LMFDB - Embedded newform 25.4.d.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(6,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, degree $4$, 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:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	25.11
Dual form			25.4.d.a.16.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.29718 - 3.12208i) q^{2} +(-1.93780 + 5.96393i) q^{3} +(6.24620 - 19.2238i) q^{4} +(-9.58545 + 5.75493i) q^{5} +(10.2928 + 31.6780i) q^{6} -9.63602 q^{7} +(-20.0464 - 61.6963i) q^{8} +(-9.96993 - 7.24358i) q^{9} +O(q^{10})$	\(q+(4.29718 - 3.12208i) q^{2} +(-1.93780 + 5.96393i) q^{3} +(6.24620 - 19.2238i) q^{4} +(-9.58545 + 5.75493i) q^{5} +(10.2928 + 31.6780i) q^{6} -9.63602 q^{7} +(-20.0464 - 61.6963i) q^{8} +(-9.96993 - 7.24358i) q^{9} +(-23.2230 + 54.6565i) q^{10} +(19.6877 - 14.3039i) q^{11} +(102.546 + 74.5038i) q^{12} +(35.7572 + 25.9791i) q^{13} +(-41.4077 + 30.0844i) q^{14} +(-15.7473 - 68.3188i) q^{15} +(-147.942 - 107.486i) q^{16} +(0.568894 + 1.75088i) q^{17} -65.4576 q^{18} +(-22.1878 - 68.2870i) q^{19} +(50.7592 + 220.216i) q^{20} +(18.6727 - 57.4685i) q^{21} +(39.9434 - 122.933i) q^{22} +(-56.7348 + 41.2202i) q^{23} +406.798 q^{24} +(58.7616 - 110.327i) q^{25} +234.764 q^{26} +(-74.4571 + 54.0962i) q^{27} +(-60.1885 + 185.241i) q^{28} +(-31.0824 + 95.6617i) q^{29} +(-280.966 - 244.414i) q^{30} +(-51.1943 - 157.560i) q^{31} -452.340 q^{32} +(47.1569 + 145.134i) q^{33} +(7.91102 + 5.74769i) q^{34} +(92.3655 - 55.4546i) q^{35} +(-201.524 + 146.415i) q^{36} +(316.532 + 229.974i) q^{37} +(-308.542 - 224.169i) q^{38} +(-224.228 + 162.911i) q^{39} +(547.211 + 476.022i) q^{40} +(-2.89600 - 2.10407i) q^{41} +(-99.1818 - 305.250i) q^{42} +9.64426 q^{43} +(-152.003 - 467.818i) q^{44} +(137.253 + 12.0567i) q^{45} +(-115.107 + 354.261i) q^{46} +(-167.342 + 515.027i) q^{47} +(927.719 - 674.027i) q^{48} -250.147 q^{49} +(-91.9413 - 657.554i) q^{50} -11.5445 q^{51} +(722.765 - 525.119i) q^{52} +(50.2766 - 154.735i) q^{53} +(-151.062 + 464.922i) q^{54} +(-106.397 + 250.411i) q^{55} +(193.167 + 594.507i) q^{56} +450.254 q^{57} +(165.097 + 508.117i) q^{58} +(-134.417 - 97.6599i) q^{59} +(-1411.71 - 124.009i) q^{60} +(692.078 - 502.824i) q^{61} +(-711.905 - 517.230i) q^{62} +(96.0704 + 69.7993i) q^{63} +(-760.253 + 552.356i) q^{64} +(-492.256 - 43.2414i) q^{65} +(655.762 + 476.439i) q^{66} +(-218.322 - 671.926i) q^{67} +37.2120 q^{68} +(-135.894 - 418.239i) q^{69} +(223.777 - 526.671i) q^{70} +(-209.430 + 644.559i) q^{71} +(-247.041 + 760.316i) q^{72} +(39.1313 - 28.4306i) q^{73} +2078.19 q^{74} +(544.115 + 564.242i) q^{75} -1451.33 q^{76} +(-189.711 + 137.833i) q^{77} +(-454.925 + 1400.12i) q^{78} +(145.637 - 448.225i) q^{79} +(2036.66 + 178.907i) q^{80} +(-281.164 - 