LMFDB - Embedded newform 63.3.j.b.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(11,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("63.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	63.11
Dual form			63.3.j.b.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.74500i q^{2} +(-0.432548 + 2.96865i) q^{3} -3.53503 q^{4} +(2.32531 + 1.34252i) q^{5} +(-8.14895 - 1.18734i) q^{6} +(0.122457 - 6.99893i) q^{7} +1.27635i q^{8} +(-8.62581 - 2.56817i) q^{9} +O(q^{10})$	\(q+2.74500i q^{2} +(-0.432548 + 2.96865i) q^{3} -3.53503 q^{4} +(2.32531 + 1.34252i) q^{5} +(-8.14895 - 1.18734i) q^{6} +(0.122457 - 6.99893i) q^{7} +1.27635i q^{8} +(-8.62581 - 2.56817i) q^{9} +(-3.68521 + 6.38297i) q^{10} +(7.18501 - 4.14827i) q^{11} +(1.52907 - 10.4943i) q^{12} +(1.91540 + 3.31756i) q^{13} +(19.2121 + 0.336144i) q^{14} +(-4.99128 + 6.32233i) q^{15} -17.6437 q^{16} +(14.6266 + 8.44469i) q^{17} +(7.04962 - 23.6778i) q^{18} +(4.77461 + 8.26987i) q^{19} +(-8.22003 - 4.74584i) q^{20} +(20.7244 + 3.39090i) q^{21} +(11.3870 + 19.7229i) q^{22} +(21.1694 + 12.2221i) q^{23} +(-3.78905 - 0.552083i) q^{24} +(-8.89529 - 15.4071i) q^{25} +(-9.10671 + 5.25776i) q^{26} +(11.3551 - 24.4962i) q^{27} +(-0.432888 + 24.7414i) q^{28} +(-41.1044 - 23.7316i) q^{29} +(-17.3548 - 13.7011i) q^{30} +39.2523 q^{31} -43.3265i q^{32} +(9.20691 + 23.1241i) q^{33} +(-23.1807 + 40.1501i) q^{34} +(9.68094 - 16.1103i) q^{35} +(30.4925 + 9.07854i) q^{36} +(-23.3078 - 40.3703i) q^{37} +(-22.7008 + 13.1063i) q^{38} +(-10.6772 + 4.25114i) q^{39} +(-1.71353 + 2.96791i) q^{40} +(-51.2064 + 29.5640i) q^{41} +(-9.30802 + 56.8886i) q^{42} +(28.0196 - 48.5314i) q^{43} +(-25.3992 + 14.6642i) q^{44} +(-16.6099 - 17.5521i) q^{45} +(-33.5498 + 58.1099i) q^{46} +21.5411i q^{47} +(7.63174 - 52.3780i) q^{48} +(-48.9700 - 1.71413i) q^{49} +(42.2925 - 24.4176i) q^{50} +(-31.3961 + 39.7687i) q^{51} +(-6.77098 - 11.7277i) q^{52} +(22.2206 + 12.8291i) q^{53} +(67.2420 + 31.1697i) q^{54} +22.2765 q^{55} +(8.93310 + 0.156298i) q^{56} +(-26.6156 + 10.5971i) q^{57} +(65.1433 - 112.832i) q^{58} -46.3648i q^{59} +(17.6443 - 22.3496i) q^{60} +60.3487 q^{61} +107.748i q^{62} +(-19.0307 + 60.0569i) q^{63} +48.3566 q^{64} +10.2858i q^{65} +(-63.4757 + 25.2730i) q^{66} -64.0822 q^{67} +(-51.7056 - 29.8522i) q^{68} +(-45.4400 + 57.5578i) q^{69} +(44.2227 + 26.5742i) q^{70} +49.6536i q^{71} +(3.27789 - 11.0096i) q^{72} +(58.7013 - 101.674i) q^{73} +(110.817 - 63.9800i) q^{74} +(49.5860 - 19.7427i) q^{75} +(-16.8784 - 29.2342i) q^{76} +(-28.1536 - 50.7953i) q^{77} +(-11.6694 - 29.3089i) q^{78} +40.5510 q^{79} +(-41.0270 - 23.6870i) q^{80} +(67.8090 + 44.3050i) q^{81} +(-81.1532 - 140.562i) q^{82} +(-64.7120 - 37.3615i) q^{83} +(-73.2614 - 11.9869i) q^{84} +(22.6743 + 39.2730i) q^{85} +(133.219 + 76.9139i) q^{86} +(88.2305 - 111.760i) q^{87} +(5.29465 + 9.17060i) q^{88} +(-59.9634 + 34.6199i) q^{89} +(48.1805 - 45.5940i) q^{90} +(23.4539 - 12.9995i) q^{91} +(-74.8342 - 43.2056i) q^{92} +(-16.9785 + 116.526i) q^{93} -59.1302 q^{94} +25.6400i q^{95} +(128.621 + 18.7408i) q^{96} +(-46.9641 + 81.3442i) q^{97} +(4.70530 - 134.423i) q^{98} +(-72.6299 + 17.3298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 19 q^{3} - 24 q^{4} + 12 q^{5} - 8 q^{6} - 37 q^{9}+O(q^{10}) $ 22 * q - 19 * q^3 - 24 * q^4 + 12 * q^5 - 8 * q^6 - 37 * q^9	\( 22 q - 19 q^{3} - 24 q^{4} + 12 q^{5} - 8 q^{6} - 37 q^{9} + 25 q^{10} + 24 q^{11} + 40 q^{12} - 18 q^{13} - 60 q^{14} + 53 q^{15} - 24 q^{16} - 6 q^{17} + 40 q^{18} + 3 q^{19} - 39 q^{20} - 11 q^{21} - 59 q^{22} + 81 q^{23} + 126 q^{24} + 57 q^{25} + 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 38 q^{30} + 58 q^{31} - 4 q^{33} - 99 q^{34} + 27 q^{35} + 76 q^{36} - 20 q^{37} - 48 q^{38} - 76 q^{39} - 105 q^{40} - 51 q^{41} + 68 q^{42} + 65 q^{43} - 54 q^{44} - 214 q^{45} + 75 q^{46} - 113 q^{48} + 4 q^{49} + 63 q^{50} + 141 q^{51} - 46 q^{52} + 63 q^{53} + 433 q^{54} - 100 q^{55} + 192 q^{56} + 224 q^{57} + 40 q^{58} - 482 q^{60} - 156 q^{61} + 19 q^{63} + 106 q^{64} + 61 q^{66} + 264 q^{67} + 27 q^{68} - 297 q^{69} + 236 q^{70} - 222 q^{72} + q^{73} + 342 q^{74} - 296 q^{75} + 233 q^{76} - 531 q^{77} - 440 q^{78} - 280 q^{79} - 96 q^{80} - 169 q^{81} - 157 q^{82} + 255 q^{83} - 13 q^{84} + 102 q^{85} + 504 q^{86} + 704 q^{87} + 408 q^{88} + 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} - 36 q^{93} - 522 q^{94} - 397 q^{96} + 178 q^{97} - 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 19 * q^3 - 24 * q^4 + 12 * q^5 - 8 * q^6 - 37 * q^9 + 25 * q^10 + 24 * q^11 + 40 * q^12 - 18 * q^13 - 60 * q^14 + 53 * q^15 - 24 * q^16 - 6 * q^17 + 40 * q^18 + 3 * q^19 - 39 * q^20 - 11 * q^21 - 59 * q^22 + 81 * q^23 + 126 * q^24 + 57 * q^25 + 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 38 * q^30 + 58 * q^31 - 4 * q^33 - 99 * q^34 + 27 * q^35 + 76 * q^36 - 20 * q^37 - 48 * q^38 - 76 * q^39 - 105 * q^40 - 51 * q^41 + 68 * q^42 + 65 * q^43 - 54 * q^44 - 214 * q^45 + 75 * q^46 - 113 * q^48 + 4 * q^49 + 63 * q^50 + 141 * q^51 - 46 * q^52 + 63 * q^53 + 433 * q^54 - 100 * q^55 + 192 * q^56 + 224 * q^57 + 40 * q^58 - 482 * q^60 - 156 * q^61 + 19 * q^63 + 106 * q^64 + 61 * q^66 + 264 * q^67 + 27 * q^68 - 297 * q^69 + 236 * q^70 - 222 * q^72 + q^73 + 342 * q^74 - 296 * q^75 + 233 * q^76 - 531 * q^77 - 440 * q^78 - 280 * q^79 - 96 * q^80 - 169 * q^81 - 157 * q^82 + 255 * q^83 - 13 * q^84 + 102 * q^85 + 504 * q^86 + 704 * q^87 + 408 * q^88 + 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 - 36 * q^93 - 522 * q^94 - 397 * q^96 + 178 * q^97 - 483 * q^98 - 103 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			2.74500i			1.37250i	0.727366	+	0.686250i	$0.240744\pi$
$2$			2.74500i			1.37250i	−0.727366	+	0.686250i	$0.759256\pi$
$3$	−0.432548	+	2.96865i	−0.144183	+	0.989551i
$3$	−0.432548	+	2.96865i	−0.144183	+	0.989551i
$4$	−3.53503			−0.883757
$5$	2.32531	+	1.34252i	0.465062	+	0.268504i	0.714170	−	0.699972i	$-0.246804\pi$
$5$	2.32531	+	1.34252i	0.465062	+	0.268504i	−0.249108	+	0.968476i	$0.580138\pi$
$6$	−8.14895	−	1.18734i	−1.35816	−	0.197891i
$7$	0.122457	−	6.99893i	0.0174938	−	0.999847i
$7$	0.122457	−	6.99893i	0.0174938	−	0.999847i
$8$			1.27635i			0.159544i
$9$	−8.62581	−	2.56817i	−0.958423	−	0.285352i
$10$	−3.68521	+	6.38297i	−0.368521	+	0.638297i
$11$	7.18501	−	4.14827i	0.653183	−	0.377115i	−0.136492	−	0.990641i	$-0.543583\pi$
$11$	7.18501	−	4.14827i	0.653183	−	0.377115i	0.789675	+	0.613526i	$0.210249\pi$
$12$	1.52907	−	10.4943i	0.127422	−	0.874522i
$13$	1.91540	+	3.31756i	0.147338	+	0.255197i	0.930243	−	0.366944i	$-0.119596\pi$
$13$	1.91540	+	3.31756i	0.147338	+	0.255197i	−0.782905	+	0.622142i	$0.786263\pi$
$14$	19.2121	+	0.336144i	1.37229	+	0.0240103i
$15$	−4.99128	+	6.32233i	−0.332752	+	0.421489i
$16$	−17.6437			−1.10273
$17$	14.6266	+	8.44469i	0.860390	+	0.496747i	0.864143	−	0.503246i	$-0.167861\pi$
$17$	14.6266	+	8.44469i	0.860390	+	0.496747i	−0.00375254	+	0.999993i	$0.501194\pi$
$18$	7.04962	−	23.6778i	0.391646	−	1.31544i
$19$	4.77461	+	8.26987i	0.251295	+	0.435256i	0.963883	−	0.266327i	$-0.0858101\pi$
$19$	4.77461	+	8.26987i	0.251295	+	0.435256i	−0.712587	+	0.701583i	$0.752477\pi$
$20$	−8.22003	−	4.74584i	−0.411001	−	0.237292i
$21$	20.7244	+	3.39090i	0.986877	+	0.161471i
$22$	11.3870	+	19.7229i	0.517591	+	0.896493i
$23$	21.1694	+	12.2221i	0.920407	+	0.531397i	0.883765	−	0.467931i	$-0.155001\pi$
$23$	21.1694	+	12.2221i	0.920407	+	0.531397i	0.0366420	+	0.999328i	$0.488334\pi$
$24$	−3.78905	−	0.552083i	−0.157877	−	0.0230035i
$25$	−8.89529	−	15.4071i	−0.355812	−	0.616284i
$26$	−9.10671	+	5.25776i	−0.350258	+	0.202222i
$27$	11.3551	−	24.4962i	0.420558	−	0.907266i
$28$	−0.432888	+	24.7414i	−0.0154603	+	0.883621i
$29$	−41.1044	−	23.7316i	−1.41739	−	0.818332i	−0.421323	−	0.906911i	$-0.638434\pi$
$29$	−41.1044	−	23.7316i	−1.41739	−	0.818332i	−0.996069	+	0.0885791i	$0.971767\pi$
$30$	−17.3548	−	13.7011i	−0.578494	−	0.456702i
$31$	39.2523			1.26620			0.633101	−	0.774069i	$-0.281782\pi$
$31$	39.2523			1.26620			0.633101	+	0.774069i	$0.281782\pi$
$32$		−	43.3265i		−	1.35395i
$33$	9.20691	+	23.1241i	0.278997	+	0.700731i
$34$	−23.1807	+	40.1501i	−0.681785	+	1.18089i
$35$	9.68094	−	16.1103i	0.276598	−	0.460293i
$36$	30.4925	+	9.07854i	0.847013	+	0.252182i
$37$	−23.3078	−	40.3703i	−0.629941	−	1.09109i	−0.987563	−	0.157224i	$-0.949746\pi$
$37$	−23.3078	−	40.3703i	−0.629941	−	1.09109i	0.357622	−	0.933866i	$-0.383588\pi$
$38$	−22.7008	+	13.1063i	−0.597389	+	0.344903i
$39$	−10.6772	+	4.25114i	−0.273774	+	0.109004i
$40$	−1.71353	+	2.96791i	−0.0428381	+	0.0741978i
$41$	−51.2064	+	29.5640i	−1.24894	+	0.721073i	−0.970897	−	0.239496i	$-0.923018\pi$
$41$	−51.2064	+	29.5640i	−1.24894	+	0.721073i	−0.278039	+	0.960570i	$0.589684\pi$
$42$	−9.30802	+	56.8886i	−0.221620	+	1.35449i
$43$	28.0196	−	48.5314i	0.651620	−	1.12864i	−0.331110	−	0.943592i	$-0.607423\pi$
$43$	28.0196	−	48.5314i	0.651620	−	1.12864i	0.982730	−	0.185046i	$-0.0592434\pi$
$44$	−25.3992	+	14.6642i	−0.577254	+	0.333278i
$45$	−16.6099	−	17.5521i	−0.369108	−	0.390046i
$46$	−33.5498	+	58.1099i	−0.729343	+	1.26326i
$47$			21.5411i			0.458320i	0.973389	+	0.229160i	$0.0735980\pi$
$47$			21.5411i			0.458320i	−0.973389	+	0.229160i	$0.926402\pi$
$48$	7.63174	−	52.3780i	0.158994	−	1.09121i
$49$	−48.9700	−	1.71413i	−0.999388	−	0.0349823i
$50$	42.2925	−	24.4176i	0.845850	−	0.488352i
$51$	−31.3961	+	39.7687i	−0.615609	+	0.779778i
