0.989890i	$0.545301\pi$
$542$	4437.25	+	7685.54i	0.351654	+	0.609082i
$543$	10754.8	+	5758.54i	0.849968	+	0.455106i
$544$		−	3890.42i		−	0.306618i
$545$	−423.753	−	733.961i	−0.0333056	−	0.0576871i
$546$	9908.92	−	6151.85i	0.776671	−	0.482189i
$547$	19.1289	−	11.0441i	0.00149524	−	0.000863275i	−0.499252	−	0.866457i	$-0.666392\pi$
$547$	19.1289	−	11.0441i	0.00149524	−	0.000863275i	0.500747	+	0.865593i	$0.333059\pi$
$548$	−9184.87	−	5302.89i	−0.715982	−	0.413372i
$549$	−5654.35	+	362.412i	−0.439566	+	0.0281737i
$550$		−	5207.03i		−	0.403689i
$551$	7324.76	−	5368.37i	0.566325	−	0.415064i
$552$	−5756.71	−	3082.37i	−0.443880	−	0.237671i
$553$	−18442.8	−	10647.9i	−1.41820	−	0.818801i
$554$	2854.66	−	4944.42i	0.218923	−	0.379185i
$555$	2965.50	−	94.9387i	0.226808	−	0.00726112i
$556$	−5444.08	+	9429.42i	−0.415253	+	0.719239i
$557$	20743.3	−	11976.1i	1.57795	−	0.911032i	0.582809	−	0.812609i	$-0.301954\pi$
$557$	20743.3	−	11976.1i	1.57795	−	0.911032i	0.995145	−	0.0984230i	$-0.0313798\pi$
$558$	1993.92	−	1328.14i	0.151271	−	0.100761i
$559$		−	23348.0i		−	1.76658i
$560$	−456.835	+	263.754i	−0.0344728	+	0.0199029i
$561$	−13447.9	+	430.528i	−1.01207	+	0.0324009i
$562$	−9918.10			−0.744430
$563$	−10450.7			−0.782315			−0.391157	−	0.920324i	$-0.627925\pi$
$563$	−10450.7			−0.782315			−0.391157	+	0.920324i	$0.627925\pi$
$564$	−117.196	−	3660.73i	−0.00874973	−	0.273306i
$565$	506.215	+	292.263i	0.0376931	+	0.0217621i
$566$	−3190.61	−	5526.30i	−0.236946	−	0.410403i
$567$	8772.40	+	11501.0i	0.649746	+	0.851844i
$568$	−1765.03	+	3057.13i	−0.130386	+	0.225835i
$569$	25832.8			1.90328			0.951642	−	0.307209i	$-0.0993950\pi$
$569$	25832.8			1.90328			0.951642	+	0.307209i	$0.0993950\pi$
$570$	−534.070	+	1326.64i	−0.0392452	+	0.0974858i
$571$	−17286.5			−1.26693			−0.633467	−	0.773770i	$-0.718369\pi$
$571$	−17286.5			−1.26693			−0.633467	+	0.773770i	$0.718369\pi$
$572$	2409.39	−	4173.19i	0.176122	−	0.305052i
$573$	3226.62	−	2003.21i	0.235243	−	0.146048i
$574$	−1615.44	−	2798.02i	−0.117469	−	0.203462i
$575$	16629.6	+	9601.08i	1.20609	+	0.696335i
$576$	−766.510	+	1548.69i	−0.0554478	+	0.112029i
$577$	5691.51			0.410642			0.205321	−	0.978695i	$-0.434176\pi$
$577$	5691.51			0.410642			0.205321	+	0.978695i	$0.434176\pi$
$578$	19735.2			1.42020
$579$	75.7837	+	2367.18i	0.00543949	+	0.169908i
$580$	631.159	−	364.400i	0.0451853	−	0.0260877i
$581$		−	23102.6i		−	1.64967i
$582$	−7270.65	−	3892.99i	−0.517832	−	0.277267i
$583$	5609.44	−	3238.61i	0.398490	−	0.230068i
$584$	−1135.21	+	1966.24i	−0.0804370	+	0.139321i
$585$	1125.62	−	2274.25i	0.0795532	−	0.160733i
$586$	9391.88	−	16267.2i	0.662073	−	1.14674i
$587$	−3650.54	−	2107.64i	−0.256685	−	0.148197i	0.366137	−	0.930561i	$-0.380680\pi$
$587$	−3650.54	−	2107.64i	−0.256685	−	0.148197i	−0.622821	+	0.782364i	$0.714014\pi$
$588$	−497.403	+	928.963i	−0.0348853	+	0.0651527i
$589$	3652.59	−	399.247i	0.255522	−	0.0279298i
$590$			897.475i			0.0626245i
$591$	868.989	−	539.503i	0.0604830	−	0.0375503i
$592$	4761.71	+	2749.17i	0.330583	+	0.190862i
$593$	9098.95	−	5253.28i	0.630100	−	0.363788i	−0.150691	−	0.988581i	$-0.548150\pi$
$593$	9098.95	−	5253.28i	0.630100	−	0.363788i	0.780791	+	0.624793i	$0.214816\pi$
$594$	5438.16	+	2478.20i	0.375641	+	0.171182i
$595$	−2004.12	−	3471.24i	−0.138086	−	0.239172i
$596$		−	11181.2i		−	0.768458i
$597$	1917.50	−	3581.17i	0.131454	−	0.245507i
$598$	8885.19	+	15389.6i	0.607596	+	1.05239i
$599$	−2441.96	−	4229.60i	−0.166571	−	0.288509i	0.770641	−	0.637269i	$-0.219936\pi$
$599$	−2441.96	−	4229.60i	−0.166571	−	0.288509i	−0.937212	+	0.348760i	$0.886603\pi$
$600$	2398.58	−	4479.65i	0.163203	−	0.304802i
$601$			9250.23i			0.627828i	0.949451	+	0.313914i	$0.101640\pi$
$601$			9250.23i			0.627828i	−0.949451	+	0.313914i	$0.898360\pi$
$602$	8190.41	+	14186.2i	0.554512	+	0.960443i
$603$	−955.723	−	14911.2i	−0.0645440	−	1.00701i
$604$	20.3236	−	11.7339i	0.00136913	−	0.000790470i
$605$	−1262.53	−	728.920i	−0.0848413	−	0.0489832i
$606$	8624.15	−	5354.22i	0.578106	−	0.358911i
$607$			4967.87i			0.332190i	0.986110	+	0.166095i	$0.0531159\pi$
$607$			4967.87i			0.332190i	−0.986110	+	0.166095i	$0.946884\pi$
$608$	−2137.58	+	1566.65i	−0.142583	+	0.104500i