865.334i) q^{81} -19.0137 q^{82} +(-185.987 - 572.410i) q^{83} +(-988.132 - 717.920i) q^{84} +(-15.5293 - 13.5090i) q^{85} +(41.4431 - 30.1102i) q^{86} +(-510.288 - 370.746i) q^{87} +(-1277.17 - 927.915i) q^{88} +(-558.915 + 406.075i) q^{89} +(627.441 - 376.704i) q^{90} +(-344.557 - 250.335i) q^{91} +(438.034 + 1348.13i) q^{92} +1038.88 q^{93} +(888.856 + 2735.62i) q^{94} +(605.666 + 526.872i) q^{95} +(876.544 - 2697.72i) q^{96} +(-190.279 + 585.617i) q^{97} +(-1074.93 + 780.980i) q^{98} -299.896 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) $ 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	4.29718	−	3.12208i	1.51928	−	1.10382i	0.557440	−	0.830217i	$-0.311784\pi$
$2$	4.29718	−	3.12208i	1.51928	−	1.10382i	0.961842	−	0.273606i	$-0.0882163\pi$
$3$	−1.93780	+	5.96393i	−0.372929	+	1.14776i	0.571936	+	0.820299i	$0.306193\pi$
$3$	−1.93780	+	5.96393i	−0.372929	+	1.14776i	−0.944865	+	0.327460i	$0.893807\pi$
$4$	6.24620	−	19.2238i	0.780775	−	2.40298i
$5$	−9.58545	+	5.75493i	−0.857348	+	0.514736i
$5$	−9.58545	+	5.75493i	−0.857348	+	0.514736i
$6$	10.2928	+	31.6780i	0.700337	+	2.15542i
$7$	−9.63602			−0.520296			−0.260148	−	0.965569i	$-0.583771\pi$
$7$	−9.63602			−0.520296			−0.260148	+	0.965569i	$0.583771\pi$
$8$	−20.0464	−	61.6963i	−0.885932	−	2.72662i
$9$	−9.96993	−	7.24358i	−0.369257	−	0.268281i
$10$	−23.2230	+	54.6565i	−0.734376	+	1.72839i
$11$	19.6877	−	14.3039i	0.539641	−	0.392072i	−0.284311	−	0.958732i	$-0.591765\pi$
$11$	19.6877	−	14.3039i	0.539641	−	0.392072i	0.823952	+	0.566660i	$0.191765\pi$
$12$	102.546	+	74.5038i	2.46687	+	1.79228i
$13$	35.7572	+	25.9791i	0.762866	+	0.554255i	0.899788	−	0.436327i	$-0.143721\pi$
$13$	35.7572	+	25.9791i	0.762866	+	0.554255i	−0.136922	+	0.990582i	$0.543721\pi$
$14$	−41.4077	+	30.0844i	−0.790476	+	0.574315i
$15$	−15.7473	−	68.3188i	−0.271063	−	1.17599i
$16$	−147.942	−	107.486i	−2.31159	−	1.67947i
$17$	0.568894	+	1.75088i	0.00811630	+	0.0249794i	0.955033	−	0.296501i	$-0.0958197\pi$
$17$	0.568894	+	1.75088i	0.00811630	+	0.0249794i	−0.946916	+	0.321480i	$0.895820\pi$
$18$	−65.4576			−0.857139
$19$	−22.1878	−	68.2870i	−0.267907	−	0.824532i	−0.991010	−	0.133791i	$-0.957285\pi$
$19$	−22.1878	−	68.2870i	−0.267907	−	0.824532i	0.723103	−	0.690740i	$-0.242715\pi$
$20$	50.7592	+	220.216i	0.567505	+	2.46208i
$21$	18.6727	−	57.4685i	0.194034	−	0.597174i
$22$	39.9434	−	122.933i	0.387089	−	1.19134i
$23$	−56.7348	+	41.2202i	−0.514349	+	0.373696i	−0.814471	−	0.580205i	$-0.802973\pi$
$23$	−56.7348	+	41.2202i	−0.514349	+	0.373696i	0.300122	+	0.953901i	$0.402973\pi$
$24$	406.798			3.45989
$25$	58.7616	−	110.327i	0.470093	−	0.882617i
$26$	234.764			1.77081
$27$	−74.4571	+	54.0962i	−0.530714	+	0.385586i
$28$	−60.1885	+	185.241i	−0.406234	+	1.25026i
$29$	−31.0824	+	95.6617i	−0.199029	+	0.612549i	0.800877	+	0.598830i	$0.204367\pi$