$52$	−6.77098	−	11.7277i	−0.130211	−	0.225532i
$53$	22.2206	+	12.8291i	0.419257	+	0.242058i	0.694759	−	0.719242i	$-0.255511\pi$
$53$	22.2206	+	12.8291i	0.419257	+	0.242058i	−0.275502	+	0.961300i	$0.588844\pi$
$54$	67.2420	+	31.1697i	1.24522	+	0.577216i
$55$	22.2765			0.405027
$56$	8.93310	+	0.156298i	0.159520	+	0.00279104i
$57$	−26.6156	+	10.5971i	−0.466941	+	0.185913i
$58$	65.1433	−	112.832i	1.12316	−	1.94537i
$59$		−	46.3648i		−	0.785843i	−0.919572	−	0.392922i	$-0.871464\pi$
$59$		−	46.3648i		−	0.785843i	0.919572	−	0.392922i	$-0.128536\pi$
$60$	17.6443	−	22.3496i	0.294072	−	0.372494i
$61$	60.3487			0.989322			0.494661	−	0.869086i	$-0.335292\pi$
$61$	60.3487			0.989322			0.494661	+	0.869086i	$0.335292\pi$
$62$			107.748i			1.73786i
$63$	−19.0307	+	60.0569i	−0.302075	+	0.953284i
$64$	48.3566			0.755572
$65$			10.2858i			0.158243i
$66$	−63.4757	+	25.2730i	−0.961753	+	0.382924i
$67$	−64.0822			−0.956451			−0.478225	−	0.878237i	$-0.658720\pi$
$67$	−64.0822			−0.956451			−0.478225	+	0.878237i	$0.658720\pi$
$68$	−51.7056	−	29.8522i	−0.760376	−	0.439003i
$69$	−45.4400	+	57.5578i	−0.658551	+	0.834171i
$70$	44.2227	+	26.5742i	0.631753	+	0.379631i
$71$			49.6536i			0.699346i	0.936872	+	0.349673i	$0.113707\pi$
$71$			49.6536i			0.699346i	−0.936872	+	0.349673i	$0.886293\pi$
$72$	3.27789	−	11.0096i	0.0455262	−	0.152911i
$73$	58.7013	−	101.674i	0.804128	−	1.39279i	−0.112750	−	0.993623i	$-0.535966\pi$
$73$	58.7013	−	101.674i	0.804128	−	1.39279i	0.916878	−	0.399167i	$-0.130701\pi$
$74$	110.817	−	63.9800i	1.49752	−	0.864594i
$75$	49.5860	−	19.7427i	0.661146	−	0.263237i
$76$	−16.8784	−	29.2342i	−0.222084	−	0.384661i
$77$	−28.1536	−	50.7953i	−0.365631	−	0.659680i
$78$	−11.6694	−	29.3089i	−0.149608	−	0.375755i
$79$	40.5510			0.513304			0.256652	−	0.966504i	$-0.417381\pi$
$79$	40.5510			0.513304			0.256652	+	0.966504i	$0.417381\pi$
$80$	−41.0270	−	23.6870i	−0.512838	−	0.296087i
$81$	67.8090	+	44.3050i	0.837149	+	0.546976i
$82$	−81.1532	−	140.562i	−0.989673	−	1.71416i
$83$	−64.7120	−	37.3615i	−0.779663	−	0.450139i	0.0566477	−	0.998394i	$-0.481959\pi$
$83$	−64.7120	−	37.3615i	−0.779663	−	0.450139i	−0.836311	+	0.548255i	$0.815292\pi$
$84$	−73.2614	−	11.9869i	−0.872159	−	0.142701i
$85$	22.6743	+	39.2730i	0.266756	+	0.462036i
$86$	133.219	+	76.9139i	1.54906	+	0.894348i
$87$	88.2305	−	111.760i	1.01414	−	1.28459i
$88$	5.29465	+	9.17060i	0.0601665	+	0.104211i
$89$	−59.9634	+	34.6199i	−0.673747	+	0.388988i	−0.797495	−	0.603326i	$-0.793842\pi$
$89$	−59.9634	+	34.6199i	−0.673747	+	0.388988i	0.123748	+	0.992314i	$0.460508\pi$
$90$	48.1805	−	45.5940i	0.535338	−	0.506601i
$91$	23.4539	−	12.9995i	0.257736	−	0.142851i
$92$	−74.8342	−	43.2056i	−0.813416	−	0.469626i
$93$	−16.9785	+	116.526i	−0.182564	+	1.25297i
$94$	−59.1302			−0.629045
$95$			25.6400i			0.269895i
$96$	128.621	+	18.7408i	1.33981	+	0.195217i
$97$	−46.9641	+	81.3442i	−0.484166	+	0.838600i	−0.999835	−	0.0181878i	$-0.994210\pi$
$97$	−46.9641	+	81.3442i	−0.484166	+	0.838600i	0.515668	+	0.856788i	$0.327544\pi$
$98$	4.70530	−	134.423i	0.0480132	−	1.37166i
$99$	−72.6299	+	17.3298i	−0.733636	+	0.175049i
$100$	31.4451	+	54.4645i	0.314451	+	0.544645i
$101$	−112.757	+	65.1000i	−1.11640	+	0.644555i	−0.940480	−	0.339849i	$-0.889624\pi$
$101$	−112.757	+	65.1000i	−1.11640	+	0.644555i	−0.175922	+	0.984404i	$0.556291\pi$
$102$	−109.165	−	86.1823i	−1.07025	−	0.844924i
$103$	−48.2918	+	83.6439i	−0.468853	+	0.812077i	−0.999366	−	0.0355999i	$-0.988666\pi$
$103$	−48.2918	+	83.6439i	−0.468853	+	0.812077i	0.530513	+	0.847677i	$0.321999\pi$
$104$	−4.23438	+	2.44472i	−0.0407152	+	0.0235069i
$105$	43.6383	+	35.7078i	0.415603	+	0.340074i
$106$	−35.2158	+	60.9956i	−0.332225	+	0.575430i
$107$	−7.05070	+	4.07073i	−0.0658944	+	0.0380442i	−0.532585	−	0.846376i	$-0.678779\pi$
$107$	−7.05070	+	4.07073i	−0.0658944	+	0.0380442i	0.466691	+	0.884421i	$0.345446\pi$
$108$	−40.1405	+	86.5946i	−0.371671	+	0.801802i
$109$	−91.4455	+	158.388i	−0.838950	+	1.45310i	0.0518242	+	0.998656i	$0.483496\pi$
$109$	−91.4455	+	158.388i	−0.838950	+	1.45310i	−0.890774	+	0.454447i	$0.849837\pi$
$110$			61.1490i			0.555900i
$111$	129.927	−	51.7308i	1.17052	−	0.466043i
$112$	−2.16059	+	123.487i	−0.0192910	+	1.10256i
$113$	65.5463	−	37.8432i	0.580056	−	0.334896i	−0.181100	−	0.983465i	$-0.557966\pi$
$113$	65.5463	−	37.8432i	0.580056	−	0.334896i	0.761156	+	0.648569i	$0.224632\pi$
$114$	−29.0889	−	73.0599i	−0.255166	−	0.640876i
$115$	32.8169	+	56.8405i	0.285364	+	0.494265i
$116$	145.305	+	83.8919i	1.25263	+	0.723206i
$117$	−8.00178	−	33.5357i	−0.0683913	−	0.286630i
$118$	127.271			1.07857
$119$	60.8949	−	101.337i	0.511722	−	0.851569i
$120$	−8.06952	−	6.37063i	−0.0672460	−	0.0530886i
$121$	−26.0838	+	45.1784i	−0.215568	+	0.373375i
$122$			165.657i			1.35785i
$123$	−65.6161	−	164.802i	−0.533464	−	1.33985i
$124$	−138.758			−1.11901
$125$		−	114.894i		−	0.919154i
$126$	−164.856	−	52.2393i	−1.30838	−	0.414598i
$127$	−38.6425			−0.304271			−0.152136	−	0.988360i	$-0.548615\pi$
$127$	−38.6425			−0.304271			−0.152136	+	0.988360i	$0.548615\pi$
$128$		−	40.5673i		−	0.316932i
$129$	131.953	+	104.173i	1.02289	+	0.807541i
$130$	−28.2346			−0.217189
$131$	4.85610	+	2.80367i	0.0370695	+	0.0214021i	0.518420	−	0.855126i	$-0.326520\pi$
$131$	4.85610	+	2.80367i	0.0370695	+	0.0214021i	−0.481351	+	0.876528i	$0.659854\pi$
$132$	−32.5467	−	81.7444i	−0.246566	−	0.619276i
$133$	58.4649	−	32.4045i	0.439586	−	0.243643i
$134$		−	175.906i		−	1.31273i
$135$	59.2906	−	41.7168i	0.439190	−	0.309013i
$136$	−10.7784	+	18.6687i	−0.0792530	+	0.137270i
$137$	−103.847	+	59.9563i	−0.758010	+	0.437637i	−0.828581	−	0.559870i	$-0.810851\pi$
$137$	−103.847	+	59.9563i	−0.758010	+	0.437637i	0.0705710	+	0.997507i	$0.477518\pi$
$138$	−157.996	−	124.733i	−1.14490	−	0.903862i
$139$	−77.4562	−	134.158i	−0.557239	−	0.965166i	−0.997726	−	0.0674071i	$-0.978527\pi$
$139$	−77.4562	−	134.158i	−0.557239	−	0.965166i	0.440487	−	0.897759i	$-0.354806\pi$
$140$	−34.2224	+	56.9502i	−0.244445	+	0.406787i
$141$	−63.9479	−	9.31753i	−0.453531	−	0.0660818i
$142$	−136.299			−0.959852
$143$	27.5243	+	15.8912i	0.192477	+	0.111127i
$144$	152.191	+	45.3120i	1.05688	+	0.314666i
$145$	−63.7202	−	110.367i	−0.439450	−	0.761150i
$146$	279.094	+	161.135i	1.91160	+	1.10367i
$147$	26.2705	−	144.634i	0.178711	−	0.983902i
$148$	82.3938	+	142.710i	0.556715	+	0.964258i
$149$	−164.676	−	95.0755i	−1.10521	−	0.638090i	−0.167622	−	0.985851i	$-0.553609\pi$
$149$	−164.676	−	95.0755i	−1.10521	−	0.638090i	−0.937583	+	0.347761i	$0.886942\pi$
$150$	54.1938	+	136.114i	0.361292	+	0.907423i
$151$	−28.9080	−	50.0702i	−0.191444	−	0.331591i	0.754285	−	0.656547i	$-0.227984\pi$
$151$	−28.9080	−	50.0702i	−0.191444	−	0.331591i	−0.945729	+	0.324957i	$0.894650\pi$
$152$	−10.5553	+	6.09409i	−0.0694425	+	0.0400927i
$153$	−104.479	−	110.406i	−0.682870	−	0.721607i
$154$	139.433	−	77.2816i	0.905411	−	0.501828i
$155$	91.2737	+	52.6969i	0.588862	+	0.339980i
$156$	37.7442	−	15.0279i	0.241950	−	0.0963327i
$157$	142.950			0.910508			0.455254	−	0.890362i	$-0.349548\pi$
$157$	142.950			0.910508			0.455254	+	0.890362i	$0.349548\pi$
$158$			111.313i			0.704510i
$159$	−47.6966	+	60.4161i	−0.299979	+	0.379976i
$160$	58.1666	−	100.748i	0.363541	−	0.629672i
$161$	88.1342	−	146.666i	0.547417	−	0.910970i
$162$	−121.617	+	186.136i	−0.750724	+	1.14899i
$163$	36.5916	+	63.3785i	0.224488	+	0.388825i	0.956166	−	0.292826i	$-0.0945956\pi$
$163$	36.5916	+	63.3785i	0.224488	+	0.388825i	−0.731677	+	0.681651i	$0.761262\pi$
$164$	181.016	−	104.510i	1.10376	−	0.637253i
$165$	−9.63564	+	66.1312i	−0.0583978	+	0.400795i
$166$	102.557	−	177.635i	0.617815	−	1.07009i
$167$	192.478	−	111.127i	1.15256	−	0.665433i	0.203053	−	0.979168i	$-0.434914\pi$
$167$	192.478	−	111.127i	1.15256	−	0.665433i	0.949510	+	0.313735i	$0.101580\pi$
$168$	−4.32798	+	26.4517i	−0.0257618	+	0.157450i
$169$	77.1625	−	133.649i	0.456583	−	0.790825i
$170$	−107.805	+	62.2410i	−0.634144	+	0.366123i
$171$	−19.9465	−	83.5963i	−0.116646	−	0.488867i
$172$	−99.0502	+	171.560i	−0.575873	+	0.997441i
$173$			243.558i			1.40785i	0.710274	+	0.703926i	$0.248571\pi$
$173$			243.558i			1.40785i	−0.710274	+	0.703926i	$0.751429\pi$
$174$	306.780	+	242.193i	1.76310	+	1.39191i
$175$	−108.922	+	60.3708i	−0.622414	+	0.344976i
$176$	−126.770	+	73.1907i	−0.720285	+	0.415857i
$177$	137.641	+	20.0550i	0.777632	+	0.113305i
$178$	−95.0317	−	164.600i	−0.533886	−	0.924717i
$179$	125.271	+	72.3251i	0.699837	+	0.404051i	0.807287	−	0.590159i	$-0.200935\pi$
$179$	125.271	+	72.3251i	0.699837	+	0.404051i	−0.107450	+	0.994211i	$0.534268\pi$
$180$	58.7163	+	62.0471i	0.326201	+	0.344706i
$181$	16.9989			0.0939167			0.0469584	−	0.998897i	$-0.485047\pi$
$181$	16.9989			0.0939167			0.0469584	+	0.998897i	$0.485047\pi$
$182$	35.6835	+	64.3811i	0.196063	+	0.353742i
$183$	−26.1037	+	179.154i	−0.142643	+	0.978985i
$184$	−15.5997	+	27.0196i	−0.0847812	+	0.146845i
$185$		−	125.165i		−	0.676566i
$186$	−319.865	−	46.6059i	−1.71970	−	0.250569i
$187$	140.123			0.749323
$188$		−	76.1482i		−	0.405044i
$189$	−170.056	−	82.4730i	−0.899770	−	0.436365i
$190$	−70.3818			−0.370431
$191$		−	71.3790i		−	0.373712i	−0.982387	−	0.186856i	$-0.940170\pi$
$191$		−	71.3790i		−	0.373712i	0.982387	−	0.186856i	$-0.0598298\pi$
$192$	−20.9165	+	143.554i	−0.108940	+	0.747677i
$193$	328.173			1.70038			0.850190	−	0.526476i	$-0.176487\pi$
$193$	328.173			1.70038			0.850190	+	0.526476i	$0.176487\pi$