$609$	5336.51	−	9966.61i	0.355084	−	0.663165i
$610$	−603.943	−	348.687i	−0.0400868	−	0.0231441i
$611$	−4983.62	+	8631.89i	−0.329977	+	0.571537i
$612$	−11767.7	−	5824.31i	−0.777256	−	0.384695i
$613$	13982.5	−	24218.3i	0.921283	−	1.59571i	0.123850	−	0.992301i	$-0.460476\pi$
$613$	13982.5	−	24218.3i	0.921283	−	1.59571i	0.797433	−	0.603408i	$-0.206191\pi$
$614$	3727.05	−	2151.81i	0.244970	−	0.141434i
$615$	−619.696	−	331.809i	−0.0406318	−	0.0217558i
$616$			3380.82i			0.221132i
$617$	−21402.3	+	12356.6i	−1.39648	+	0.806256i	−0.994022	−	0.109184i	$-0.965176\pi$
$617$	−21402.3	+	12356.6i	−1.39648	+	0.806256i	−0.402455	+	0.915440i	$0.631843\pi$
$618$	137.377	+	4291.10i	0.00894192	+	0.279309i
$619$	1597.89			0.103755			0.0518776	−	0.998653i	$-0.483479\pi$
$619$	1597.89			0.103755			0.0518776	+	0.998653i	$0.483479\pi$
$620$	294.874			0.0191007
$621$	−17941.8	+	12798.2i	−1.15939	+	0.827014i
$622$	−15302.1	−	8834.65i	−0.986426	−	0.569513i
$623$	643.590	+	1114.73i	0.0413883	+	0.0716866i
$624$	3995.16	−	2480.36i	0.256305	−	0.159125i
$625$	−7298.64	+	12641.6i	−0.467113	+	0.809063i
$626$	−18674.4			−1.19230
$627$	5651.95	+	7215.56i	0.359996	+	0.459588i
$628$	−9249.58			−0.587736
$629$	−20889.5	+	36181.7i	−1.32420	+	2.29357i
$630$	113.876	+	1776.69i	0.00720148	+	0.112357i
$631$	3925.45	+	6799.07i	0.247654	+	0.428949i	0.962874	−	0.269950i	$-0.0870071\pi$
$631$	3925.45	+	6799.07i	0.247654	+	0.428949i	−0.715221	+	0.698899i	$0.753674\pi$
$632$	−7435.92	−	4293.13i	−0.468014	−	0.270208i
$633$	779.588	+	24351.2i	0.0489508	+	1.52902i
$634$	8810.97			0.551938
$635$	2075.11			0.129682
$636$	6317.69	−	202.257i	0.393888	−	0.0126101i
$637$	2483.43	−	1433.81i	0.154469	−	0.0891829i
$638$		−	4670.92i		−	0.289848i
$639$	6604.75	+	9915.66i	0.408889	+	0.613861i
$640$	−184.191	+	106.342i	−0.0113762	+	0.00656805i
$641$	−680.198	+	1178.14i	−0.0419129	+	0.0725953i	−0.886221	−	0.463263i	$-0.846679\pi$
$641$	−680.198	+	1178.14i	−0.0419129	+	0.0725953i	0.844308	+	0.535858i	$0.180012\pi$
$642$	9276.89	−	296.994i	0.570295	−	0.0182577i
$643$	−15760.3	+	27297.6i	−0.966603	+	1.67421i	−0.261358	+	0.965242i	$0.584170\pi$
$643$	−15760.3	+	27297.6i	−0.966603	+	1.67421i	−0.705245	+	0.708964i	$0.749163\pi$
$644$	−10797.2	−	6233.79i	−0.660669	−	0.381437i
$645$	3141.92	+	1682.30i	0.191803	+	0.102699i
$646$	−11904.1	−	16242.3i	−0.725017	−	0.989234i
$647$			5359.04i			0.325635i	0.986656	+	0.162817i	$0.0520581\pi$
$647$			5359.04i			0.325635i	−0.986656	+	0.162817i	$0.947942\pi$
$648$	3536.93	+	4637.06i	0.214419	+	0.281113i
$649$	4981.35	+	2875.98i	0.301287	+	0.173948i
$650$	−11975.6	+	6914.12i	−0.722649	+	0.417222i
$651$	3886.15	−	2412.68i	0.233963	−	0.145254i
$652$	−2141.57	−	3709.31i	−0.128636	−	0.222803i
$653$		−	32229.2i		−	1.93143i	−0.259597	−	0.965717i	$-0.583590\pi$
$653$		−	32229.2i		−	1.93143i	0.259597	−	0.965717i	$-0.416410\pi$
$654$	−4672.94	−	2502.07i	−0.279398	−	0.149601i
$655$	1663.64	+	2881.51i	0.0992426	+	0.171893i
$656$	−651.325	−	1128.13i	−0.0387652	−	0.0671433i
$657$	4247.94	+	6377.40i	0.252250	+	0.378700i
$658$		−	6992.95i		−	0.414306i
$659$	2795.97	+	4842.76i	0.165274	+	0.286262i	0.936752	−	0.349993i	$-0.113816\pi$
$659$	2795.97	+	4842.76i	0.165274	+	0.286262i	−0.771479	+	0.636255i	$0.780483\pi$
$660$	387.976	+	624.920i	0.0228817	+	0.0368561i
$661$	13576.6	−	7838.45i	0.798894	−	0.461241i	−0.0441906	−	0.999023i	$-0.514071\pi$
$661$	13576.6	−	7838.45i	0.798894	−	0.461241i	0.843084	+	0.537782i	$0.180738\pi$
$662$	−10771.8	−	6219.09i	−0.632413	−	0.365124i
$663$	18846.9	+	30357.1i	1.10400	+	1.77824i
$664$		−	9314.72i		−	0.544400i
$665$	−1100.22	+	2499.01i	−0.0641573	+	0.145725i
$666$	15444.4	−	10287.4i	0.898584	−	0.598541i
$667$	14917.4	+	8612.55i	0.865972	+	0.499969i
$668$	−6336.97	+	10975.9i	−0.367043	+	0.635737i
$669$	−107.103	−	3345.48i	−0.00618962	−	0.193339i
$670$	919.527	−	1592.67i	0.0530216	−	0.0918360i
$671$	−3870.70	+	2234.75i	−0.222693	+	0.128572i
$672$	−1557.35	+	2908.55i	−0.0893989	+	0.166964i
$673$		−	3619.35i		−	0.207304i	−0.994614	−	0.103652i	$-0.966947\pi$
$673$		−	3619.35i		−	0.207304i	0.994614	−	0.103652i	$-0.0330529\pi$
$674$	−20907.0	+	12070.6i	−1.19482	+	0.689828i