$29$	−31.0824	+	95.6617i	−0.199029	+	0.612549i	−0.999906	+	0.0137199i	$0.995633\pi$
$30$	−280.966	−	244.414i	−1.70990	−	1.48745i
$31$	−51.1943	−	157.560i	−0.296605	−	0.912857i	−0.982678	−	0.185324i	$-0.940667\pi$
$31$	−51.1943	−	157.560i	−0.296605	−	0.912857i	0.686072	−	0.727533i	$-0.259333\pi$
$32$	−452.340			−2.49885
$33$	47.1569	+	145.134i	0.248756	+	0.765593i
$34$	7.91102	+	5.74769i	0.0399038	+	0.0289918i
$35$	92.3655	−	55.4546i	0.446075	−	0.267815i
$36$	−201.524	+	146.415i	−0.932980	+	0.677849i
$37$	316.532	+	229.974i	1.40642	+	1.02182i	0.993831	+	0.110906i	$0.0353752\pi$
$37$	316.532	+	229.974i	1.40642	+	1.02182i	0.412588	+	0.910918i	$0.364625\pi$
$38$	−308.542	−	224.169i	−1.31716	−	0.956975i
$39$	−224.228	+	162.911i	−0.920646	+	0.668888i
$40$	547.211	+	476.022i	2.16304	+	1.88164i
$41$	−2.89600	−	2.10407i	−0.0110312	−	0.00801463i	0.582256	−	0.813006i	$-0.302170\pi$
$41$	−2.89600	−	2.10407i	−0.0110312	−	0.00801463i	−0.593287	+	0.804991i	$0.702170\pi$
$42$	−99.1818	−	305.250i	−0.364383	−	1.12145i
$43$	9.64426			0.0342032			0.0171016	−	0.999854i	$-0.494556\pi$
$43$	9.64426			0.0342032			0.0171016	+	0.999854i	$0.494556\pi$
$44$	−152.003	−	467.818i	−0.520803	−	1.60287i
$45$	137.253	+	12.0567i	0.454676	+	0.0399402i
$46$	−115.107	+	354.261i	−0.368946	+	1.13550i
$47$	−167.342	+	515.027i	−0.519349	+	1.59839i	0.255879	+	0.966709i	$0.417635\pi$
$47$	−167.342	+	515.027i	−0.519349	+	1.59839i	−0.775228	+	0.631682i	$0.782365\pi$
$48$	927.719	−	674.027i	2.78968	−	2.02682i
$49$	−250.147			−0.729292
$50$	−91.9413	−	657.554i	−0.260049	−	1.85984i
$51$	−11.5445			−0.0316971
$52$	722.765	−	525.119i	1.92749	−	1.40040i
$53$	50.2766	−	154.735i	0.130302	−	0.401029i	−0.864528	−	0.502585i	$-0.832382\pi$
$53$	50.2766	−	154.735i	0.130302	−	0.401029i	0.994830	+	0.101556i	$0.0323822\pi$
$54$	−151.062	+	464.922i	−0.380685	+	1.17163i
$55$	−106.397	+	250.411i	−0.260847	+	0.613915i
$56$	193.167	+	594.507i	0.460947	+	1.41865i
$57$	450.254			1.04627
$58$	165.097	+	508.117i	0.373764	+	1.15033i
$59$	−134.417	−	97.6599i	−0.296604	−	0.215496i	0.429523	−	0.903056i	$-0.358682\pi$
$59$	−134.417	−	97.6599i	−0.296604	−	0.215496i	−0.726127	+	0.687560i	$0.758682\pi$
$60$	−1411.71	−	124.009i	−3.03752	−	0.266825i
$61$	692.078	−	502.824i	1.45265	−	1.05541i	0.467444	−	0.884023i	$-0.345175\pi$
$61$	692.078	−	502.824i	1.45265	−	1.05541i	0.985204	−	0.171387i	$-0.0548250\pi$
$62$	−711.905	−	517.230i	−1.45826	−	1.05949i
$63$	96.0704	+	69.7993i	0.192123	+	0.139585i
$64$	−760.253	+	552.356i	−1.48487	+	1.07882i
$65$	−492.256	−	43.2414i	−0.939337	−	0.0825144i
$66$	655.762	+	476.439i	1.22301	+	0.888569i
$67$	−218.322	−	671.926i	−0.398094	−	1.22521i	−0.926526	−	0.376231i	$-0.877220\pi$
$67$	−218.322	−	671.926i	−0.398094	−	1.22521i	0.528432	−	0.848975i	$-0.322780\pi$