$194$	−223.290	−	128.917i	−1.15098	−	0.664518i
$195$	−30.5350	−	4.44910i	−0.156590	−	0.0228159i
$196$	173.110	+	6.05951i	0.883216	+	0.0309158i
$197$			171.288i			0.869481i	0.900556	+	0.434741i	$0.143160\pi$
$197$			171.288i			0.869481i	−0.900556	+	0.434741i	$0.856840\pi$
$198$	−47.5704	−	199.369i	−0.240255	−	1.00692i
$199$	−139.848	+	242.224i	−0.702755	+	1.21721i	0.264740	+	0.964320i	$0.414714\pi$
$199$	−139.848	+	242.224i	−0.702755	+	1.21721i	−0.967496	+	0.252888i	$0.918620\pi$
$200$	19.6649	−	11.3535i	0.0983244	−	0.0567676i
$201$	27.7186	−	190.238i	0.137903	−	0.946457i
$202$	−178.700	−	309.517i	−0.884652	−	1.53226i
$203$	−171.129	+	284.780i	−0.843002	+	1.40286i
$204$	110.986	−	140.583i	0.544049	−	0.689134i
$205$	−158.761			−0.774443
$206$	−229.603	−	132.561i	−1.11458	−	0.643500i
$207$	−151.214	−	159.792i	−0.730504	−	0.771943i
$208$	−33.7947	−	58.5341i	−0.162474	−	0.281414i
$209$	68.6113	+	39.6127i	0.328284	+	0.189535i
$210$	−98.0179	+	119.787i	−0.466752	+	0.570416i
$211$	−17.0206	−	29.4806i	−0.0806664	−	0.139718i	0.822870	−	0.568230i	$-0.192372\pi$
$211$	−17.0206	−	29.4806i	−0.0806664	−	0.139718i	−0.903536	+	0.428511i	$0.859038\pi$
$212$	−78.5505	−	45.3512i	−0.370521	−	0.213921i
$213$	−147.404	−	21.4775i	−0.692038	−	0.100833i
$214$	−11.1741	−	19.3542i	−0.0522156	−	0.0904401i
$215$	130.309	−	75.2337i	0.606087	−	0.349924i
$216$	31.2657	+	14.4931i	0.144749	+	0.0670975i
$217$	4.80671	−	274.724i	0.0221507	−	1.26601i
$218$	−434.776	−	251.018i	−1.99438	−	1.15146i
$219$	276.443	+	218.243i	1.26230	+	0.996542i
$220$	−78.7480			−0.357945
$221$			64.6997i			0.292759i
$222$	142.001	+	356.650i	0.639644	+	1.60653i
$223$	−175.785	+	304.469i	−0.788274	+	1.36533i	0.138750	+	0.990327i	$0.455692\pi$
$223$	−175.785	+	304.469i	−0.788274	+	1.36533i	−0.927024	+	0.375003i	$0.877642\pi$
$224$	−303.239	−	5.30563i	−1.35375	−	0.0236858i
$225$	37.1611	+	155.743i	0.165160	+	0.692192i
$226$	103.880	+	179.925i	0.459644	+	0.796127i
$227$	202.316	−	116.807i	0.891258	−	0.514568i	0.0169042	−	0.999857i	$-0.494619\pi$
$227$	202.316	−	116.807i	0.891258	−	0.514568i	0.874354	+	0.485289i	$0.161286\pi$
$228$	94.0869	−	37.4609i	0.412662	−	0.164302i
$229$	25.4071	−	44.0065i	0.110948	−	0.192168i	−0.805205	−	0.592997i	$-0.797945\pi$
$229$	25.4071	−	44.0065i	0.110948	−	0.192168i	0.916153	+	0.400829i	$0.131278\pi$
$230$	−156.027	+	90.0823i	−0.678379	+	0.391662i
$231$	162.972	−	61.6068i	0.705505	−	0.266696i
$232$	30.2899	−	52.4637i	0.130560	−	0.226136i
$233$	−13.2624	+	7.65706i	−0.0569203	+	0.0328629i	−0.528190	−	0.849126i	$-0.677129\pi$
$233$	−13.2624	+	7.65706i	−0.0569203	+	0.0328629i	0.471270	+	0.881989i	$0.343796\pi$
$234$	92.0556	−	21.9649i	0.393400	−	0.0938670i
$235$	−28.9192	+	50.0896i	−0.123061	+	0.213147i
$236$			163.901i			0.694494i
$237$	−17.5402	+	120.382i	−0.0740095	+	0.507941i
$238$	278.169	+	167.157i	1.16878	+	0.702339i
$239$	214.220	−	123.680i	0.896316	−	0.517488i	0.0203128	−	0.999794i	$-0.493534\pi$
$239$	214.220	−	123.680i	0.896316	−	0.517488i	0.876003	+	0.482305i	$0.160200\pi$
$240$	88.0645	−	111.549i	0.366936	−	0.464789i
$241$	1.60606	+	2.78179i	0.00666417	+	0.0115427i	0.869338	−	0.494218i	$-0.164545\pi$
$241$	1.60606	+	2.78179i	0.00666417	+	0.0115427i	−0.862674	+	0.505760i	$0.831212\pi$
$242$	−124.015	−	71.5999i	−0.512458	−	0.295868i
$243$	−160.857	+	182.137i	−0.661962	+	0.749537i
$244$	−213.334			−0.874320
$245$	−111.569	−	69.7290i	−0.455384	−	0.284608i
$246$	452.381	−	180.116i	1.83895	−	0.732180i
$247$	−18.2905	+	31.6802i	−0.0740508	+	0.128260i
$248$			50.0997i			0.202015i
$249$	138.904	−	175.947i	0.557849	−	0.706614i
$250$	315.385			1.26154
$251$			91.5892i			0.364897i	0.983215	+	0.182449i	$0.0584023\pi$
$251$			91.5892i			0.364897i	−0.983215	+	0.182449i	$0.941598\pi$
$252$	67.2741	−	212.303i	0.266961	−	0.842471i
$253$	202.803			0.801592
$254$		−	106.074i		−	0.417612i
$255$	−126.396	+	50.3247i	−0.495670	+	0.197352i
$256$	304.784			1.19056
$257$	−100.659	−	58.1156i	−0.391670	−	0.226131i	0.291213	−	0.956658i	$-0.405941\pi$
$257$	−100.659	−	58.1156i	−0.391670	−	0.226131i	−0.682884	+	0.730527i	$0.739274\pi$
$258$	−285.954	+	362.212i	−1.10835	+	1.40392i
$259$	−285.403	+	158.186i	−1.10194	+	0.610757i
$260$		−	36.3606i		−	0.139849i
$261$	293.612	+	310.267i	1.12495	+	1.18876i
$262$	−7.69608	+	13.3300i	−0.0293743	+	0.0508778i
$263$	−35.5315	+	20.5141i	−0.135101	+	0.0780005i	−0.566027	−	0.824387i	$-0.691520\pi$
$263$	−35.5315	+	20.5141i	−0.135101	+	0.0780005i	0.430926	+	0.902387i	$0.358187\pi$
$264$	−29.5145	+	11.7513i	−0.111797	+	0.0445123i
$265$	34.4465	+	59.6632i	0.129987	+	0.225144i
$266$	88.9503	+	160.486i	0.334400	+	0.603332i
$267$	−76.8375	−	192.985i	−0.287781	−	0.722792i
$268$	226.532			0.845270
$269$	−320.521	−	185.053i	−1.19153	−	0.687930i	−0.232876	−	0.972506i	$-0.574814\pi$
$269$	−320.521	−	185.053i	−1.19153	−	0.687930i	−0.958653	+	0.284577i	$0.908147\pi$
$270$	114.513	+	162.753i	0.424121	+	0.602788i
$271$	−88.3608	−	153.045i	−0.326055	−	0.564743i	0.655671	−	0.755047i	$-0.272386\pi$
$271$	−88.3608	−	153.045i	−0.326055	−	0.564743i	−0.981725	+	0.190304i	$0.939053\pi$
$272$	−258.068	−	148.996i	−0.948779	−	0.547778i
$273$	28.4460	+	75.2495i	0.104198	+	0.275639i
$274$	−164.580	−	285.061i	−0.600657	−	1.04037i
$275$	−127.826	−	73.8001i	−0.464820	−	0.268364i
$276$	160.632	−	203.468i	0.581999	−	0.737205i
$277$	−98.9588	−	171.402i	−0.357252	−	0.618778i	0.630249	−	0.776393i	$-0.282953\pi$
$277$	−98.9588	−	171.402i	−0.357252	−	0.618778i	−0.987501	+	0.157615i	$0.949620\pi$
$278$	368.264	−	212.617i	1.32469	−	0.764811i
$279$	−338.582	−	100.806i	−1.21356	−	0.361313i
$280$	20.5624	+	12.3563i	0.0734371	+	0.0441296i
$281$	327.590	+	189.134i	1.16580	+	0.673076i	0.952688	−	0.303951i	$-0.0983059\pi$
$281$	327.590	+	189.134i	1.16580	+	0.673076i	0.213115	+	0.977027i	$0.431639\pi$
$282$	25.5766	−	175.537i	0.0906972	−	0.622472i
$283$	238.641			0.843256			0.421628	−	0.906769i	$-0.361459\pi$
$283$	238.641			0.843256			0.421628	+	0.906769i	$0.361459\pi$
$284$		−	175.527i		−	0.618052i
$285$	−76.1163	−	11.0905i	−0.267075	−	0.0389141i
$286$	−43.6212	+	75.5542i	−0.152522	+	0.264175i
$287$	200.646	+	362.010i	0.699114	+	1.26136i
$288$	−111.270	+	373.726i	−0.386353	+	1.29766i
$289$	−1.87430	−	3.24638i	−0.00648546	−	0.0112331i
$290$	302.957	−	174.912i	1.04468	−	0.603145i
$291$	−221.169	−	174.605i	−0.760030	−	0.600019i
$292$	−207.511	+	359.419i	−0.710653	+	1.23089i
$293$	154.593	−	89.2544i	0.527622	−	0.304622i	−0.212426	−	0.977177i	$-0.568136\pi$
$293$	154.593	−	89.2544i	0.527622	−	0.304622i	0.740047	+	0.672555i	$0.234803\pi$
$294$	397.019	+	72.1126i	1.35041	+	0.245281i
$295$	62.2455	−	107.812i	0.211002	−	0.365466i
$296$	51.5268	−	29.7490i	0.174077	−	0.100503i
$297$	−20.0304	−	223.109i	−0.0674424	−	0.751209i
$298$	260.982	−	452.034i	0.875779	−	1.51689i
$299$			93.6409i			0.313180i
$300$	−175.288	+	69.7911i	−0.584292	+	0.232637i
$301$	−336.237	−	202.050i	−1.11707	−	0.671264i
$302$	137.443	−	79.3525i	0.455108	−	0.262757i
$303$	−144.487	−	362.894i	−0.476854	−	1.19767i
$304$	−84.2418	−	145.911i	−0.277111	−	0.479971i
$305$	140.329	+	81.0191i	0.460096	+	0.265637i
$306$	303.064	−	286.795i	0.990406	−	0.937240i
$307$	29.6153			0.0964667			0.0482333	−	0.998836i	$-0.484641\pi$
$307$	29.6153			0.0964667			0.0482333	+	0.998836i	$0.484641\pi$
$308$	99.5236	+	179.563i	0.323129	+	0.582996i
$309$	−227.421	−	179.542i	−0.735991	−	0.581041i
$310$	−144.653	+	250.546i	−0.466622	+	0.808214i
$311$			207.684i			0.667796i	0.942609	+	0.333898i	$0.108364\pi$
$311$			207.684i			0.667796i	−0.942609	+	0.333898i	$0.891636\pi$
$312$	−5.42596	−	13.6279i	−0.0173909	−	0.0436791i
$313$	−143.311			−0.457863			−0.228932	−	0.973443i	$-0.573523\pi$
$313$	−143.311			−0.457863			−0.228932	+	0.973443i	$0.573523\pi$
$314$			392.397i			1.24967i
$315$	−124.880	+	114.102i	−0.396444	+	0.362228i
$316$	−143.349			−0.453636
$317$			73.2166i			0.230967i	0.993309	+	0.115484i	$0.0368417\pi$
$317$			73.2166i			0.230967i	−0.993309	+	0.115484i	$0.963158\pi$
$318$	−165.842	−	130.927i	−0.521517	−	0.411721i
$319$	−393.780			−1.23442
$320$	112.444	+	64.9196i	0.351387	+	0.202874i
$321$	−9.03481	−	22.6919i	−0.0281458	−	0.0706912i
$322$	402.599	+	241.928i	1.25031	+	0.751330i
$323$			161.281i			0.499321i
$324$	−239.707	−	156.619i	−0.739836	−	0.483393i
$325$	34.0760	−	59.0214i	0.104849	−	0.181604i
$326$	−173.974	+	100.444i	−0.533663	+	0.308110i
$327$	−430.645	−	339.980i	−1.31696	−	1.03970i
$328$	−37.7341	−	65.3574i	−0.115043	−	0.199260i
$329$	150.764	+	2.63785i	0.458250	+	0.00801778i
$330$	−181.530	−	26.4498i	−0.550091	−	0.0801510i
$331$	43.2136			0.130555			0.0652773	−	0.997867i	$-0.479207\pi$
$331$	43.2136			0.130555			0.0652773	+	0.997867i	$0.479207\pi$
$332$	228.759	+	132.074i	0.689032	+	0.397813i
$333$	97.3710	+	408.085i	0.292405	+	1.22548i
$334$	305.044	+	528.352i	0.913306	+	1.58189i
$335$	−149.011	−	86.0315i	−0.444809	−	0.256810i
$336$	−365.655	−	59.8280i	−1.08826	−	0.178060i
$337$	23.8185	+	41.2549i	0.0706781	+	0.122418i	0.899199	−	0.437541i	$-0.144150\pi$
$337$	23.8185	+	41.2549i	0.0706781	+	0.122418i	−0.828521	+	0.559959i	$0.810817\pi$
$338$	366.868	+	211.811i	1.08541	+	0.626660i
$339$	83.9914	+	210.953i	0.247762	+	0.622281i
$340$	−80.1543	−	138.831i	−0.235748	−	0.408327i
$341$	282.028	−	162.829i	0.827061	−	0.477504i
$342$	229.472	−	54.7530i	0.670970	−	0.160097i
$343$	−17.9938	+	342.528i	−0.0524601	+	0.998623i