$675$	−9959.10	−	13961.6i	−0.567891	−	0.796124i
$676$	−4009.15			−0.228104
$677$	−12482.2			−0.708614			−0.354307	−	0.935129i	$-0.615283\pi$
$677$	−12482.2			−0.708614			−0.354307	+	0.935129i	$0.615283\pi$
$678$	3653.99	−	116.980i	0.206977	−	0.00662624i
$679$	−13636.8	−	7873.19i	−0.770738	−	0.444986i
$680$	−808.040	−	1399.57i	−0.0455690	−	0.0789278i
$681$	6129.99	+	9873.70i	0.344936	+	0.555596i
$682$	944.932	−	1636.67i	0.0530547	−	0.0918934i
$683$	−4153.53			−0.232695			−0.116347	−	0.993209i	$-0.537119\pi$
$683$	−4153.53			−0.232695			−0.116347	+	0.993209i	$0.537119\pi$
$684$	1538.62	+	8811.13i	0.0860099	+	0.492547i
$685$	−4405.64			−0.245738
$686$	5799.80	−	10045.5i	0.322795	−	0.559097i
$687$	4015.01	+	6467.06i	0.222973	+	0.359147i
$688$	3302.28	+	5719.72i	0.182992	+	0.316951i
$689$	−14896.9	−	8600.73i	−0.823696	−	0.475561i
$690$	−2711.17	+	86.7963i	−0.149583	+	0.00478881i
$691$	−29674.9			−1.63370			−0.816850	−	0.576850i	$-0.804282\pi$
$691$	−29674.9			−1.63370			−0.816850	+	0.576850i	$0.804282\pi$
$692$	631.407			0.0346857
$693$	10226.3	+	5061.40i	0.560554	+	0.277441i
$694$	−7252.87	+	4187.45i	−0.396708	+	0.229039i
$695$			4522.94i			0.246856i
$696$	2151.62	−	4018.42i	0.117180	−	0.218848i
$697$	8572.05	−	4949.07i	0.465838	−	0.268952i
$698$	−8340.81	+	14446.7i	−0.452299	+	0.783404i
$699$	717.547	+	22413.3i	0.0388271	+	1.21280i
$700$	4850.90	−	8402.00i	0.261924	−	0.453665i
$701$	−23296.8	−	13450.4i	−1.25522	−	0.724702i	−0.283079	−	0.959097i	$-0.591356\pi$
$701$	−23296.8	−	13450.4i	−1.25522	−	0.724702i	−0.972142	+	0.234395i	$0.924689\pi$
$702$	−1521.43	−	15797.8i	−0.0817989	−	0.849360i
$703$	28292.0	−	3092.46i	1.51786	−	0.165909i
$704$			1363.11i			0.0729745i
$705$	−802.495	−	1292.60i	−0.0428705	−	0.0690525i
$706$	20345.8	+	11746.7i	1.08460	+	0.626192i
$707$	16784.6	−	9690.59i	0.892857	−	0.515491i
$708$	2960.69	+	4768.85i	0.157160	+	0.253142i
$709$	2899.32	+	5021.77i	0.153577	+	0.266004i	0.932540	−	0.361066i	$-0.117587\pi$
$709$	2899.32	+	5021.77i	0.153577	+	0.266004i	−0.778963	+	0.627070i	$0.784254\pi$
$710$			1466.39i			0.0775108i
$711$	−24118.1	+	16064.9i	−1.27215	+	0.847370i
$712$	259.488	+	449.447i	0.0136583	+	0.0236569i
$713$	3484.66	+	6035.61i	0.183032	+	0.317020i
$714$	−22100.5	−	11833.5i	−1.15839	−	0.620247i
$715$		−	2001.72i		−	0.104700i
$716$	−9192.14	−	15921.3i	−0.479786	−	0.831013i
$717$	−2780.91	+	1726.50i	−0.144847	+	0.0899266i
$718$	−17585.3	+	10152.9i	−0.914034	+	0.527718i
$719$	−1009.42	−	582.789i	−0.0523574	−	0.0302286i	0.473593	−	0.880744i	$-0.342957\pi$
$719$	−1009.42	−	582.789i	−0.0523574	−	0.0302286i	−0.525950	+	0.850515i	$0.676290\pi$
$720$	45.9135	+	716.342i	0.00237652	+	0.0370784i
$721$			8197.11i			0.423407i
$722$	−4130.58	+	13081.4i	−0.212915	+	0.674290i
$723$	−3389.75	−	1815.00i	−0.174365	−	0.0933619i
$724$	8132.96	+	4695.57i	0.417485	+	0.241035i
$725$	−6701.96	+	11608.1i	−0.343317	+	0.594642i
$726$	−9113.24	+	291.755i	−0.465873	+	0.0149146i
$727$	−3374.62	+	5845.01i	−0.172156	+	0.298183i	−0.939173	−	0.343443i	$-0.888407\pi$
$727$	−3374.62	+	5845.01i	−0.172156	+	0.298183i	0.767017	+	0.641626i	$0.221740\pi$
$728$	7775.51	−	4489.20i	0.395851	−	0.228545i
$729$	19321.2	−	3756.36i	0.981621	−	0.190843i
$730$			943.131i			0.0478176i
$731$	−43461.1	+	25092.3i	−2.19900	+	1.26959i
$732$	−4359.42	+	139.564i	−0.220121	+	0.00704704i
$733$	−6306.15			−0.317767			−0.158883	−	0.987297i	$-0.550789\pi$
$733$	−6306.15			−0.317767			−0.158883	+	0.987297i	$0.550789\pi$
$734$	17794.3			0.894821
$735$	14.0064	+	437.502i	0.000702901	+	0.0219558i
$736$	−4353.32	−	2513.39i	−0.218024	−	0.125876i
$737$	−5893.30	−	10207.5i	−0.294549	−	0.510173i
$738$	−4387.44	+	281.211i	−0.218840	+	0.0140264i
$739$	13944.7	−	24153.0i	0.694134	−	1.20228i	−0.276338	−	0.961061i	$-0.589121\pi$
$739$	13944.7	−	24153.0i	0.694134	−	1.20228i	0.970472	−	0.241215i	$-0.0775458\pi$
$740$	2284.01			0.113462
$741$	9090.10	−	22580.0i	0.450652	−	1.11943i
$742$	12068.4			0.597097
$743$	10961.7	−	18986.3i	0.541247	−	0.937468i	−0.457586	−	0.889166i	$-0.651286\pi$
$743$	10961.7	−	18986.3i	0.541247	−	0.937468i	0.998833	−	0.0483021i	$-0.0153810\pi$
$744$	1566.85	−	972.764i	0.0772091	−	0.0479345i