$68$	37.2120			0.0663620
$69$	−135.894	−	418.239i	−0.237097	−	0.729711i
$70$	223.777	−	526.671i	0.382093	−	0.899275i
$71$	−209.430	+	644.559i	−0.350067	+	1.07740i	0.608748	+	0.793364i	$0.291672\pi$
$71$	−209.430	+	644.559i	−0.350067	+	1.07740i	−0.958815	+	0.284032i	$0.908328\pi$
$72$	−247.041	+	760.316i	−0.404363	+	1.24450i
$73$	39.1313	−	28.4306i	0.0627394	−	0.0455829i	−0.555974	−	0.831200i	$-0.687654\pi$
$73$	39.1313	−	28.4306i	0.0627394	−	0.0455829i	0.618713	+	0.785617i	$0.287654\pi$
$74$	2078.19			3.26466
$75$	544.115	+	564.242i	0.837720	+	0.868707i
$76$	−1451.33			−2.19051
$77$	−189.711	+	137.833i	−0.280773	+	0.203994i
$78$	−454.925	+	1400.12i	−0.660386	+	2.03246i
$79$	145.637	−	448.225i	0.207411	−	0.638345i	−0.792195	−	0.610268i	$-0.791062\pi$
$79$	145.637	−	448.225i	0.207411	−	0.638345i	0.999606	−	0.0280766i	$-0.00893822\pi$
$80$	2036.66	+	178.907i	2.84632	+	0.250030i
$81$	−281.164	−	865.334i	−0.385685	−	1.18701i
$82$	−19.0137			−0.0256062
$83$	−185.987	−	572.410i	−0.245961	−	0.756989i	−0.995477	−	0.0950033i	$-0.969714\pi$
$83$	−185.987	−	572.410i	−0.245961	−	0.756989i	0.749516	−	0.661986i	$-0.230286\pi$
$84$	−988.132	−	717.920i	−1.28350	−	0.932518i
$85$	−15.5293	−	13.5090i	−0.0198163	−	0.0172383i
$86$	41.4431	−	30.1102i	0.0519643	−	0.0377542i
$87$	−510.288	−	370.746i	−0.628835	−	0.456875i
$88$	−1277.17	−	927.915i	−1.54712	−	1.12405i
$89$	−558.915	+	406.075i	−0.665672	+	0.483639i	−0.868574	−	0.495560i	$-0.834963\pi$
$89$	−558.915	+	406.075i	−0.665672	+	0.483639i	0.202902	+	0.979199i	$0.434963\pi$
$90$	627.441	−	376.704i	0.734867	−	0.441201i
$91$	−344.557	−	250.335i	−0.396916	−	0.288376i
$92$	438.034	+	1348.13i	0.496394	+	1.52774i
$93$	1038.88			1.15835
$94$	888.856	+	2735.62i	0.975303	+	3.00168i
$95$	605.666	+	526.872i	0.654106	+	0.569010i
$96$	876.544	−	2697.72i	0.931895	−	2.86808i
$97$	−190.279	+	585.617i	−0.199174	+	0.612994i	0.800729	+	0.599027i	$0.204446\pi$
$97$	−190.279	+	585.617i	−0.199174	+	0.612994i	−0.999902	+	0.0139669i	$0.995554\pi$
$98$	−1074.93	+	780.980i	−1.10800	+	0.805009i
$99$	−299.896			−0.304452
$100$	−1753.87	−	1818.75i	−1.75387	−	1.81875i
$101$	626.998			0.617709			0.308855	−	0.951109i	$-0.400054\pi$
$101$	626.998			0.617709			0.308855	+	0.951109i	$0.400054\pi$
$102$	−49.6088	+	36.0429i	−0.0481569	+	0.0349880i
$103$	470.599	−	1448.36i	0.450189	−	1.38554i	−0.426502	−	0.904487i	$-0.640254\pi$
$103$	470.599	−	1448.36i	0.450189	−	1.38554i	0.876691	−	0.481054i	$-0.159746\pi$
$104$	886.015	−	2726.87i	0.835393	−	2.57108i
$105$	151.742	+	658.321i	0.141033	+	0.611863i
$106$	−267.049	−	821.893i	−0.244699	−	0.753107i
$107$	−435.652			−0.393608			−0.196804	−	0.980443i	$-0.563056\pi$
$107$	−435.652			−0.393608			−0.196804	+	0.980443i	$0.563056\pi$