$344$	61.9432	+	35.7629i	0.180067	+	0.103962i
$345$	−182.935	+	72.8357i	−0.530245	+	0.211118i
$346$	−668.568			−1.93228
$347$		−	321.547i		−	0.926650i	−0.886189	−	0.463325i	$-0.846656\pi$
$347$		−	321.547i		−	0.926650i	0.886189	−	0.463325i	$-0.153344\pi$
$348$	−311.897	+	395.073i	−0.896257	+	1.13527i
$349$	−7.57794	+	13.1254i	−0.0217133	+	0.0376085i	−0.876678	−	0.481078i	$-0.840245\pi$
$349$	−7.57794	+	13.1254i	−0.0217133	+	0.0376085i	0.854965	+	0.518686i	$0.173579\pi$
$350$	−165.718	−	298.992i	−0.473480	−	0.854264i
$351$	103.017	−	9.24871i	0.293496	−	0.0263496i
$352$	−179.730	−	311.302i	−0.510597	−	0.884379i
$353$	−304.779	+	175.964i	−0.863397	+	0.498482i	−0.865148	−	0.501516i	$-0.832776\pi$
$353$	−304.779	+	175.964i	−0.863397	+	0.498482i	0.00175142	+	0.999998i	$0.499443\pi$
$354$	−55.0509	+	377.824i	−0.155511	+	1.06730i
$355$	−66.6608	+	115.460i	−0.187777	+	0.325239i
$356$	211.972	−	122.382i	0.595428	−	0.343770i
$357$	274.494	+	224.609i	0.768889	+	0.629157i
$358$	−198.533	+	343.868i	−0.554560	+	0.960526i
$359$	20.3965	−	11.7759i	0.0568147	−	0.0328020i	−0.471324	−	0.881960i	$-0.656224\pi$
$359$	20.3965	−	11.7759i	0.0568147	−	0.0328020i	0.528138	+	0.849158i	$0.322890\pi$
$360$	22.4026	−	21.2000i	0.0622295	−	0.0588889i
$361$	134.906	−	233.664i	0.373701	−	0.647270i
$362$			46.6621i			0.128901i
$363$	−122.837	−	96.9755i	−0.338393	−	0.267150i
$364$	−82.9103	+	45.9535i	−0.227776	+	0.126246i
$365$	272.997	−	157.615i	0.747938	−	0.431822i
$366$	−491.779	−	71.6546i	−1.34366	−	0.195778i
$367$	166.446	+	288.293i	0.453531	+	0.785539i	0.998602	−	0.0528507i	$-0.0168308\pi$
$367$	166.446	+	288.293i	0.453531	+	0.785539i	−0.545071	+	0.838390i	$0.683497\pi$
$368$	−373.506	−	215.644i	−1.01496	−	0.585988i
$369$	517.622	−	123.507i	1.40277	−	0.334707i
$370$	343.577			0.928587
$371$	92.5109	−	153.950i	0.249356	−	0.414958i
$372$	60.0194	−	411.924i	0.161342	−	1.10732i
$373$	41.1419	−	71.2599i	0.110300	−	0.191045i	−0.805591	−	0.592472i	$-0.798152\pi$
$373$	41.1419	−	71.2599i	0.110300	−	0.191045i	0.915891	+	0.401427i	$0.131486\pi$
$374$			384.639i			1.02845i
$375$	341.081	+	49.6972i	0.909550	+	0.132526i
$376$	−27.4940			−0.0731223
$377$		−	181.822i		−	0.482286i
$378$	226.389	−	466.805i	0.598911	−	1.23493i
$379$	−182.889			−0.482557			−0.241278	−	0.970456i	$-0.577567\pi$
$379$	−182.889			−0.482557			−0.241278	+	0.970456i	$0.577567\pi$
$380$		−	90.6381i		−	0.238521i
$381$	16.7147	−	114.716i	0.0438706	−	0.301092i
$382$	195.935			0.512920
$383$	111.369	+	64.2991i	0.290781	+	0.167883i	0.638294	−	0.769793i	$-0.279640\pi$
$383$	111.369	+	64.2991i	0.290781	+	0.167883i	−0.347513	+	0.937675i	$0.612974\pi$
$384$	120.430	+	17.5473i	0.313621	+	0.0456961i
$385$	2.72791	−	155.912i	0.00708547	−	0.404965i
$386$			900.836i			2.33377i
$387$	−366.329	+	346.664i	−0.946586	+	0.895772i
$388$	166.019	−	287.554i	0.427885	−	0.741119i
$389$	−410.812	+	237.183i	−1.05607	+	0.609724i	−0.924343	−	0.381562i	$-0.875386\pi$
$389$	−410.812	+	237.183i	−1.05607	+	0.609724i	−0.131730	+	0.991286i	$0.542053\pi$
$390$	12.2128	−	83.8186i	0.0313148	−	0.214920i
$391$	206.424	+	357.537i	0.527940	+	0.914418i
$392$	2.18784	−	62.5030i	0.00558122	−	0.159446i
$393$	−10.4236	+	13.2034i	−0.0265232	+	0.0335963i
$394$	−470.185			−1.19336
$395$	94.2936	+	54.4405i	0.238718	+	0.137824i
$396$	256.749	−	61.2614i	0.648355	−	0.154701i
$397$	123.800	+	214.429i	0.311840	+	0.540122i	0.978761	−	0.205006i	$-0.0657214\pi$
$397$	123.800	+	214.429i	0.311840	+	0.540122i	−0.666921	+	0.745129i	$0.732388\pi$
$398$	−664.906	−	383.884i	−1.67062	−	0.964532i
$399$	70.9088	+	187.579i	0.177716	+	0.470122i
$400$	156.946	+	271.838i	0.392365	+	0.679595i
$401$	−342.807	−	197.920i	−0.854881	−	0.493566i	0.00741350	−	0.999973i	$-0.497640\pi$
$401$	−342.807	−	197.920i	−0.854881	−	0.493566i	−0.862295	+	0.506407i	$0.830974\pi$
$402$	522.203	+	76.0876i	1.29901	+	0.189273i
$403$	75.1837	+	130.222i	0.186560	+	0.323131i
$404$	398.598	−	230.130i	0.986628	−	0.569630i
$405$	98.1967	+	194.058i	0.242461	+	0.479155i
$406$	−781.722	−	469.750i	−1.92542	−	1.15702i
$407$	−334.934	−	193.374i	−0.822933	−	0.475121i
$408$	−50.7589	−	40.0725i	−0.124409	−	0.0982168i
$409$	473.300			1.15721			0.578607	−	0.815607i	$-0.303597\pi$
$409$	473.300			1.15721			0.578607	+	0.815607i	$0.303597\pi$
$410$		−	435.799i		−	1.06292i
$411$	−133.071	−	334.221i	−0.323773	−	0.813189i
$412$	170.713	−	295.683i	0.414352	−	0.717678i
$413$	−324.504	−	5.67768i	−0.785723	−	0.0137474i
$414$	438.630	−	415.083i	1.05949	−	1.00262i
$415$	−100.317	−	173.754i	−0.241728	−	0.418685i
$416$	143.739	−	82.9875i	0.345525	−	0.199489i
$417$	431.772	−	171.911i	1.03543	−	0.412256i
$418$	−108.737	+	188.338i	−0.260136	+	0.450569i
$419$	−126.657	+	73.1253i	−0.302283	+	0.174523i	−0.643468	−	0.765473i	$-0.722505\pi$
$419$	−126.657	+	73.1253i	−0.302283	+	0.174523i	0.341185	+	0.939996i	$0.389172\pi$
$420$	−154.263	−	126.228i	−0.367292	−	0.300543i
$421$	−246.784	+	427.443i	−0.586186	+	1.01530i	0.408540	+	0.912740i	$0.366038\pi$
$421$	−246.784	+	427.443i	−0.586186	+	1.01530i	−0.994726	+	0.102564i	$0.967295\pi$
$422$	80.9242	−	46.7216i	0.191763	−	0.110715i
$423$	55.3210	−	185.809i	0.130783	−	0.439265i
$424$	−16.3744	+	28.3613i	−0.0386189	+	0.0668900i
$425$		−	300.472i		−	0.706993i
$426$	58.9558	−	404.625i	0.138394	−	0.949823i
$427$	7.39011	−	422.376i	0.0173070	−	0.989171i
$428$	24.9244	−	14.3901i	0.0582346	−	0.0336218i
$429$	−59.0809	+	74.8364i	−0.137718	+	0.174444i
$430$	206.517	+	357.697i	0.480271	+	0.831854i
$431$	68.6770	+	39.6507i	0.159343	+	0.0919969i	0.577551	−	0.816354i	$-0.304008\pi$
$431$	68.6770	+	39.6507i	0.159343	+	0.0919969i	−0.418208	+	0.908351i	$0.637342\pi$
$432$	−200.345	+	432.203i	−0.463762	+	1.00047i
$433$	707.731			1.63448			0.817241	−	0.576296i	$-0.195503\pi$
$433$	707.731			1.63448			0.817241	+	0.576296i	$0.195503\pi$
$434$	754.117	+	13.1944i	1.73760	+	0.0304019i
$435$	355.202	−	141.424i	0.816557	−	0.325114i
$436$	323.262	−	559.907i	0.741427	−	1.28419i
$437$			233.424i			0.534151i
$438$	−599.076	+	758.836i	−1.36775	+	1.73250i
$439$	−6.54467			−0.0149081			−0.00745407	−	0.999972i	$-0.502373\pi$
$439$	−6.54467			−0.0149081			−0.00745407	+	0.999972i	$0.502373\pi$
$440$			28.4326i			0.0646196i
$441$	418.004	+	140.549i	0.947854	+	0.318705i
$442$	−177.601			−0.401812
$443$		−	170.094i		−	0.383959i	−0.981399	−	0.191980i	$-0.938509\pi$
$443$		−	170.094i		−	0.383959i	0.981399	−	0.191980i	$-0.0614908\pi$
$444$	−459.296	+	182.870i	−1.03445	+	0.411869i
$445$	−185.911			−0.417778
$446$	−835.767	−	482.530i	−1.87392	−	1.08191i
$447$	353.476	−	447.740i	0.790774	−	1.00166i
$448$	5.92159	−	338.444i	0.0132178	−	0.755456i
$449$		−	0.562541i		−	0.00125288i	−1.00000		0.000626438i	$-0.999801\pi$
$449$		−	0.562541i		−	0.00125288i	1.00000		0.000626438i	$-0.000199401\pi$
$450$	−427.515	+	102.007i	−0.950034	+	0.226682i
$451$	−245.279	+	424.835i	−0.543855	+	0.941985i
$452$	−231.708	+	133.777i	−0.512628	+	0.295966i
$453$	161.145	−	64.1602i	0.355729	−	0.141634i
$454$	320.635	+	555.356i	0.706245	+	1.22325i
$455$	71.9897	+	1.25957i	0.158219	+	0.00276828i
$456$	−13.5256	−	33.9709i	−0.0296613	−	0.0744976i
$457$	737.696			1.61422			0.807108	−	0.590404i	$-0.201032\pi$
$457$	737.696			1.61422			0.807108	+	0.590404i	$0.201032\pi$
$458$	120.798	+	69.7426i	0.263751	+	0.152276i
$459$	372.949	−	262.407i	0.812525	−	0.571692i
$460$	−116.008	−	200.933i	−0.252192	−	0.436810i
$461$	−18.3873	−	10.6159i	−0.0398857	−	0.0230280i	0.479925	−	0.877310i	$-0.340664\pi$
$461$	−18.3873	−	10.6159i	−0.0398857	−	0.0230280i	−0.519810	+	0.854282i	$0.673997\pi$
$462$	169.111	+	447.357i	0.366040	+	0.968305i
$463$	−256.649	−	444.530i	−0.554318	−	0.960108i	−0.997956	−	0.0639015i	$-0.979646\pi$
$463$	−256.649	−	444.530i	−0.554318	−	0.960108i	0.443638	−	0.896206i	$-0.353688\pi$
$464$	725.233	+	418.713i	1.56300	+	0.902400i
$465$	−195.919	+	248.166i	−0.421331	+	0.533690i
$466$	−21.0186	−	36.4053i	−0.0451044	−	0.0781231i
$467$	−391.478	+	226.020i	−0.838282	+	0.483982i	−0.856680	−	0.515848i	$-0.827477\pi$
$467$	−391.478	+	226.020i	−0.838282	+	0.483982i	0.0183979	+	0.999831i	$0.494143\pi$
$468$	28.2865	+	118.550i	0.0604412	+	0.253311i
$469$	−7.84730	+	448.507i	−0.0167320	+	0.956305i
$470$	−137.496	−	79.3833i	−0.292545	−	0.168901i
$471$	−61.8326	+	424.368i	−0.131279	+	0.900994i
$472$	59.1778			0.125377
$473$		−	464.932i		−	0.982942i
$474$	−330.448	−	48.1480i	−0.697149	−	0.101578i
$475$	84.9431	−	147.126i	0.178828	−	0.309739i
$476$	−215.265	+	358.228i	−0.452238	+	0.752580i
$477$	−158.724	−	167.727i	−0.332754	−	0.351630i
$478$	339.501	+	588.033i	0.710253	+	1.23019i
$479$	130.064	−	75.0926i	0.271533	−	0.156770i	−0.358051	−	0.933702i	$-0.616559\pi$
$479$	130.064	−	75.0926i	0.271533	−	0.156770i	0.629584	+	0.776932i	$0.283225\pi$
$480$	273.925	+	216.255i	0.570677	+	0.450531i
$481$	89.2874	−	154.650i	0.185629	−	0.321519i
$482$	−7.63600	+	4.40865i	−0.0158423	+	0.00914657i
$483$	397.279	+	325.080i	0.822523	+	0.673043i
$484$	92.2068	−	159.707i	0.190510	−	0.329973i
$485$	−218.412	+	126.100i	−0.450334	+	0.260001i
$486$	−499.967	−	441.552i	−1.02874	−	0.908544i
$487$	−78.8441	+	136.562i	−0.161897	+	0.280415i	−0.935549	−	0.353196i	$-0.885095\pi$
$487$	−78.8441	+	136.562i	−0.161897	+	0.280415i	0.773652	+	0.633611i	$0.218428\pi$
$488$			77.0262i			0.157840i
$489$	−203.976	+	81.2136i	−0.417130	+	0.166081i
$490$	191.406	−	306.257i	0.390625	−	0.625015i