$745$	−2322.34	−	4022.41i	−0.114207	−	0.197812i
$746$	16769.5	+	9681.90i	0.823025	+	0.475174i
$747$	−28175.1	−	13945.0i	−1.38002	−	0.683026i
$748$	−10357.5			−0.506296
$749$	17721.3			0.864514
$750$	−136.609	−	4267.10i	−0.00665099	−	0.207750i
$751$	−21651.2	+	12500.3i	−1.05201	+	0.607381i	−0.923213	−	0.384289i	$-0.874447\pi$
$751$	−21651.2	+	12500.3i	−1.05201	+	0.607381i	−0.128802	+	0.991670i	$0.541113\pi$
$752$		−	2819.48i		−	0.136723i
$753$	32985.5	+	17661.7i	1.59636	+	0.854754i
$754$	−10742.6	+	6202.24i	−0.518862	+	0.299565i
$755$	4.87425	−	8.44244i	0.000234956	−	0.000406956i
$756$	6466.24	+	9065.01i	0.311078	+	0.436099i
$757$	−3225.59	+	5586.89i	−0.154869	+	0.268241i	−0.933011	−	0.359847i	$-0.882829\pi$
$757$	−3225.59	+	5586.89i	−0.154869	+	0.268241i	0.778142	+	0.628088i	$0.216162\pi$
$758$	−9649.88	−	5571.36i	−0.462400	−	0.266967i
$759$	−8206.25	+	15326.2i	−0.392448	+	0.732946i
$760$	−443.595	+	1007.57i	−0.0211722	+	0.0480901i
$761$			10924.0i			0.520361i	0.965560	+	0.260181i	$0.0837822\pi$
$761$			10924.0i			0.520361i	−0.965560	+	0.260181i	$0.916218\pi$
$762$	11026.4	−	6845.61i	0.524204	−	0.325447i
$763$	−8764.53	−	5060.20i	−0.415855	−	0.240094i
$764$	2531.92	−	1461.81i	0.119898	−	0.0692230i
$765$	−5443.10	+	348.872i	−0.257249	+	0.0164883i
$766$	6479.58	+	11223.0i	0.305635	+	0.529376i
$767$		−	15275.4i		−	0.719117i
$768$	−627.905	+	1172.69i	−0.0295021	+	0.0550988i
$769$	−8420.12	−	14584.1i	−0.394847	−	0.683895i	0.598235	−	0.801321i	$-0.295869\pi$
$769$	−8420.12	−	14584.1i	−0.394847	−	0.683895i	−0.993082	+	0.117426i	$0.962536\pi$
$770$	702.197	+	1216.24i	0.0328642	+	0.0569224i
$771$	−8243.73	+	15396.2i	−0.385072	+	0.719171i
$772$			1823.19i			0.0849973i
$773$	1496.61	+	2592.20i	0.0696368	+	0.120614i	0.898741	−	0.438479i	$-0.144483\pi$
$773$	1496.61	+	2592.20i	0.0696368	+	0.120614i	−0.829105	+	0.559093i	$0.811149\pi$
$774$	22244.7	−	1425.76i	1.03304	−	0.0662119i
$775$	−4696.68	+	2711.63i	−0.217690	+	0.125683i
$776$	−5498.19	−	3174.38i	−0.254347	−	0.146847i
$777$	30101.0	−	18687.9i	1.38979	−	0.862839i
$778$		−	6548.04i		−	0.301746i
$779$	−6171.16	−	2716.92i	−0.283832	−	0.124960i
$780$	922.078	−	1722.10i	0.0423278	−	0.0790525i
$781$	8139.06	+	4699.09i	0.372905	+	0.215297i
$782$	19097.9	−	33078.6i	0.873326	−	1.51264i
$783$	−8933.71	−	12524.1i	−0.407745	−	0.571617i
$784$	−405.587	+	702.498i	−0.0184761	+	0.0320015i
$785$	−3327.51	+	1921.14i	−0.151292	+	0.0873482i
$786$	18345.8	+	9823.08i	0.832537	+	0.445773i
$787$			3057.28i			0.138475i	0.997600	+	0.0692377i	$0.0220567\pi$
$787$			3057.28i			0.138475i	−0.997600	+	0.0692377i	$0.977943\pi$
$788$	681.895	−	393.692i	0.0308268	−	0.0177978i
$789$	−996.528	−	31127.5i	−0.0449649	−	1.40452i
$790$	−3566.73			−0.160631
$791$	6980.06			0.313758
$792$	4123.11	+	2040.70i	0.184985	+	0.0915568i
$793$	10279.4	+	5934.79i	0.460316	+	0.265764i
$794$	7270.51	+	12592.9i	0.324963	+	0.562853i
$795$	2230.76	−	1384.95i	0.0995182	−	0.0617848i
$796$	1563.55	−	2708.14i	0.0696212	−	0.120587i
$797$	9999.76			0.444429			0.222214	−	0.974998i	$-0.428672\pi$
$797$	9999.76			0.444429			0.222214	+	0.974998i	$0.428672\pi$
$798$	2397.86	+	16908.3i	0.106370	+	0.750060i
$799$	21423.7			0.948581
$800$	1955.83	−	3387.59i	0.0864361	−	0.149712i
$801$	1747.96	−	112.034i	0.0771049	−	0.00494200i
$802$	−2684.91	−	4650.41i	−0.118214	−	0.204753i
$803$	5234.76	+	3022.29i	0.230050	+	0.132820i
$804$	−368.046	−	11496.3i	−0.0161443	−	0.504282i
$805$	−5179.03			−0.226754
$806$	−5018.88			−0.219333
$807$	17933.6	−	574.134i	0.782272	−	0.0250440i
$808$	6767.36	−	3907.14i	0.294647	−	0.170115i
$809$		−	35278.6i		−	1.53316i	−0.642147	−	0.766582i	$-0.721956\pi$
$809$		−	35278.6i		−	1.53316i	0.642147	−	0.766582i	$-0.278044\pi$
$810$	2235.52	+	933.550i	0.0969730	+	0.0404958i
$811$	−9037.32	+	5217.70i	−0.391299	+	0.225916i	−0.682723	−	0.730678i	$-0.739204\pi$
$811$	−9037.32	+	5217.70i	−0.391299	+	0.225916i	0.291424	+	0.956594i	$0.405871\pi$
$812$	4351.44	−	7536.92i	0.188061	−	0.325732i
$813$	23044.8	−	737.766i	0.994117	−	0.0318260i
$814$	7319.18	−	12677.2i	0.315156	−	0.545866i
$815$	−1540.85	−	889.609i	−0.0662253	−	0.0382352i
$816$	−8910.67	−	4771.12i	−0.382274	−	0.204685i