$108$	574.863	+	1769.25i	0.512187	+	1.57635i
$109$	1426.54	+	1036.44i	1.25356	+	0.910764i	0.998423	−	0.0561410i	$-0.0178796\pi$
$109$	1426.54	+	1036.44i	1.25356	+	0.910764i	0.255136	+	0.966905i	$0.417880\pi$
$110$	324.596	+	1408.24i	0.281354	+	1.22064i
$111$	−1984.92	+	1442.13i	−1.69730	+	1.23316i
$112$	1425.57	+	1035.74i	1.20271	+	0.873820i
$113$	−744.284	−	540.754i	−0.619614	−	0.450176i	0.233173	−	0.972435i	$-0.425089\pi$
$113$	−744.284	−	540.754i	−0.619614	−	0.450176i	−0.852786	+	0.522260i	$0.825089\pi$
$114$	1934.82	−	1405.73i	1.58958	−	1.15490i
$115$	306.609	−	721.619i	0.248621	−	0.585142i
$116$	1644.84	+	1195.04i	1.31655	+	0.956527i
$117$	−168.315	−	518.020i	−0.132998	−	0.409324i
$118$	−882.517			−0.688494
$119$	−5.48187	−	16.8715i	−0.00422288	−	0.0129967i
$120$	−3899.34	+	2341.10i	−2.96633	+	1.78093i
$121$	−228.300	+	702.635i	−0.171525	+	0.527900i
$122$	1404.12	−	4321.45i	1.04200	−	3.20693i
$123$	18.1604	−	13.1943i	0.0133127	−	0.00967226i
$124$	−3348.67			−2.42516
$125$	71.6685	+	1395.70i	0.0512818	+	0.998684i
$126$	630.751			0.445966
$127$	−833.392	+	605.495i	−0.582296	+	0.423063i	−0.839551	−	0.543281i	$-0.817182\pi$
$127$	−833.392	+	605.495i	−0.582296	+	0.423063i	0.257255	+	0.966344i	$0.417182\pi$
$128$	−424.196	+	1305.54i	−0.292922	+	0.901520i
$129$	−18.6886	+	57.5177i	−0.0127554	+	0.0392570i
$130$	−2250.32	+	1351.05i	−1.51820	+	0.911499i
$131$	94.1854	+	289.873i	0.0628169	+	0.193331i	0.977540	−	0.210751i	$-0.0675911\pi$
$131$	94.1854	+	289.873i	0.0628169	+	0.193331i	−0.914723	+	0.404082i	$0.867591\pi$
$132$	3084.58			2.03393
$133$	213.802	+	658.014i	0.139391	+	0.429001i
$134$	−3035.98	−	2205.77i	−1.95723	−	1.42201i
$135$	402.384	−	947.032i	0.256531	−	0.603759i
$136$	96.6184	−	70.1974i	0.0609188	−	0.0442601i
$137$	1466.78	+	1065.68i	0.914712	+	0.664577i	0.942202	−	0.335045i	$-0.108752\pi$
$137$	1466.78	+	1065.68i	0.914712	+	0.664577i	−0.0274903	+	0.999622i	$0.508752\pi$
$138$	−1889.74	−	1372.97i	−1.16569	−	0.846923i
$139$	579.242	−	420.844i	0.353458	−	0.256802i	−0.396860	−	0.917879i	$-0.629900\pi$
$139$	579.242	−	420.844i	0.353458	−	0.256802i	0.750318	+	0.661077i	$0.229900\pi$
$140$	−489.116	−	2122.00i	−0.295270	−	1.28101i
$141$	−2747.31	−	1996.04i	−1.64089	−	1.19217i
$142$	1112.41	+	3423.64i	0.657404	+	2.02328i
$143$	1075.58			0.628982
$144$	696.385	+	2143.25i	0.403001	+	1.24031i
$145$	−252.588	−	1095.84i	−0.144664	−	0.627616i
$146$	79.3917	−	244.343i	0.0450035	−	0.138506i
$147$	484.735	−	1491.86i	0.271974	−	0.837051i
$148$	6398.10	−	4648.49i	3.55352	−	2.58178i
$149$	725.618			0.398959			0.199480	−	0.979902i	$-0.436075\pi$
$149$	725.618			0.398959			0.199480	+	0.979902i	$0.436075\pi$
$150$	4099.77	+	725.875i	2.23163	+	0.395116i
$151$	3051.31			1.64445			0.822227	−	0.569160i	$-0.192732\pi$