$491$	−327.632	+	189.158i	−0.667274	+	0.385251i	−0.795043	−	0.606553i	$-0.792552\pi$
$491$	−327.632	+	189.158i	−0.667274	+	0.385251i	0.127769	+	0.991804i	$0.459218\pi$
$492$	231.955	+	582.579i	0.471453	+	1.18410i
$493$	−400.812	−	694.228i	−0.813007	−	1.40817i
$494$	−86.9620	−	50.2076i	−0.176037	−	0.101635i
$495$	−192.153	−	57.2097i	−0.388187	−	0.115575i
$496$	−692.555			−1.39628
$497$	347.522	+	6.08042i	0.699239	+	0.0122342i
$498$	482.975	+	381.293i	0.969828	+	0.765648i
$499$	384.778	−	666.454i	0.771097	−	1.33558i	−0.165865	−	0.986149i	$-0.553041\pi$
$499$	384.778	−	666.454i	0.771097	−	1.33558i	0.936962	−	0.349431i	$-0.113625\pi$
$500$			406.154i			0.812308i
$501$	246.642	+	619.468i	0.492300	+	1.23646i
$502$	−251.412			−0.500821
$503$		−	313.393i		−	0.623047i	−0.950238	−	0.311524i	$-0.899161\pi$
$503$		−	313.393i		−	0.623047i	0.950238	−	0.311524i	$-0.100839\pi$
$504$	−76.6538	−	24.2899i	−0.152091	−	0.0481942i
$505$	−349.592			−0.692261
$506$			556.693i			1.10018i
$507$	363.382	+	286.878i	0.716730	+	0.565835i
$508$	136.602			0.268902
$509$	91.2624	+	52.6904i	0.179298	+	0.103517i	0.586963	−	0.809614i	$-0.300324\pi$
$509$	91.2624	+	52.6904i	0.179298	+	0.103517i	−0.407665	+	0.913132i	$0.633657\pi$
$510$	−138.141	−	346.956i	−0.270865	−	0.680307i
$511$	−704.419	−	423.297i	−1.37851	−	0.828370i
$512$			674.362i			1.31711i
$513$	256.796	−	23.0548i	0.500577	−	0.0449411i
$514$	159.527	−	276.310i	0.310365	−	0.537567i
$515$	−224.587	+	129.665i	−0.436091	+	0.251777i
$516$	−466.458	−	368.253i	−0.903988	−	0.713669i
$517$	89.3581	+	154.773i	0.172840	+	0.299367i
$518$	−434.221	−	783.432i	−0.838265	−	1.51242i
$519$	−723.040	−	105.351i	−1.39314	−	0.202988i
$520$	−13.1283			−0.0252468
$521$	−446.856	−	257.992i	−0.857689	−	0.495187i	0.00554870	−	0.999985i	$-0.498234\pi$
$521$	−446.856	−	257.992i	−0.857689	−	0.495187i	−0.863238	+	0.504798i	$0.831567\pi$
$522$	−851.684	+	805.964i	−1.63158	+	1.54399i
$523$	361.692	+	626.468i	0.691571	+	1.19784i	0.971323	+	0.237764i	$0.0764144\pi$
$523$	361.692	+	626.468i	0.691571	+	1.19784i	−0.279752	+	0.960072i	$0.590252\pi$
$524$	−17.1664	−	9.91105i	−0.0327604	−	0.0189142i
$525$	−132.106	−	349.466i	−0.251630	−	0.665650i
$526$	−56.3113	−	97.5341i	−0.107056	−	0.185426i
$527$	574.129	+	331.473i	1.08943	+	0.628982i
$528$	−162.444	−	407.995i	−0.307659	−	0.772718i
$529$	34.2611	+	59.3420i	0.0647658	+	0.112178i
$530$	−163.775	+	94.5558i	−0.309010	+	0.178407i
$531$	−119.072	+	399.933i	−0.224242	+	0.753170i
$532$	−206.675	+	114.551i	−0.388487	+	0.215321i
$533$	−196.161	−	113.254i	−0.368032	−	0.212483i
$534$	529.745	−	210.919i	0.992032	−	0.394979i
$535$	−21.8601			−0.0408600
$536$		−	81.7915i		−	0.152596i
$537$	−268.894	+	340.602i	−0.500733	+	0.634267i
$538$	507.971	−	879.831i	0.944183	−	1.63537i
$539$	−358.961	+	190.825i	−0.665975	+	0.354035i
$540$	−209.594	+	147.470i	−0.388137	+	0.273092i
$541$	−285.742	−	494.920i	−0.528174	−	0.914825i	−0.999460	−	0.0328442i	$-0.989543\pi$
$541$	−285.742	−	494.920i	−0.528174	−	0.914825i	0.471286	−	0.881980i	$-0.343790\pi$
$542$	420.110	−	242.550i	0.775110	−	0.447510i
$543$	−7.35284	+	50.4639i	−0.0135412	+	0.0929354i
$544$	365.879	−	633.722i	0.672572	−	1.16493i
$545$	−425.278	+	245.534i	−0.780327	+	0.450522i
$546$	−206.560	+	78.0842i	−0.378315	+	0.143011i
$547$	441.232	−	764.235i	0.806639	−	1.39714i	−0.108540	−	0.994092i	$-0.534618\pi$
$547$	441.232	−	764.235i	0.806639	−	1.39714i	0.915179	−	0.403048i	$-0.132049\pi$
$548$	367.103	−	211.947i	0.669896	−	0.386765i
$549$	−520.556	−	154.985i	−0.948189	−	0.282305i
$550$	202.581	−	350.881i	0.368330	−	0.637966i
$551$		−	453.237i		−	0.822572i
$552$	−73.4641	−	57.9975i	−0.133087	−	0.105068i
$553$	4.96575	−	283.814i	0.00897965	−	0.513226i
$554$	470.497	−	271.642i	0.849273	−	0.490328i
$555$	371.570	+	54.1397i	0.669496	+	0.0975489i
$556$	273.810	+	474.252i	0.492464	+	0.852972i
$557$	139.724	+	80.6697i	0.250851	+	0.144829i	0.620154	−	0.784480i	$-0.287070\pi$
$557$	139.724	+	80.6697i	0.250851	+	0.144829i	−0.369303	+	0.929309i	$0.620403\pi$
$558$	276.714	−	929.409i	0.495903	−	1.66561i
$559$	214.675			0.384034
$560$	−170.807	+	284.245i	−0.305013	+	0.507580i
$561$	−60.6100	+	415.978i	−0.108039	+	0.741493i
$562$	−519.174	+	899.236i	−0.923797	+	1.60006i
$563$		−	489.510i		−	0.869466i	−0.900559	−	0.434733i	$-0.856843\pi$
$563$		−	489.510i		−	0.869466i	0.900559	−	0.434733i	$-0.143157\pi$
$564$	226.058	+	32.9377i	0.400811	+	0.0584002i
$565$	203.221			0.359683
$566$			655.071i			1.15737i
$567$	318.391	−	469.165i	0.561537	−	0.827452i
$568$	−63.3754			−0.111576
$569$		−	200.244i		−	0.351922i	−0.984397	−	0.175961i	$-0.943697\pi$
$569$		−	200.244i		−	0.351922i	0.984397	−	0.175961i	$-0.0563033\pi$
$570$	30.4435	−	208.939i	0.0534096	−	0.366560i
$571$	−88.4911			−0.154976			−0.0774878	−	0.996993i	$-0.524690\pi$
$571$	−88.4911			−0.154976			−0.0774878	+	0.996993i	$0.524690\pi$
$572$	−97.2991	−	56.1756i	−0.170103	−	0.0982092i
$573$	211.900	+	30.8748i	0.369807	+	0.0538828i
$574$	−993.718	+	550.773i	−1.73122	+	0.959535i
$575$		−	434.878i		−	0.756309i
$576$	−417.114	−	124.188i	−0.724157	−	0.215604i
$577$	−91.3150	+	158.162i	−0.158258	+	0.274111i	−0.934241	−	0.356643i	$-0.883921\pi$
$577$	−91.3150	+	158.162i	−0.158258	+	0.274111i	0.775982	+	0.630755i	$0.217255\pi$
$578$	8.91131	−	5.14495i	0.0154175	−	0.00890130i
$579$	−141.951	+	974.233i	−0.245165	+	1.68261i
$580$	225.253	+	390.149i	0.388367	+	0.672671i
$581$	−269.415	+	448.340i	−0.463709	+	0.771669i
$582$	479.292	−	607.108i	0.823526	−	1.04314i
$583$	212.874			0.365135
$584$	129.771	+	74.9236i	0.222211	+	0.128294i
$585$	26.4157	−	88.7234i	0.0451550	−	0.151664i
$586$	245.003	+	424.358i	0.418094	+	0.724161i
$587$	540.196	+	311.882i	0.920266	+	0.531316i	0.883720	−	0.468016i	$-0.155031\pi$
$587$	540.196	+	311.882i	0.920266	+	0.531316i	0.0365462	+	0.999332i	$0.488364\pi$
$588$	−92.8670	+	511.283i	−0.157937	+	0.869530i
$589$	187.414	+	324.611i	0.318191	+	0.551123i
$590$	295.945	+	170.864i	0.501602	+	0.289600i
$591$	−508.494	−	74.0901i	−0.860396	−	0.125364i
$592$	411.236	+	712.282i	0.694656	+	1.20318i
$593$	940.956	−	543.261i	1.58677	−	0.916124i	0.592939	−	0.805247i	$-0.297968\pi$
$593$	940.956	−	543.261i	1.58677	−	0.916124i	0.993834	−	0.110876i	$-0.0353658\pi$
$594$	612.434	−	54.9834i	1.03103	−	0.0925647i
$595$	277.646	−	153.887i	0.466632	−	0.258633i
$596$	582.132	+	336.094i	0.976732	+	0.563917i
$597$	−658.589	−	519.935i	−1.10316	−	0.870912i
$598$	−257.044			−0.429840
$599$			1100.06i			1.83650i	0.395999	+	0.918251i	$0.370398\pi$
$599$			1100.06i			1.83650i	−0.395999	+	0.918251i	$0.629602\pi$
$600$	25.1987	+	63.2892i	0.0419978	+	0.105482i
$601$	−359.808	+	623.206i	−0.598683	+	1.03695i	0.394333	+	0.918968i	$0.370976\pi$
$601$	−359.808	+	623.206i	−0.598683	+	1.03695i	−0.993016	+	0.117982i	$0.962358\pi$
$602$	554.629	−	922.970i	0.921310	−	1.53317i
$603$	552.761	+	164.574i	0.916684	+	0.272925i
$604$	102.191	+	176.999i	0.169190	+	0.293045i
$605$	−121.306	+	70.0358i	−0.200505	+	0.115762i
$606$	996.144	−	396.617i	1.64380	−	0.654483i
$607$	−447.216	+	774.600i	−0.736764	+	1.27611i	0.217181	+	0.976131i	$0.430314\pi$
$607$	−447.216	+	774.600i	−0.736764	+	1.27611i	−0.953945	+	0.299981i	$0.903020\pi$
$608$	358.305	−	206.867i	0.589317	−	0.340242i
$609$	−771.393	−	631.205i	−1.26665	−	1.03646i
$610$	−222.398	+	385.204i	−0.364586	+	0.631482i
$611$	−71.4638	+	41.2597i	−0.116962	+	0.0675281i
$612$	369.337	+	390.288i	0.603491	+	0.637725i
$613$	187.261	−	324.346i	0.305483	−	0.529113i	−0.671885	−	0.740655i	$-0.734515\pi$
$613$	187.261	−	324.346i	0.305483	−	0.529113i	0.977369	+	0.211542i	$0.0678486\pi$
$614$			81.2939i			0.132401i
$615$	68.6716	−	471.306i	0.111661	−	0.766351i
$616$	64.8328	−	35.9339i	0.105248	−	0.0583342i
$617$	−753.256	+	434.892i	−1.22084	+	0.704850i	−0.965096	−	0.261896i	$-0.915652\pi$
$617$	−753.256	+	434.892i	−1.22084	+	0.704850i	−0.255740	+	0.966746i	$0.582319\pi$
$618$	492.842	−	624.271i	0.797479	−	1.01015i
$619$	−8.48535	−	14.6971i	−0.0137082	−	0.0237432i	0.859090	−	0.511825i	$-0.171030\pi$
$619$	−8.48535	−	14.6971i	−0.0137082	−	0.0237432i	−0.872798	+	0.488081i	$0.837697\pi$
$620$	−322.655	−	186.285i	−0.520411	−	0.300459i
$621$	539.775	−	379.785i	0.869203	−	0.611570i
$622$	−570.094			−0.916550
$623$	234.959	+	423.919i	0.377142	+	0.680448i
$624$	188.385	−	75.0059i	0.301899	−	0.120202i
$625$	−68.1348	+	118.013i	−0.109016	+	0.188821i
$626$		−	393.389i		−	0.628417i
$627$	−147.274	+	186.549i	−0.234887	+	0.297526i
$628$	−505.331			−0.804668
$629$		−	787.310i		−	1.25168i
$630$	−313.209	−	342.795i	−0.497158	−	0.544119i
$631$	638.650			1.01212			0.506062	−	0.862497i	$-0.331101\pi$
$631$	638.650			1.01212			0.506062	+	0.862497i	$0.331101\pi$
$632$			51.7574i			0.0818946i
$633$	94.8798	−	37.7766i	0.149889	−	0.0596786i
$634$	−200.979			−0.317002
$635$	−89.8557	−	51.8782i	−0.141505	−	0.0816979i
$636$	168.609	−	213.573i	0.265108	−	0.335806i
$637$	−88.1102	−	165.744i	−0.138321	−	0.260195i
$638$		−	1080.93i		−	1.69424i
$639$	127.519	−	428.302i	0.199560	−	0.670269i
$640$	54.4623	−	94.3316i	0.0850974	−	0.147393i
$641$	553.558	−	319.597i	0.863585	−	0.498591i	−0.00162627	−	0.999999i	$-0.500518\pi$
$641$	553.558	−	319.597i	0.863585	−	0.498591i	0.865211	+	0.501408i	$0.167184\pi$
$642$	62.2892	−	24.8006i	0.0970237	−	0.0386301i
$643$	362.332	+	627.578i	0.563503	+	0.976015i	0.997187	+	0.0749505i	$0.0238799\pi$