$817$	31288.4	+	13775.1i	1.33983	+	0.589876i
$818$			8334.83i			0.356260i
$819$	−1938.22	−	30240.0i	−0.0826945	−	1.29020i
$820$	−468.625	−	270.560i	−0.0199574	−	0.0115224i
$821$	16732.2	−	9660.37i	0.711278	−	0.410657i	−0.100256	−	0.994962i	$-0.531966\pi$
$821$	16732.2	−	9660.37i	0.711278	−	0.410657i	0.811534	+	0.584305i	$0.198633\pi$
$822$	−23409.9	+	14533.8i	−0.993327	+	0.616697i
$823$	3657.69	+	6335.31i	0.154920	+	0.268329i	0.933030	−	0.359799i	$-0.117155\pi$
$823$	3657.69	+	6335.31i	0.154920	+	0.268329i	−0.778110	+	0.628128i	$0.783821\pi$
$824$			3304.98i			0.139726i
$825$	−11926.3	−	6385.79i	−0.503296	−	0.269484i
$826$	5358.56	+	9281.29i	0.225724	+	0.390965i
$827$	9210.80	+	15953.6i	0.387293	+	0.670810i	0.992084	−	0.125573i	$-0.0400770\pi$
$827$	9210.80	+	15953.6i	0.387293	+	0.670810i	−0.604792	+	0.796384i	$0.706744\pi$
$828$	−14119.8	+	9405.10i	−0.592629	+	0.394746i
$829$		−	11039.7i		−	0.462513i	−0.972893	−	0.231257i	$-0.925716\pi$
$829$		−	11039.7i		−	0.462513i	0.972893	−	0.231257i	$-0.0742837\pi$
$830$	−1934.67	−	3350.94i	−0.0809076	−	0.140136i
$831$	−7823.88	−	12602.1i	−0.326604	−	0.526067i
$832$	3135.00	−	1809.99i	0.130633	−	0.0754209i
$833$	−5337.91	−	3081.84i	−0.222026	−	0.128187i
$834$	14920.8	+	24033.2i	0.619502	+	0.997845i
$835$			5264.75i			0.218197i
$836$	4170.91	+	5690.92i	0.172553	+	0.235436i
$837$	−596.687	−	6195.71i	−0.0246410	−	0.255860i
$838$	−3006.53	−	1735.82i	−0.123937	−	0.0715548i
$839$	13867.9	−	24020.0i	0.570649	−	0.988393i	−0.425850	−	0.904794i	$-0.640025\pi$
$839$	13867.9	−	24020.0i	0.570649	−	0.988393i	0.996499	−	0.0835996i	$-0.0266417\pi$
$840$	43.8534	+	1369.80i	0.00180129	+	0.0562651i
$841$	6182.58	−	10708.5i	0.253499	−	0.439073i
$842$	−10016.6	+	5783.12i	−0.409972	+	0.236698i
$843$	−12163.3	+	22716.6i	−0.496948	+	0.928114i
$844$			18755.1i			0.764904i
$845$	−1442.28	+	832.701i	−0.0587171	+	0.0339004i
$846$	−8528.32	−	4221.01i	−0.346584	−	0.171538i
$847$	−17408.7			−0.706220
$848$	4865.85			0.197045
$849$	−16570.4	+	530.492i	−0.669841	+	0.0214446i
$850$	25740.5	+	14861.3i	1.03870	+	0.599691i
$851$	26991.2	+	46750.1i	1.08725	+	1.88317i
$852$	4837.50	+	7791.86i	0.194519	+	0.313315i
$853$	14698.8	−	25459.0i	0.590008	−	1.02192i	−0.404223	−	0.914661i	$-0.632458\pi$
$853$	14698.8	−	25459.0i	0.590008	−	1.02192i	0.994231	−	0.107263i	$-0.0342087\pi$
$854$	−8327.62			−0.333683
$855$	2383.59	+	2850.21i	0.0953415	+	0.114006i
$856$	7145.01			0.285294
$857$	−17408.3	+	30152.0i	−0.693880	+	1.20183i	0.276677	+	0.960963i	$0.410767\pi$
$857$	−17408.3	+	30152.0i	−0.693880	+	1.20183i	−0.970557	+	0.240872i	$0.922567\pi$
$858$	−6603.50	−	10636.4i	−0.262750	−	0.423218i
$859$	−1678.87	−	2907.89i	−0.0666849	−	0.115502i	0.830755	−	0.556638i	$-0.187909\pi$
$859$	−1678.87	−	2907.89i	−0.0666849	−	0.115502i	−0.897440	+	0.441136i	$0.854576\pi$
$860$	2375.97	+	1371.77i	0.0942092	+	0.0543917i
$861$	−8389.75	+	268.593i	−0.332081	+	0.0106314i
$862$	−20268.7			−0.800876
$863$	−39097.2			−1.54216			−0.771081	−	0.636738i	$-0.780283\pi$
$863$	−39097.2			−1.54216			−0.771081	+	0.636738i	$0.780283\pi$
$864$	2607.11	+	3654.91i	0.102657	+	0.143915i
$865$	227.147	−	131.143i	0.00892858	−	0.00515492i
$866$		−	3910.82i		−	0.153459i
$867$	24202.8	−	45201.8i	0.948063	−	1.77063i
$868$	3049.46	−	1760.60i	0.119246	−	0.0688466i
$869$	−11429.7	+	19796.8i	−0.446175	+	0.772797i
$870$	−60.5875	−	1892.51i	−0.00236104	−	0.0737495i
$871$	−15650.7	+	27107.9i	−0.608846	+	1.05455i
$872$	−3533.76	−	2040.22i	−0.137234	−	0.0792321i
$873$	−17833.1	+	11878.5i	−0.691362	+	0.460512i
$874$	−25865.5	+	2827.23i	−1.00105	+	0.109419i
$875$		−	8151.28i		−	0.314930i
$876$	3111.31	+	5011.45i	0.120001	+	0.193289i
$877$	−27055.5	−	15620.5i	−1.04173	−	0.601445i	−0.121410	−	0.992602i	$-0.538742\pi$
$877$	−27055.5	−	15620.5i	−1.04173	−	0.601445i	−0.920324	+	0.391157i	$0.872075\pi$
$878$	27235.5	−	15724.4i	1.04687	−	0.604412i
$879$	−25740.7	−	41461.0i	−0.987726	−	1.59095i
$880$	283.118	+	490.374i	0.0108453	+	0.0187847i
$881$		−	31459.6i		−	1.20306i	−0.798848	−	0.601532i	$-0.794557\pi$
$881$		−	31459.6i		−	1.20306i	0.798848	−	0.601532i	$-0.205443\pi$
$882$	1517.71	+	2278.52i	0.0579408	+	0.0869860i
$883$	−11978.3	−	20747.1i	−0.456515	−	0.790707i	0.542259	−	0.840211i	$-0.317569\pi$
$883$	−11978.3	−	20747.1i	−0.456515	−	0.790707i	−0.998774	+	0.0495043i	$0.984236\pi$
$884$	13753.2	+	23821.2i	0.523268	+	0.906327i
$885$	2055.59	+	1100.64i	0.0780768	+	0.0418053i
$886$			729.924i			0.0276775i
$887$	−2205.24	−	3819.59i	−0.0834778	−	0.144588i	0.821264	−	0.570549i	$-0.193269\pi$
$887$	−2205.24	−	3819.59i	−0.0834778	−	0.144588i	−0.904742	+	0.425961i	$0.859936\pi$
$888$	12136.4	−	7534.76i	0.458638	−	0.284741i
$889$	21459.9	−	12389.9i	0.809608	−	0.467427i
$890$	186.700	+	107.791i	0.00703169	+	0.00405975i
$891$	12345.4	−	9416.44i	0.464180	−	0.354055i
$892$		−	2576.67i		−	0.0967189i
$893$	−8627.19	−	11771.2i	−0.323290	−	0.441106i
$894$	−25609.6	−	13712.4i	−0.958070	−	0.512988i
$895$	−6613.69	−	3818.42i	−0.247007	−	0.142610i
$896$	−1269.88	+	2199.49i	−0.0473478	+	0.0820088i
$897$	46145.2	−	1477.31i	1.71766	−	0.0549899i
$898$	7524.39	−	13032.6i	0.279612	−	0.484303i
$899$	−4213.11	+	2432.44i	−0.156301	+	0.0902406i
$900$	−7318.69	−	10987.5i	−0.271063	−	0.406944i
$901$			36973.0i			1.36709i
$902$	−3003.44	+	1734.04i	−0.110869	+	0.0640101i
$903$	42536.8	−	1361.79i	1.56759	−	0.0501855i
$904$	2814.28			0.103542
$905$	3901.08			0.143289
$906$	−1.95095	−	60.9397i	−7.15407e−5	−	0.00223464i
$907$	2739.06	+	1581.39i	0.100274	+	0.0578934i	0.549299	−	0.835626i	$-0.314895\pi$
$907$	2739.06	+	1581.39i	0.100274	+	0.0578934i	−0.449024	+	0.893520i	$0.648228\pi$
$908$	4473.24	+	7747.88i	0.163491	+	0.283174i
$909$	−1686.91	−	26319.2i	−0.0615526	−	0.960343i
$910$	1864.81	−	3229.95i	0.0679318	−	0.117661i
$911$	45584.8			1.65784			0.828920	−	0.559367i	$-0.188956\pi$
$911$	45584.8			1.65784			0.828920	+	0.559367i	$0.188956\pi$
$912$	966.791	+	6817.24i	0.0351027	+	0.247523i
$913$	−24798.8			−0.898927
$914$	−8316.45	+	14404.5i	−0.300967	+	0.521290i
$915$	−1539.30	+	955.659i	−0.0556149	+	0.0345280i
$916$	2929.88	+	5074.69i	0.105683	+	0.183049i
$917$	34409.3	+	19866.2i	1.23914	+	0.715420i
$918$	−27771.7	+	19810.1i	−0.998478	+	0.712233i
$919$	12058.0			0.432816			0.216408	−	0.976303i	$-0.430566\pi$
$919$	12058.0			0.432816			0.216408	+	0.976303i	$0.430566\pi$
$920$	−2088.13			−0.0748299
$921$	−357.775	−	11175.4i	−0.0128003	−	0.399830i
$922$	17941.2	−	10358.4i	0.640849	−	0.369995i
$923$		−	24958.6i		−	0.890056i
$924$	7743.48	+	4146.16i	0.275695	+	0.147618i
$925$	−36379.2	+	21003.5i	−1.29312	+	0.746585i
$926$	3365.82	−	5829.77i	0.119447	−	0.206888i
$927$	9996.86	+	4947.85i	0.354196	+	0.175306i
$928$	1754.45	−	3038.80i	0.0620611	−	0.107493i
$929$	3115.72	+	1798.86i	0.110036	+	0.0635293i	0.554008	−	0.832511i	$-0.313098\pi$
$929$	3115.72	+	1798.86i	0.110036	+	0.0635293i	−0.443972	+	0.896041i	$0.646431\pi$
$930$	361.627	−	675.384i	0.0127508	−	0.0238137i
$931$	456.232	+	4173.93i	0.0160606	+	0.146934i
$932$			17262.6i			0.606711i
$933$	−39001.1	+	24213.5i	−1.36853	+	0.849639i
$934$	−3941.30	−	2275.51i	−0.138076	−	0.0797183i
$935$	−3726.09	+	2151.26i	−0.130328	+	0.0752447i
$936$	−781.467	−	12192.4i	−0.0272896	−	0.425771i
$937$	−17827.4	−	30877.9i	−0.621553	−	1.07656i	−0.989197	−	0.146595i	$-0.953169\pi$
$937$	−17827.4	−	30877.9i	−0.621553	−	1.07656i	0.367644	−	0.929967i	$-0.380165\pi$
$938$		−	21960.9i		−	0.764444i
$939$	−22901.9	+	42772.1i	−0.795926	+	1.48649i
$940$	−585.606	−	1014.30i	−0.0203195	−	0.0351944i
$941$	14029.5	+	24299.8i	0.486025	+	0.841819i	0.999871	−	0.0160630i	$-0.00511324\pi$
$941$	14029.5	+	24299.8i	0.486025	+	0.841819i	−0.513846	+	0.857882i	$0.671780\pi$
$942$	−11343.5	+	21185.4i	−0.392346	+	0.732756i
$943$		−	12789.3i		−	0.441652i
$944$	2160.51	+	3742.11i	0.0744900	+	0.129020i
$945$	4209.01	+	1918.07i	0.144888	+	0.0660263i
$946$	15227.7	−	8791.73i	0.523357	−	0.302160i
$947$	−29959.3	−	17297.0i	−1.02803	−	0.593534i	−0.111611	−	0.993752i	$-0.535601\pi$
$947$	−29959.3	−	17297.0i	−1.02803	−	0.593534i	−0.916420	+	0.400218i	$0.868934\pi$
$948$	−18952.3	+	11766.3i	−0.649306	+	0.403115i
$949$		−	16052.5i		−	0.549089i
$950$	−2200.04	−	20127.6i	−0.0751357	−	0.687395i
$951$	10805.6	−	20180.8i	0.368449	−	0.688125i
$952$	−16712.8	−	9649.12i	−0.568975	−	0.328498i
$953$	28358.2	−	49117.8i	0.963915	−	1.66955i	0.251412	−	0.967880i	$-0.419105\pi$