$643$	362.332	+	627.578i	0.563503	+	0.976015i	−0.433685	+	0.901065i	$0.642787\pi$
$644$	−311.557	+	518.469i	−0.483784	+	0.805076i
$645$	166.978	+	419.383i	0.258881	+	0.650207i
$646$	−442.715			−0.685318
$647$	220.212	+	127.140i	0.340359	+	0.196506i	0.660431	−	0.750887i	$-0.270374\pi$
$647$	220.212	+	127.140i	0.340359	+	0.196506i	−0.320072	+	0.947393i	$0.603707\pi$
$648$	−56.5488	+	86.5482i	−0.0872667	+	0.133562i
$649$	−192.333	−	333.131i	−0.296353	−	0.513299i
$650$	162.014	+	93.5387i	0.249252	+	0.143906i
$651$	813.481	+	133.101i	1.24959	+	0.204456i
$652$	−129.352	−	224.045i	−0.198393	−	0.343627i
$653$	−708.083	−	408.812i	−1.08435	−	0.626052i	−0.152286	−	0.988336i	$-0.548663\pi$
$653$	−708.083	−	408.812i	−1.08435	−	0.626052i	−0.932067	+	0.362285i	$0.881997\pi$
$654$	933.246	−	1182.12i	1.42698	−	1.80753i
$655$	7.52795	+	13.0388i	0.0114931	+	0.0199066i
$656$	903.470	−	521.618i	1.37724	−	0.795150i
$657$	−767.461	+	726.263i	−1.16813	+	1.10542i
$658$	−7.24090	+	413.848i	−0.0110044	+	0.628948i
$659$	−771.870	−	445.640i	−1.17128	−	0.676236i	−0.217295	−	0.976106i	$-0.569723\pi$
$659$	−771.870	−	445.640i	−1.17128	−	0.676236i	−0.953980	+	0.299870i	$0.903057\pi$
$660$	34.0622	−	233.775i	0.0516095	−	0.354205i
$661$	−493.060			−0.745931			−0.372965	−	0.927845i	$-0.621659\pi$
$661$	−493.060			−0.745931			−0.372965	+	0.927845i	$0.621659\pi$
$662$			118.621i			0.179186i
$663$	−192.071	−	27.9857i	−0.289700	−	0.0422107i
$664$	47.6865	−	82.5954i	0.0718169	−	0.124391i
$665$	179.453	+	3.13979i	0.269853	+	0.00472149i
$666$	−1120.19	+	267.283i	−1.68197	+	0.401326i
$667$	−580.102	−	1004.77i	−0.869718	−	1.50640i
$668$	−680.415	+	392.838i	−1.01859	+	0.588080i
$669$	−827.827	−	653.542i	−1.23741	−	0.976894i
$670$	236.156	−	409.035i	0.352472	−	0.610500i
$671$	433.606	−	250.342i	0.646208	−	0.373088i
$672$	146.916	−	897.918i	0.218625	−	1.33619i
$673$	−442.879	+	767.089i	−0.658067	+	1.13981i	0.323048	+	0.946383i	$0.395292\pi$
$673$	−442.879	+	767.089i	−0.658067	+	1.13981i	−0.981115	+	0.193423i	$0.938041\pi$
$674$	−113.245	+	65.3819i	−0.168019	+	0.0970057i
$675$	−478.422	+	42.9519i	−0.708773	+	0.0636325i
$676$	−272.772	+	472.454i	−0.403508	+	0.698897i
$677$			1024.53i			1.51334i	0.653798	+	0.756669i	$0.273175\pi$
$677$			1024.53i			1.51334i	−0.653798	+	0.756669i	$0.726825\pi$
$678$	−579.067	+	230.556i	−0.854081	+	0.340054i
$679$	563.572	+	338.660i	0.830002	+	0.498762i
$680$	−50.1262	+	28.9404i	−0.0737150	+	0.0425594i
$681$	259.248	+	651.129i	0.380688	+	0.956137i
$682$	446.965	+	774.167i	0.655374	+	1.13514i
$683$	−263.216	−	151.968i	−0.385382	−	0.222500i	0.294775	−	0.955567i	$-0.404755\pi$
$683$	−263.216	−	151.968i	−0.385382	−	0.222500i	−0.680157	+	0.733066i	$0.738089\pi$
$684$	70.5113	+	295.515i	0.103087	+	0.432040i
$685$	−321.969			−0.470028
$686$	−940.239	−	49.3930i	−1.37061	−	0.0720015i
$687$	119.650	+	94.4599i	0.174163	+	0.137496i
$688$	−494.370	+	856.274i	−0.718561	+	1.24458i
$689$			98.2911i			0.142658i
$690$	−199.934	−	502.155i	−0.289759	−	0.727761i
$691$	−617.452			−0.893563			−0.446781	−	0.894643i	$-0.647430\pi$
$691$	−617.452			−0.893563			−0.446781	+	0.894643i	$0.647430\pi$
$692$		−	860.985i		−	1.24420i
$693$	112.396	+	510.454i	0.162188	+	0.736586i
$694$	882.648			1.27183
$695$		−	415.945i		−	0.598483i
$696$	142.645	+	112.613i	0.204949	+	0.161801i
$697$	−998.636			−1.43276
$698$	−36.0291	−	20.8014i	−0.0516177	−	0.0298015i
$699$	−16.9945	−	42.6836i	−0.0243126	−	0.0610638i
$700$	385.044	−	213.412i	0.550063	−	0.304875i
$701$			793.809i			1.13239i	0.824270	+	0.566197i	$0.191586\pi$
$701$			793.809i			1.13239i	−0.824270	+	0.566197i	$0.808414\pi$
$702$	25.3877	+	282.782i	0.0361648	+	0.402823i
$703$	222.572	−	385.505i	0.316603	−	0.548372i
$704$	347.442	−	200.596i	0.493526	−	0.284937i
$705$	−136.190	−	107.517i	−0.193177	−	0.152507i
$706$	−483.022	−	836.619i	−0.684167	−	1.18501i
$707$	441.823	+	797.147i	0.624926	+	1.12751i
$708$	−486.564	−	70.8948i	−0.687238	−	0.100134i
$709$	869.189			1.22594			0.612969	−	0.790107i	$-0.289975\pi$
$709$	869.189			1.22594			0.612969	+	0.790107i	$0.289975\pi$
$710$	−316.937	−	182.984i	−0.446391	−	0.257724i
$711$	−349.785	−	104.142i	−0.491962	−	0.146472i
$712$	−44.1872	−	76.5345i	−0.0620607	−	0.107492i
$713$	830.945	+	479.747i	1.16542	+	0.672856i
$714$	−616.552	+	753.485i	−0.863518	+	1.05530i
$715$	42.6683	+	73.9037i	0.0596759	+	0.103362i
$716$	−442.836	−	255.671i	−0.618486	−	0.357083i
$717$	274.502	+	689.441i	0.382848	+	0.961563i
$718$	32.3249	+	55.9883i	0.0450207	+	0.0779782i
$719$	−1146.88	+	662.152i	−1.59510	+	0.920934i	−0.602693	+	0.797973i	$0.705906\pi$
$719$	−1146.88	+	662.152i	−1.59510	+	0.920934i	−0.992412	+	0.122961i	$0.960761\pi$
$720$	293.059	+	309.683i	0.407027	+	0.430116i
$721$	579.504	+	348.234i	0.803750	+	0.482987i
$722$	641.409	+	370.317i	0.888378	+	0.512905i
$723$	−8.95286	+	3.56459i	−0.0123829	+	0.00493028i
$724$	−60.0917			−0.0829995
$725$			844.399i			1.16469i
$726$	266.198	−	337.186i	0.366663	−	0.464444i
$727$	413.149	−	715.595i	0.568293	−	0.984313i	−0.428442	−	0.903569i	$-0.640937\pi$
$727$	413.149	−	715.595i	0.568293	−	0.984313i	0.996735	−	0.0807432i	$-0.0257294\pi$
$728$	16.5919	+	29.9355i	0.0227911	+	0.0411202i
$729$	−471.125	−	556.311i	−0.646262	−	0.763116i
$730$	432.654	+	749.378i	0.592676	+	1.02655i
$731$	819.666	−	473.235i	1.12129	−	0.647380i
$732$	92.2771	−	633.315i	0.126062	−	0.865185i
$733$	30.8923	−	53.5070i	0.0421450	−	0.0729973i	−0.844183	−	0.536054i	$-0.819914\pi$
$733$	30.8923	−	53.5070i	0.0421450	−	0.0729973i	0.886328	+	0.463057i	$0.153248\pi$
$734$	−791.364	+	456.894i	−1.07815	+	0.622472i
$735$	255.260	−	301.049i	0.347293	−	0.409590i
$736$	529.543	−	917.195i	0.719487	−	1.24619i
$737$	−460.431	+	265.830i	−0.624737	+	0.360692i
$738$	339.026	+	1420.87i	0.459385	+	1.92530i
$739$	659.374	−	1142.07i	0.892252	−	1.54543i	0.0550835	−	0.998482i	$-0.482457\pi$
$739$	659.374	−	1142.07i	0.892252	−	1.54543i	0.837169	−	0.546945i	$-0.184209\pi$
$740$			442.460i			0.597919i
$741$	−86.1359	−	68.0015i	−0.116243	−	0.0917699i
$742$	422.592	+	253.942i	0.569530	+	0.342241i
$743$	1171.10	−	676.136i	1.57618	−	0.910008i	0.580795	−	0.814050i	$-0.302742\pi$
$743$	1171.10	−	676.136i	1.57618	−	0.910008i	0.995385	−	0.0959588i	$-0.0305917\pi$
$744$	−148.729	−	21.6705i	−0.199904	−	0.0291270i
$745$	−255.281	−	442.160i	−0.342659	−	0.593503i
$746$	195.608	+	112.935i	0.262210	+	0.151387i
$747$	462.243	+	488.464i	0.618799	+	0.653902i
$748$	−495.340			−0.662219
$749$	27.6273	+	49.8459i	0.0368856	+	0.0665499i
$750$	−136.419	+	936.268i	−0.181892	+	1.24836i
$751$	−428.558	+	742.285i	−0.570650	+	0.988395i	0.425849	+	0.904794i	$0.359976\pi$
$751$	−428.558	+	742.285i	−0.570650	+	0.988395i	−0.996499	+	0.0836012i	$0.973358\pi$
$752$		−	380.064i		−	0.505404i
$753$	−271.897	−	39.6167i	−0.361084	−	0.0526118i
$754$	499.101			0.661938
$755$		−	155.238i		−	0.205613i
$756$	601.154	+	291.544i	0.795177	+	0.385641i
$757$	−903.868			−1.19401			−0.597007	−	0.802236i	$-0.703643\pi$
$757$	−903.868			−1.19401			−0.597007	+	0.802236i	$0.703643\pi$
$758$		−	502.030i		−	0.662309i
$759$	−87.7218	+	602.051i	−0.115575	+	0.793216i
$760$	−32.7257			−0.0430601
$761$	594.021	+	342.958i	0.780580	+	0.450668i	0.836636	−	0.547760i	$-0.184519\pi$
$761$	594.021	+	342.958i	0.780580	+	0.450668i	−0.0560560	+	0.998428i	$0.517853\pi$
$762$	314.896	+	45.8819i	0.413249	+	0.0602124i
$763$	1097.35	+	659.416i	1.43820	+	0.864242i
$764$			252.327i			0.330271i
$765$	−94.7244	−	396.993i	−0.123823	−	0.518945i
$766$	−176.501	+	305.709i	−0.230419	+	0.399097i
$767$	153.818	−	88.8069i	0.200545	−	0.115785i
$768$	−131.833	+	904.797i	−0.171658	+	1.17812i
$769$	−700.427	−	1213.17i	−0.910828	−	1.57760i	−0.812897	−	0.582407i	$-0.802111\pi$
$769$	−700.427	−	1213.17i	−0.910828	−	1.57760i	−0.0979303	−	0.995193i	$-0.531222\pi$
$770$	427.977	+	7.48811i	0.555815	+	0.00972481i
$771$	216.065	−	273.685i	0.280240	−	0.354973i
$772$	−1160.10			−1.50272
$773$	884.334	+	510.570i	1.14403	+	0.660505i	0.947425	−	0.319978i	$-0.103676\pi$
$773$	884.334	+	510.570i	1.14403	+	0.660505i	0.196603	+	0.980483i	$0.437009\pi$
$774$	−951.592	−	1005.57i	−1.22945	−	1.29919i
$775$	−349.160	−	604.764i	−0.450530	−	0.780340i
$776$	−103.824	−	59.9428i	−0.133794	−	0.0772458i
$777$	−346.149	−	915.687i	−0.445495	−	1.17849i
$778$	−651.067	−	1127.68i	−0.836846	−	1.44946i
$779$	−488.981	−	282.313i	−0.627704	−	0.362405i
$780$	107.942	+	15.7277i	0.138387	+	0.0201637i
$781$	205.976	+	356.761i	0.263734	+	0.456801i
$782$	−981.440	+	566.635i	−1.25504	+	0.724597i
$783$	−1048.08	+	737.425i	−1.33854	+	0.941795i
$784$	864.012	+	30.2436i	1.10206	+	0.0385761i
$785$	332.402	+	191.913i	0.423443	+	0.244475i
$786$	−36.2432	−	28.6128i	−0.0461110	−	0.0364031i
$787$	113.737			0.144520			0.0722600	−	0.997386i	$-0.476979\pi$
$787$	113.737			0.144520			0.0722600	+	0.997386i	$0.476979\pi$
$788$		−	605.507i		−	0.768410i
$789$	−45.5303	−	114.354i	−0.0577063	−	0.144936i
$790$	−149.439	+	258.836i	−0.189163	+	0.327641i
$791$	−256.835	−	463.388i	−0.324697	−	0.585826i
$792$	−22.1190	−	92.7014i	−0.0279280	−	0.117047i
$793$	115.592	+	200.211i	0.145765	+	0.252472i
$794$	−588.607	+	339.832i	−0.741318	+	0.428000i
$795$	−192.019	+	76.4527i	−0.241533	+	0.0961669i
$796$	494.367	−	856.269i	0.621065	−	1.07572i
$797$	20.9995	−	12.1241i	0.0263482	−	0.0152121i	−0.486768	−	0.873531i	$-0.661824\pi$
$797$	20.9995	−	12.1241i	0.0263482	−	0.0152121i	0.513116	+	0.858319i	$0.328491\pi$