$953$	28358.2	−	49117.8i	0.963915	−	1.66955i	0.712503	−	0.701669i	$-0.247561\pi$
$954$	7284.62	−	14718.2i	0.247220	−	0.499495i
$955$	607.235	−	1051.76i	0.0205756	−	0.0356379i
$956$	−2182.18	+	1259.88i	−0.0738250	+	0.0426229i
$957$	−10698.3	−	5728.31i	−0.361367	−	0.193490i
$958$			17632.3i			0.594648i
$959$	−45561.2	+	26304.7i	−1.53415	+	0.885740i
$960$	17.6812	+	552.289i	0.000594435	+	0.0185677i
$961$	27822.7			0.933928
$962$	−38874.8			−1.30288
$963$	10696.7	−	21612.1i	0.357941	−	0.723200i
$964$	−2563.38	−	1479.97i	−0.0856443	−	0.0494467i
$965$	378.676	+	655.886i	0.0126321	+	0.0218795i
$966$	−27519.4	+	17085.2i	−0.916588	+	0.569054i
$967$	−10799.9	+	18706.0i	−0.359153	+	0.622072i	−0.987820	−	0.155603i	$-0.950268\pi$
$967$	−10799.9	+	18706.0i	−0.359153	+	0.622072i	0.628666	+	0.777675i	$0.283601\pi$
$968$	−7018.97			−0.233056
$969$	−51800.6	+	7346.13i	−1.71731	+	0.243542i
$970$	−2637.28			−0.0872967
$971$	3415.85	−	5916.42i	0.112894	−	0.195538i	−0.804042	−	0.594572i	$-0.797321\pi$
$971$	3415.85	−	5916.42i	0.112894	−	0.195538i	0.916936	+	0.399035i	$0.130655\pi$
$972$	14958.4	−	2414.24i	0.493612	−	0.0796676i
$973$	27005.1	+	46774.3i	0.889769	+	1.54112i
$974$	8701.13	+	5023.60i	0.286245	+	0.165263i
$975$	1149.59	+	35908.4i	0.0377602	+	1.17948i
$976$	−3357.60			−0.110117
$977$	41915.0			1.37255			0.686274	−	0.727344i	$-0.259245\pi$
$977$	41915.0			1.37255			0.686274	+	0.727344i	$0.259245\pi$
$978$	−11122.2	+	356.072i	−0.363650	+	0.0116420i
$979$	1196.57	−	690.840i	0.0390629	−	0.0225530i
$980$			336.962i			0.0109835i
$981$	−11461.6	+	7634.48i	−0.373027	+	0.248471i
$982$	9911.83	−	5722.60i	0.322097	−	0.185963i
$983$	−17009.9	+	29462.0i	−0.551914	+	0.955943i	0.446223	+	0.894922i	$0.352769\pi$
$983$	−17009.9	+	29462.0i	−0.551914	+	0.955943i	−0.998136	+	0.0610209i	$0.980564\pi$
$984$	−3382.65	+	108.293i	−0.109588	+	0.00350840i
$985$	163.540	−	283.259i	0.00529016	−	0.00916283i
$986$	23090.2	+	13331.2i	0.745784	+	0.430578i
$987$	−16016.8	−	8576.00i	−0.516534	−	0.276572i
$988$	7550.17	−	17149.3i	0.243120	−	0.552218i
$989$			64843.1i			2.08482i
$990$	1907.13	−	122.237i	0.0612249	−	0.00392417i
$991$	−34484.8	−	19909.8i	−1.10540	−	0.638200i	−0.167763	−	0.985827i	$-0.553654\pi$
$991$	−34484.8	−	19909.8i	−1.10540	−	0.638200i	−0.937633	+	0.347627i	$0.886988\pi$
$992$	1229.51	−	709.856i	0.0393517	−	0.0227197i
$993$	−27454.6	+	17044.9i	−0.877386	+	0.544717i
$994$	8755.38	+	15164.8i	0.279380	+	0.483901i
$995$		−	1299.00i		−	0.0413879i
$996$	−21334.6	−	11423.4i	−0.678727	−	0.363417i
$997$	20660.1	+	35784.3i	0.656280	+	1.13671i	0.981571	+	0.191096i	$0.0612042\pi$
$997$	20660.1	+	35784.3i	0.656280	+	1.13671i	−0.325292	+	0.945614i	$0.605462\pi$
$998$	−3222.72	−	5581.92i	−0.102218	−	0.177047i
$999$	−4621.77	−	47990.2i	−0.146373	−	1.51986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.h.b.65.3	yes	20
3.2	odd	2		114.4.h.a.65.1	✓	20
19.12	odd	6		114.4.h.a.107.1	yes	20
57.50	even	6	inner	114.4.h.b.107.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.h.a.65.1	✓	20	3.2	odd	2
114.4.h.a.107.1	yes	20	19.12	odd	6
114.4.h.b.65.3	yes	20	1.1	even	1	trivial
114.4.h.b.107.3	yes	20	57.50	even	6	inner

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.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.74074 - 4.41456i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.43899 - 0.830800i) q^{5} +(-10.3870 + 0.332533i) q^{6} -19.8418 q^{7} -8.00000 q^{8} +(-11.9767 + 24.1983i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.74074 - 4.41456i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.43899 - 0.830800i) q^{5} +(-10.3870 + 0.332533i) q^{6} -19.8418 q^{7} -8.00000 q^{8} +(-11.9767 + 24.1983i) q^{9} +(-2.87798 + 1.66160i) q^{10} +21.2986i q^{11} +(-9.81102 + 18.3233i) q^{12} +(48.9843 - 28.2811i) q^{13} +(-19.8418 + 34.3671i) q^{14} +(0.276268 + 8.62951i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-105.287 - 60.7878i) q^{17} +(29.9360 + 44.9426i) q^{18} +(8.99894 + 82.3287i) q^{19} +6.64640i q^{20} +(54.3812 + 87.5930i) q^{21} +(36.8902 + 21.2986i) q^{22} +(-136.041 + 78.5435i) q^{23} +(21.9259 + 35.3165i) q^{24} +(-61.1195 - 105.862i) q^{25} -113.125i