$798$	−514.903	+	194.645i	−0.645242	+	0.243916i
$799$	−181.908	+	315.073i	−0.227669	+	0.394334i
$800$	−667.536	+	385.402i	−0.834420	+	0.481753i
$801$	606.143	−	144.628i	0.756732	−	0.180560i
$802$	543.290	−	941.006i	0.677419	−	1.17332i
$803$		−	974.035i		−	1.21300i
$804$	−97.9860	+	672.496i	−0.121873	+	0.836438i
$805$	401.841	−	222.722i	0.499181	−	0.276674i
$806$	−357.459	+	206.379i	−0.443498	+	0.256054i
$807$	687.999	−	871.472i	0.852539	−	1.07989i
$808$	−83.0906	−	143.917i	−0.102835	−	0.178115i
$809$	828.117	+	478.113i	1.02363	+	0.590993i	0.915153	−	0.403106i	$-0.132069\pi$
$809$	828.117	+	478.113i	1.02363	+	0.590993i	0.108477	+	0.994099i	$0.465403\pi$
$810$	−532.688	+	269.550i	−0.657640	+	0.332778i
$811$	−1352.18			−1.66730			−0.833650	−	0.552293i	$-0.813753\pi$
$811$	−1352.18			−1.66730			−0.833650	+	0.552293i	$0.813753\pi$
$812$	604.947	−	1006.71i	0.745009	−	1.23979i
$813$	492.559	−	196.113i	0.605854	−	0.241222i
$814$	530.812	−	919.394i	0.652103	−	1.12948i
$815$			196.500i			0.241104i
$816$	553.943	−	701.667i	0.678852	−	0.859885i
$817$	535.132			0.654996
$818$			1299.21i			1.58828i
$819$	−235.694	+	51.8972i	−0.287783	+	0.0633665i
$820$	561.224			0.684419
$821$		−	723.831i		−	0.881645i	−0.897594	−	0.440823i	$-0.854687\pi$
$821$		−	723.831i		−	0.881645i	0.897594	−	0.440823i	$-0.145313\pi$
$822$	917.436	−	365.279i	1.11610	−	0.444378i
$823$	−94.3087			−0.114591			−0.0572957	−	0.998357i	$-0.518248\pi$
$823$	−94.3087			−0.114591			−0.0572957	+	0.998357i	$0.518248\pi$
$824$	−106.759	−	61.6374i	−0.129562	−	0.0748026i
$825$	274.378	−	347.548i	0.332579	−	0.421270i
$826$	15.5852	−	890.763i	0.0188683	−	1.07841i
$827$		−	838.852i		−	1.01433i	−0.861849	−	0.507166i	$-0.830693\pi$
$827$		−	838.852i		−	1.01433i	0.861849	−	0.507166i	$-0.169307\pi$
$828$	534.546	+	564.870i	0.645588	+	0.682210i
$829$	−249.593	+	432.307i	−0.301077	+	0.521481i	−0.976380	−	0.216060i	$-0.930679\pi$
$829$	−249.593	+	432.307i	−0.301077	+	0.521481i	0.675303	+	0.737540i	$0.264013\pi$
$830$	476.955	−	275.370i	0.574645	−	0.331771i
$831$	551.636	−	219.635i	0.663822	−	0.264302i
$832$	92.6220	+	160.426i	0.111325	+	0.192820i
$833$	−701.791	−	438.609i	−0.842487	−	0.526541i
$834$	471.896	+	1185.22i	0.565822	+	1.42112i
$835$	596.761			0.714684
$836$	−242.543	−	140.032i	−0.290123	−	0.167502i
$837$	445.712	−	961.530i	0.532512	−	1.14878i
$838$	−200.729	−	347.673i	−0.239533	−	0.414884i
$839$	419.220	+	242.037i	0.499667	+	0.288483i	0.728576	−	0.684965i	$-0.240183\pi$
$839$	419.220	+	242.037i	0.499667	+	0.288483i	−0.228909	+	0.973448i	$0.573516\pi$
$840$	−45.5757	+	55.6979i	−0.0542568	+	0.0663070i
$841$	705.879	+	1222.62i	0.839333	+	1.45377i
$842$	−1173.33	−	677.423i	−1.39351	−	0.804541i
$843$	−703.173	+	890.693i	−0.834132	+	1.05658i
$844$	60.1683	+	104.215i	0.0712895	+	0.123477i
$845$	358.853	−	207.184i	0.424679	−	0.245188i
$846$	510.046	+	151.856i	0.602891	+	0.179499i
$847$	313.006	+	188.091i	0.369547	+	0.222067i
$848$	−392.054	−	226.352i	−0.462328	−	0.266925i
$849$	−103.224	+	708.443i	−0.121583	+	0.834445i
$850$	824.796			0.970348
$851$		−	1139.49i		−	1.33900i
$852$	521.078	+	75.9236i	0.611594	+	0.0891122i
$853$	83.1713	−	144.057i	0.0975045	−	0.168883i	−0.813147	−	0.582059i	$-0.802247\pi$
$853$	83.1713	−	144.057i	0.0975045	−	0.168883i	0.910651	+	0.413176i	$0.135581\pi$
$854$	1159.42	+	20.2858i	1.35764	+	0.0237539i
$855$	65.8478	−	221.166i	0.0770150	−	0.258673i
$856$	−5.19568	−	8.99918i	−0.00606972	−	0.0105131i
$857$	−679.210	+	392.142i	−0.792543	+	0.457575i	−0.840857	−	0.541257i	$-0.817949\pi$
$857$	−679.210	+	392.142i	−0.792543	+	0.457575i	0.0483138	+	0.998832i	$0.484615\pi$
$858$	−205.426	−	162.177i	−0.239424	−	0.189018i
$859$	710.815	−	1231.17i	0.827492	−	1.43326i	−0.0725085	−	0.997368i	$-0.523100\pi$
$859$	710.815	−	1231.17i	0.827492	−	1.43326i	0.900000	−	0.435890i	$-0.143566\pi$
$860$	−460.644	+	265.953i	−0.535633	+	0.309248i
$861$	−1161.47	+	439.061i	−1.34898	+	0.509944i
$862$	−108.841	+	188.518i	−0.126266	+	0.218699i
$863$	−710.341	+	410.116i	−0.823107	+	0.475221i	−0.851487	−	0.524376i	$-0.824298\pi$
$863$	−710.341	+	410.116i	−0.823107	+	0.475221i	0.0283800	+	0.999597i	$0.490965\pi$
$864$	−1061.33	−	491.976i	−1.22840	−	0.569416i
$865$	−326.981	+	566.348i	−0.378013	+	0.654738i
$866$			1942.72i			2.24333i
$867$	10.4481	−	4.15993i	0.0120509	−	0.00479807i
$868$	−16.9918	+	971.156i	−0.0195759	+	1.11884i
$869$	291.359	−	168.216i	0.335281	−	0.193575i
$870$	388.210	+	975.031i	0.446219	+	1.12073i
$871$	−122.743	−	212.597i	−0.140922	−	0.244084i
$872$	−202.159	−	116.717i	−0.231834	−	0.133849i
$873$	614.009	−	581.048i	0.703332	−	0.665576i
$874$	−640.748			−0.733122
$875$	−804.137	−	14.0696i	−0.919013	−	0.0160795i
$876$	−977.233	−	771.493i	−1.11556	−	0.880700i
$877$	−339.987	+	588.874i	−0.387670	+	0.671464i	−0.992136	−	0.125167i	$-0.960053\pi$
$877$	−339.987	+	588.874i	−0.387670	+	0.671464i	0.604466	+	0.796631i	$0.293387\pi$
$878$		−	17.9651i		−	0.0204614i
$879$	198.096	+	497.540i	0.225366	+	0.566030i
$880$	−393.039			−0.446636
$881$		−	169.140i		−	0.191986i	−0.995382	−	0.0959932i	$-0.969397\pi$
$881$		−	169.140i		−	0.191986i	0.995382	−	0.0959932i	$-0.0306027\pi$
$882$	−385.807	+	1147.42i	−0.437423	+	1.30093i
$883$	−118.699			−0.134427			−0.0672135	−	0.997739i	$-0.521411\pi$
$883$	−118.699			−0.134427			−0.0672135	+	0.997739i	$0.521411\pi$
$884$		−	228.715i		−	0.258728i
$885$	293.133	+	231.419i	0.331224	+	0.261491i
$886$	466.908			0.526984
$887$	800.577	+	462.213i	0.902567	+	0.521097i	0.878032	−	0.478601i	$-0.158856\pi$
$887$	800.577	+	462.213i	0.902567	+	0.521097i	0.0245351	+	0.999699i	$0.492189\pi$
$888$	66.0267	+	165.833i	0.0743544	+	0.186749i
$889$	−4.73203	+	270.456i	−0.00532287	+	0.304225i
$890$		−	510.327i		−	0.573401i
$891$	670.998	+	37.0420i	0.753084	+	0.0415735i
$892$	621.405	−	1076.30i	0.696642	−	1.20662i
$893$	−178.142	+	102.850i	−0.199487	+	0.115174i
$894$	1229.05	+	970.292i	1.37477	+	1.08534i
$895$	194.196	+	336.357i	0.216978	+	0.375817i
$896$	−283.928	−	4.96775i	−0.316884	−	0.00554436i
$897$	−277.987	−	40.5042i	−0.309908	−	0.0451551i
$898$	1.54418			0.00171957
$899$	−1613.44	−	931.520i	−1.79471	−	1.03617i
$900$	−131.365	−	550.556i	−0.145961	−	0.611729i
$901$	216.675	+	375.293i	0.240483	+	0.416529i
$902$	−1166.17	−	673.290i	−1.29288	−	0.746442i
$903$	745.256	−	910.774i	0.825311	−	1.00861i
$904$	48.3012	+	83.6602i	0.0534306	+	0.0925445i
$905$	39.5278	+	22.8214i	0.0436771	+	0.0252170i
$906$	176.120	+	442.343i	0.194393	+	0.488238i
$907$	206.084	+	356.948i	0.227215	+	0.393548i	0.956982	−	0.290148i	$-0.0937046\pi$
$907$	206.084	+	356.948i	0.227215	+	0.393548i	−0.729767	+	0.683696i	$0.760371\pi$
$908$	−715.191	+	412.916i	−0.787655	+	0.454753i
$909$	1139.80	−	271.963i	1.25391	−	0.299189i
$910$	−3.45751	+	197.612i	−0.00379947	+	0.217156i
$911$	−487.377	−	281.387i	−0.534991	−	0.308877i	0.208056	−	0.978117i	$-0.433287\pi$
$911$	−487.377	−	281.387i	−0.534991	−	0.308877i	−0.743046	+	0.669240i	$0.766620\pi$
$912$	469.598	−	186.971i	0.514910	−	0.205012i
$913$	−619.942			−0.679017
$914$			2024.98i			2.21551i
$915$	−301.217	+	381.544i	−0.329199	+	0.416988i
$916$	−89.8149	+	155.564i	−0.0980513	+	0.169830i
$917$	20.2173	−	33.6442i	0.0220473	−	0.0366894i
$918$	720.306	+	1023.75i	0.784647	+	1.11519i
$919$	230.981	+	400.070i	0.251339	+	0.435332i	0.963895	−	0.266284i	$-0.0857957\pi$
$919$	230.981	+	400.070i	0.251339	+	0.435332i	−0.712556	+	0.701616i	$0.752462\pi$
$920$	−72.5485	+	41.8859i	−0.0788570	+	0.0455281i
$921$	−12.8100	+	87.9175i	−0.0139088	+	0.0954587i
$922$	29.1407	−	50.4731i	0.0316059	−	0.0547431i
$923$	−164.729	+	95.1062i	−0.178471	+	0.103040i
$924$	−576.109	+	217.782i	−0.623494	+	0.235694i
$925$	−414.660	+	718.212i	−0.448281	+	0.776445i
$926$	1220.23	−	704.503i	1.31775	−	0.760802i
$927$	631.367	−	597.474i	0.681087	−	0.644525i
$928$	−1028.21	+	1780.91i	−1.10798	+	1.91908i
$929$		−	535.866i		−	0.576821i	−0.957507	−	0.288410i	$-0.906873\pi$
$929$		−	535.866i		−	0.576821i	0.957507	−	0.288410i	$-0.0931267\pi$
$930$	−681.216	−	537.798i	−0.732490	−	0.578277i
$931$	−219.637	−	413.160i	−0.235915	−	0.443781i
$932$	46.8830	−	27.0679i	0.0503037	−	0.0290428i
$933$	−616.543	−	89.8334i	−0.660818	−	0.0962845i
$934$	−620.424	−	1074.61i	−0.664266	−	1.15054i
$935$	325.830	+	188.118i	0.348481	+	0.201196i
$936$	42.8034	−	10.2131i	0.0457301	−	0.0109114i
$937$	−449.946			−0.480199			−0.240099	−	0.970748i	$-0.577180\pi$
$937$	−449.946			−0.480199			−0.240099	+	0.970748i	$0.577180\pi$
$938$	−1231.15	−	21.5409i	−1.31253	−	0.0229647i
$939$	61.9889	−	425.441i	0.0660159	−	0.453079i
$940$	102.230	−	177.068i	0.108756	−	0.188370i
$941$		−	1705.50i		−	1.81244i	−0.422810	−	0.906218i	$-0.638956\pi$
$941$		−	1705.50i		−	1.81244i	0.422810	−	0.906218i	$-0.361044\pi$
$942$	−1164.89	−	169.730i	−1.23662	−	0.180181i
$943$	−1445.34			−1.53271
$944$			818.046i			0.866574i
$945$	−284.712	−	420.079i	−0.301283	−	0.444528i
$946$	1276.24			1.34909
$947$			1754.52i			1.85271i	0.376653	+	0.926354i	$0.377075\pi$
$947$			1754.52i			1.85271i	−0.376653	+	0.926354i	$0.622925\pi$
$948$	62.0052	−	425.553i	0.0654064	−	0.448896i
$949$	449.745			0.473915
$950$	403.860	+	233.169i	0.425116	+	0.245441i
$951$	−217.355	−	31.6696i	−0.228554	−	0.0333014i
$952$	129.341	+	77.7234i	0.135863	+	0.0816422i
$953$		−	946.668i		−	0.993356i	−0.867935	−	0.496678i	$-0.834553\pi$
$953$		−	946.668i		−	0.993356i	0.867935	−	0.496678i	$-0.165447\pi$
$954$	460.412	−	435.696i	0.482612	−	0.456705i
$955$	95.8276	−	165.978i	0.100343	−	0.173799i
$956$	−757.272	+	437.211i	−0.792125	+	0.457334i
$957$	170.329	−	1169.00i	0.177982	−	1.22152i
$958$	206.129	+	357.026i	0.215166	+	0.372679i
$959$	406.913	+	734.162i	0.424310	+	0.765550i
$960$	−241.361	+	305.726i	−0.251418	+	0.318465i
$961$	579.741			0.603268
$962$	424.515	+	245.094i	0.441284	+	0.254776i
$963$	71.2723	−	17.0059i	0.0740107	−	0.0176593i
$964$	−5.67748	−	9.83369i	−0.00588950	−	0.0102009i
$965$	763.104	+	440.579i	0.790782	+	0.456558i
$966$	−892.344	+	1090.53i	−0.923752	+	1.12891i
$967$	269.581	+	466.929i	0.278781	+	0.482863i	0.971082	−	0.238746i	$-0.0767362\pi$
$967$	269.581	+	466.929i	0.278781	+	0.482863i	−0.692301	+	0.721609i	$0.743403\pi$
$968$	−57.6636	−	33.2921i	−0.0595698	−	0.0343926i
$969$	−478.786	−	69.7615i	−0.494103	−	0.0719933i
$970$	−346.145	−	599.541i	−0.356851	−	0.618084i
$971$	−1150.15	+	664.038i	−1.18450	+	0.683870i	−0.957051	−	0.289921i	$-0.906371\pi$
$971$	−1150.15	+	664.038i	−1.18450	+	0.683870i	−0.227447	+	0.973790i	$0.573038\pi$
$972$	568.633	−	643.861i	0.585014	−	0.662408i
$973$	−948.448	+	525.682i	−0.974767	+	0.540269i
$974$	−374.863	−	216.427i	−0.384869	−	0.222204i
$975$	160.475	+	126.689i	0.164589	+	0.129938i
$976$	−1064.77			−1.09096
$977$		−	104.484i		−	0.106943i	−0.998569	−	0.0534717i	$-0.982971\pi$
$977$		−	104.484i		−	0.106943i	0.998569	−	0.0534717i	$-0.0170287\pi$
$978$	−222.931	−	559.915i	−0.227946	−	0.572511i
$979$	−287.225	+	497.489i	−0.293386	+	0.508160i
$980$	394.400	+	246.494i	0.402449	+	0.251524i
$981$	1195.56	−	1131.38i	1.21871	−	1.15329i
$982$	−519.239	−	899.349i	−0.528757	−	0.915834i
$983$	836.870	−	483.167i	0.851343	−	0.491523i	−0.00976103	−	0.999952i	$-0.503107\pi$
$983$	836.870	−	483.167i	0.851343	−	0.491523i	0.861104	+	0.508429i	$0.169774\pi$
$984$	210.345	−	83.7493i	0.213765	−	0.0851111i
$985$	−229.957	+	398.297i	−0.233459	+	0.404362i
$986$	1905.65	−	1100.23i	1.93271	−	1.11585i
$987$	−73.0436	+	446.426i	−0.0740057	+	0.452306i
$988$	64.6576	−	111.990i	0.0654429	−	0.113350i
$989$	1186.32	−	684.920i	1.19951	−	0.692537i
$990$	157.041	−	527.459i	0.158627	−	0.532787i
$991$	−408.045	+	706.755i	−0.411751	+	0.713174i	−0.995081	−	0.0990613i	$-0.968416\pi$
$991$	−408.045	+	706.755i	−0.411751	+	0.713174i	0.583330	+	0.812235i	$0.301749\pi$
$992$		−	1700.67i		−	1.71438i
$993$	−18.6919	+	128.286i	−0.0188237	+	0.129190i
$994$	−16.6907	+	953.947i	−0.0167915	+	0.959705i
$995$	−650.381	+	375.498i	−0.653649	+	0.377384i
$996$	−491.031	+	621.977i	−0.493003	+	0.624475i
$997$	−44.2643	−	76.6681i	−0.0443975	−	0.0768988i	0.842973	−	0.537956i	$-0.180803\pi$
$997$	−44.2643	−	76.6681i	−0.0443975	−	0.0768988i	−0.887370	+	0.461058i	$0.847470\pi$
$998$	1829.42	+	1056.21i	1.83308	+	1.05833i
$999$	−1253.58	+	112.545i	−1.25484	+	0.112657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.j.b.11.10	✓	22
3.2	odd	2		189.3.j.b.116.2		22
7.2	even	3		63.3.n.b.2.10	yes	22
7.3	odd	6		441.3.r.f.344.2		22
7.4	even	3		441.3.r.g.344.2		22
7.5	odd	6		441.3.n.f.128.10		22
7.6	odd	2		441.3.j.f.263.10		22
9.4	even	3		189.3.n.b.179.2		22
9.5	odd	6		63.3.n.b.32.10	yes	22
21.2	odd	6		189.3.n.b.170.2		22
63.5	even	6		441.3.j.f.275.2		22
63.23	odd	6	inner	63.3.j.b.23.2	yes	22
63.32	odd	6		441.3.r.g.50.2		22
63.41	even	6		441.3.n.f.410.10		22
63.58	even	3		189.3.j.b.44.10		22
63.59	even	6		441.3.r.f.50.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.10	✓	22	1.1	even	1	trivial
63.3.j.b.23.2	yes	22	63.23	odd	6	inner
63.3.n.b.2.10	yes	22	7.2	even	3
63.3.n.b.32.10	yes	22	9.5	odd	6
189.3.j.b.44.10		22	63.58	even	3
189.3.j.b.116.2		22	3.2	odd	2
189.3.n.b.170.2		22	21.2	odd	6
189.3.n.b.179.2		22	9.4	even	3
441.3.j.f.263.10		22	7.6	odd	2
441.3.j.f.275.2		22	63.5	even	6
441.3.n.f.128.10		22	7.5	odd	6
441.3.n.f.410.10		22	63.41	even	6
441.3.r.f.50.2		22	63.59	even	6
441.3.r.f.344.2		22	7.3	odd	6
441.3.r.g.50.2		22	63.32	odd	6
441.3.r.g.344.2		22	7.4	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.74500i q^{2} +(-0.432548 + 2.96865i) q^{3} -3.53503 q^{4} +(2.32531 + 1.34252i) q^{5} +(-8.14895 - 1.18734i) q^{6} +(0.122457 - 6.99893i) q^{7} +1.27635i q^{8} +(-8.62581 - 2.56817i) q^{9} +O(q^{10})\)	\(q+2.74500i q^{2} +(-0.432548 + 2.96865i) q^{3} -3.53503 q^{4} +(2.32531 + 1.34252i) q^{5} +(-8.14895 - 1.18734i) q^{6} +(0.122457 - 6.99893i) q^{7} +1.27635i q^{8} +(-8.62581 - 2.56817i) q^{9} +(-3.68521 + 6.38297i) q^{10} +(7.18501 - 4.14827i) q^{11} +(1.52907 - 10.4943i) q^{12} +(1.91540 + 3.31756i) q^{13} +(19.2121 + 0.336144i) q^{14} +(-4.99128 + 6.32233i) q^{15} -17.6437 q^{16} +(14.6266 + 8.44469i) q^{17} +(7.04962 - 23.6778i) q^{18} +(4.77461 + 8.26987i) q^{19} +(-8.22003 - 4.74584i) q^{20} +(20.7244 + 3.39090i) q^{21} +(11.3870 + 19.7229i) q^{22} +(21.1694 + 12.2221i) q^{23} +(-3.78905 - 0.552083i) q^{24} +(-8.89529 - 15.4071i) q^{25} +(-9.10671 + 5.25776i) q^{26} +(11.3551 - 24.4962i) q^{27} +(-0.432888 + 24.7414i) q^{28} +(-41.1044 - 23.7316i) q^{29} +(-17.3548 - 13.7011i) q^{30} +39.2523 q^{31} -43.3265i q^{32} +(9.20691 + 23.1241i) q^{33} +(-23.1807 + 40.1501i) q^{34} +(9.68094 - 16.1103i) q^{35} +(30.4925 + 9.07854i) q^{36} +(-23.3078 - 40.3703i) q^{37} +(-22.7008 + 13.1063i) q^{38} +(-10.6772 + 4.25114i) q^{39} +(-1.71353 + 2.96791i) q^{40} +(-51.2064 + 29.5640i) q^{41} +(-9.30802 + 56.8886i) q^{42} +(28.0196 - 48.5314i) q^{43} +(-25.3992 + 14.6642i) q^{44} +(-16.6099 - 17.5521i) q^{45} +(-33.5498 + 58.1099i) q^{46} +21.5411i q^{47} +(7.63174 - 52.3780i) q^{48} +(-48.9700 - 1.71413i) q^{49} +(42.2925 - 24.4176i) q^{50} +(-31.3961 + 39.7687i) q^{51} +(-6.77098 - 11.7277i) q^{52} +(22.2206 + 12.8291i) q^{53} +(67.2420 + 31.1697i) q^{54} +22.2765 q^{55} +(8.93310 + 0.156298i) q^{56} +(-26.6156 + 10.5971i) q^{57} +(65.1433 - 112.832i) q^{58} -46.3648i q^{59} +(17.6443 - 22.3496i) q^{60} +60.3487 q^{61} +107.748i q^{62} +(-19.0307 + 60.0569i) q^{63} +48.3566 q^{64} +10.2858i q^{65} +(-63.4757 + 25.2730i) q^{66} -64.0822 q^{67} +(-51.7056 - 29.8522i) q^{68} +(-45.4400 + 57.5578i) q^{69} +(44.2227 + 26.5742i) q^{70} +49.6536i q^{71} +(3.27789 - 11.0096i) q^{72} +(58.7013 - 101.674i) q^{73} +(110.817 - 63.9800i) q^{74} +(49.5860 - 19.7427i) q^{75} +(-16.8784 - 29.2342i) q^{76} +(-28.1536 - 50.7953i) q^{77} +(-11.6694 - 29.3089i) q^{78} +40.5510 q^{79} +(-41.0270 - 23.6870i) q^{80} +(67.8090 + 44.3050i) q^{81} +(-81.1532 - 140.562i) q^{82} +(-64.7120 - 37.3615i) q^{83} +(-73.2614 - 11.9869i) q^{84} +(22.6743 + 39.2730i) q^{85} +(133.219 + 76.9139i) q^{86} +(88.2305 - 111.760i) q^{87} +(5.29465 + 9.17060i) q^{88} +(-59.9634 + 34.6199i) q^{89} +(48.1805 - 45.5940i) q^{90} +(23.4539 - 12.9995i) q^{91} +(-74.8342 - 43.2056i) q^{92} +(-16.9785 + 116.526i) q^{93} -59.1302 q^{94} +25.6400i q^{95} +(128.621 + 18.7408i) q^{96} +(-46.9641 + 81.3442i) q^{97} +(4.70530 - 134.423i) q^{98} +(-72.6299 + 17.3298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 19 q^{3} - 24 q^{4} + 12 q^{5} - 8 q^{6} - 37 q^{9}+O(q^{10}) \) 22 * q - 19 * q^3 - 24 * q^4 + 12 * q^5 - 8 * q^6 - 37 * q^9	\( 22 q - 19 q^{3} - 24 q^{4} + 12 q^{5} - 8 q^{6} - 37 q^{9} + 25 q^{10} + 24 q^{11} + 40 q^{12} - 18 q^{13} - 60 q^{14} + 53 q^{15} - 24 q^{16} - 6 q^{17} + 40 q^{18} + 3 q^{19} - 39 q^{20} - 11 q^{21} - 59 q^{22} + 81 q^{23} + 126 q^{24} + 57 q^{25} + 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 38 q^{30} + 58 q^{31} - 4 q^{33} - 99 q^{34} + 27 q^{35} + 76 q^{36} - 20 q^{37} - 48 q^{38} - 76 q^{39} - 105 q^{40} - 51 q^{41} + 68 q^{42} + 65 q^{43} - 54 q^{44} - 214 q^{45} + 75 q^{46} - 113 q^{48} + 4 q^{49} + 63 q^{50} + 141 q^{51} - 46 q^{52} + 63 q^{53} + 433 q^{54} - 100 q^{55} + 192 q^{56} + 224 q^{57} + 40 q^{58} - 482 q^{60} - 156 q^{61} + 19 q^{63} + 106 q^{64} + 61 q^{66} + 264 q^{67} + 27 q^{68} - 297 q^{69} + 236 q^{70} - 222 q^{72} + q^{73} + 342 q^{74} - 296 q^{75} + 233 q^{76} - 531 q^{77} - 440 q^{78} - 280 q^{79} - 96 q^{80} - 169 q^{81} - 157 q^{82} + 255 q^{83} - 13 q^{84} + 102 q^{85} + 504 q^{86} + 704 q^{87} + 408 q^{88} + 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} - 36 q^{93} - 522 q^{94} - 397 q^{96} + 178 q^{97} - 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 19 * q^3 - 24 * q^4 + 12 * q^5 - 8 * q^6 - 37 * q^9 + 25 * q^10 + 24 * q^11 + 40 * q^12 - 18 * q^13 - 60 * q^14 + 53 * q^15 - 24 * q^16 - 6 * q^17 + 40 * q^18 + 3 * q^19 - 39 * q^20 - 11 * q^21 - 59 * q^22 + 81 * q^23 + 126 * q^24 + 57 * q^25 + 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 38 * q^30 + 58 * q^31 - 4 * q^33 - 99 * q^34 + 27 * q^35 + 76 * q^36 - 20 * q^37 - 48 * q^38 - 76 * q^39 - 105 * q^40 - 51 * q^41 + 68 * q^42 + 65 * q^43 - 54 * q^44 - 214 * q^45 + 75 * q^46 - 113 * q^48 + 4 * q^49 + 63 * q^50 + 141 * q^51 - 46 * q^52 + 63 * q^53 + 433 * q^54 - 100 * q^55 + 192 * q^56 + 224 * q^57 + 40 * q^58 - 482 * q^60 - 156 * q^61 + 19 * q^63 + 106 * q^64 + 61 * q^66 + 264 * q^67 + 27 * q^68 - 297 * q^69 + 236 * q^70 - 222 * q^72 + q^73 + 342 * q^74 - 296 * q^75 + 233 * q^76 - 531 * q^77 - 440 * q^78 - 280 * q^79 - 96 * q^80 - 169 * q^81 - 157 * q^82 + 255 * q^83 - 13 * q^84 + 102 * q^85 + 504 * q^86 + 704 * q^87 + 408 * q^88 + 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 - 36 * q^93 - 522 * q^94 - 397 * q^96 + 178 * q^97 - 483 * q^98 - 103 * q^99

Introduction

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