q^{26} +(139.650 - 13.4492i) q^{27} +(39.6837 + 68.7341i) q^{28} +(-54.8266 - 94.9625i) q^{29} +(15.2230 + 8.15100i) q^{30} -44.3660i q^{31} +(16.0000 + 27.7128i) q^{32} +(94.0239 - 58.3738i) q^{33} +(-210.575 + 121.576i) q^{34} +(28.5522 + 16.4846i) q^{35} +(107.779 - 6.90803i) q^{36} -343.647i q^{37} +(151.596 + 66.7421i) q^{38} +(-259.102 - 138.733i) q^{39} +(11.5119 + 6.64640i) q^{40} +(-40.7078 + 70.5080i) q^{41} +(206.097 - 6.59806i) q^{42} +(206.392 - 357.482i) q^{43} +(73.7804 - 42.5971i) q^{44} +(37.3383 - 24.8708i) q^{45} +314.174i q^{46} +(-152.609 + 88.1087i) q^{47} +(83.0959 - 2.66026i) q^{48} +50.6984 q^{49} -244.478 q^{50} +(20.2139 + 631.401i) q^{51} +(-195.937 - 113.125i) q^{52} +(-152.058 - 263.372i) q^{53} +(116.355 - 255.330i) q^{54} +(17.6949 - 30.6484i) q^{55} +158.735 q^{56} +(338.782 - 265.368i) q^{57} -219.307 q^{58} +(135.032 - 233.882i) q^{59} +(29.3410 - 18.2160i) q^{60} +(104.925 + 181.735i) q^{61} +(-76.8441 - 44.3660i) q^{62} +(237.640 - 480.139i) q^{63} +64.0000 q^{64} -93.9839 q^{65} +(-7.08247 - 221.228i) q^{66} +(-479.257 + 276.699i) q^{67} +486.302i q^{68} +(719.589 + 385.296i) q^{69} +(57.1043 - 32.9692i) q^{70} +(220.629 - 382.141i) q^{71} +(95.8138 - 193.586i) q^{72} +(141.901 - 245.780i) q^{73} +(-595.213 - 343.647i) q^{74} +(-299.823 + 559.956i) q^{75} +(267.197 - 195.831i) q^{76} -422.603i q^{77} +(-499.395 + 310.044i) q^{78} +(929.490 + 536.641i) q^{79} +(23.0238 - 13.2928i) q^{80} +(-442.116 - 579.633i) q^{81} +(81.4156 + 141.016i) q^{82} +1164.34i q^{83} +(194.669 - 363.568i) q^{84} +(101.005 + 174.946i) q^{85} +(-412.785 - 714.964i) q^{86} +(-268.953 + 502.303i) q^{87} -170.389i q^{88} +(-32.4360 - 56.1808i) q^{89} +(-5.73919 - 89.5427i) q^{90} +(-971.939 + 561.149i) q^{91} +(544.165 + 314.174i) q^{92} +(-195.856 + 121.595i) q^{93} +352.435i q^{94} +(55.4494 - 125.946i) q^{95} +(78.4882 - 146.587i) q^{96} +(687.273 + 396.797i) q^{97} +(50.6984 - 87.8122i) q^{98} +(-515.389 - 255.087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9	\( 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9} - 20 q^{12} - 111 q^{13} - 10 q^{14} - 133 q^{15} - 160 q^{16} - 90 q^{17} - 10 q^{18} - 143 q^{19} + 191 q^{21} - 54 q^{22} - 8 q^{24} + 184 q^{25} - 524 q^{27} + 20 q^{28} - 96 q^{29} - 292 q^{30} + 320 q^{32} - 55 q^{33} - 180 q^{34} + 774 q^{35} + 128 q^{36} - 314 q^{38} + 1002 q^{39} + 537 q^{41} - 382 q^{42} + 571 q^{43} - 108 q^{44} + 1516 q^{45} - 126 q^{47} + 64 q^{48} + 558 q^{49} + 736 q^{50} - 757 q^{51} + 444 q^{52} + 126 q^{53} - 1388 q^{54} + 366 q^{55} + 80 q^{56} - 281 q^{57} - 384 q^{58} - 1383 q^{59} - 52 q^{60} + 149 q^{61} - 222 q^{62} + 1153 q^{63} + 1280 q^{64} + 3636 q^{65} + 32 q^{66} - 1626 q^{67} + 236 q^{69} + 1548 q^{70} - 1368 q^{71} + 296 q^{72} + 946 q^{73} + 474 q^{74} - 669 q^{75} - 56 q^{76} + 132 q^{78} - 2109 q^{79} + 311 q^{81} - 1074 q^{82} - 1528 q^{84} + 786 q^{85} - 1142 q^{86} - 816 q^{87} - 1938 q^{89} + 1234 q^{90} - 3459 q^{91} - 705 q^{93} + 2502 q^{95} + 160 q^{96} + 1791 q^{97} + 558 q^{98} - 2285 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9 - 20 * q^12 - 111 * q^13 - 10 * q^14 - 133 * q^15 - 160 * q^16 - 90 * q^17 - 10 * q^18 - 143 * q^19 + 191 * q^21 - 54 * q^22 - 8 * q^24 + 184 * q^25 - 524 * q^27 + 20 * q^28 - 96 * q^29 - 292 * q^30 + 320 * q^32 - 55 * q^33 - 180 * q^34 + 774 * q^35 + 128 * q^36 - 314 * q^38 + 1002 * q^39 + 537 * q^41 - 382 * q^42 + 571 * q^43 - 108 * q^44 + 1516 * q^45 - 126 * q^47 + 64 * q^48 + 558 * q^49 + 736 * q^50 - 757 * q^51 + 444 * q^52 + 126 * q^53 - 1388 * q^54 + 366 * q^55 + 80 * q^56 - 281 * q^57 - 384 * q^58 - 1383 * q^59 - 52 * q^60 + 149 * q^61 - 222 * q^62 + 1153 * q^63 + 1280 * q^64 + 3636 * q^65 + 32 * q^66 - 1626 * q^67 + 236 * q^69 + 1548 * q^70 - 1368 * q^71 + 296 * q^72 + 946 * q^73 + 474 * q^74 - 669 * q^75 - 56 * q^76 + 132 * q^78 - 2109 * q^79 + 311 * q^81 - 1074 * q^82 - 1528 * q^84 + 786 * q^85 - 1142 * q^86 - 816 * q^87 - 1938 * q^89 + 1234 * q^90 - 3459 * q^91 - 705 * q^93 + 2502 * q^95 + 160 * q^96 + 1791 * q^97 + 558 * q^98 - 2285 * q^99

Introduction

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