$151$	3051.31			1.64445			0.822227	+	0.569160i	$0.192732\pi$
$152$	−3768.27	+	2737.81i	−2.01084	+	1.46096i
$153$	7.01077	−	21.5769i	0.00370449	−	0.0114013i
$154$	−384.895	+	1184.58i	−0.201401	+	0.619848i
$155$	1397.46	+	1215.66i	0.724175	+	0.629963i
$156$	1731.20	+	5328.09i	0.888507	+	2.73454i
$157$	−2166.76			−1.10144			−0.550722	−	0.834689i	$-0.685647\pi$
$157$	−2166.76			−1.10144			−0.550722	+	0.834689i	$0.685647\pi$
$158$	−773.566	−	2380.79i	−0.389504	−	1.19877i
$159$	825.405	+	599.692i	0.411691	+	0.299111i
$160$	4335.88	−	2603.19i	2.14239	−	1.28625i
$161$	546.698	−	397.199i	0.267614	−	0.194433i
$162$	−3909.86	−	2840.68i	−1.89622	−	1.37768i
$163$	62.9438	+	45.7313i	0.0302463	+	0.0219752i	0.602806	−	0.797888i	$-0.294049\pi$
$163$	62.9438	+	45.7313i	0.0302463	+	0.0219752i	−0.572559	+	0.819863i	$0.694049\pi$
$164$	−58.5372	+	42.5298i	−0.0278719	+	0.0202501i
$165$	−1287.25	−	1119.79i	−0.607349	−	0.528336i
$166$	−2586.33	−	1879.08i	−1.20927	−	0.878583i
$167$	−39.0563	−	120.203i	−0.0180974	−	0.0556981i	0.941600	−	0.336734i	$-0.109322\pi$
$167$	−39.0563	−	120.203i	−0.0180974	−	0.0556981i	−0.959697	+	0.281035i	$0.909322\pi$
$168$	−3919.92			−1.80017
$169$	−75.2487	−	231.592i	−0.0342506	−	0.105413i
$170$	−108.908	−	9.56685i	−0.0491346	−	0.00431614i
$171$	−273.431	+	841.535i	−0.122280	+	0.376338i
$172$	60.2400	−	185.400i	0.0267050	−	0.0821895i
$173$	−2620.45	+	1903.87i	−1.15161	+	0.836697i	−0.988695	−	0.149943i	$-0.952091\pi$
$173$	−2620.45	+	1903.87i	−1.15161	+	0.836697i	−0.162919	+	0.986639i	$0.552091\pi$
$174$	−3350.30			−1.45969
$175$	−566.228	+	1063.11i	−0.244587	+	0.459222i
$176$	−4450.09			−1.90590
$177$	842.910	−	612.410i	0.357949	−	0.260065i
$178$	−1133.96	+	3489.95i	−0.477492	+	1.46957i
$179$	438.802	−	1350.49i	0.183227	−	0.563914i	−0.816686	−	0.577082i	$-0.804191\pi$
$179$	438.802	−	1350.49i	0.183227	−	0.563914i	0.999913	+	0.0131674i	$0.00419144\pi$
$180$	1089.08	−	2563.21i	0.450975	−	1.06139i
$181$	−131.635	−	405.129i	−0.0540570	−	0.166370i	0.920383	−	0.391018i	$-0.127877\pi$
$181$	−131.635	−	405.129i	−0.0540570	−	0.166370i	−0.974440	+	0.224648i	$0.927877\pi$
$182$	−2262.19			−0.921344
$183$	1657.70	+	5101.88i	0.669621	+	2.06088i
$184$	3680.46	+	2674.01i	1.47461	+	1.07136i
$185$	−4357.58	−	382.784i	−1.73176	−	0.152123i
$186$	4464.25	−	3243.47i	1.75986	−	1.27862i
$187$	36.2446	+	26.3332i	0.0141736	+	0.0102977i
$188$	8855.54	+	6433.92i	3.43541	+	2.49597i
$189$	717.470	−	521.272i	0.276128	−	0.200619i
$190$	4247.59	+	373.122i	1.62186	+	0.142469i
$191$	1193.36	+	867.030i	0.452088	+	0.328461i	0.790420	−	0.612566i	$-0.209862\pi$
$191$	1193.36	+	867.030i	0.452088	+	0.328461i	−0.338331	+	0.941027i	$0.609862\pi$
$192$	−1821.00	−	5604.45i	−0.684475	−	2.10660i
$193$	−1535.93			−0.572841			−0.286421	−	0.958104i	$-0.592465\pi$
$193$	−1535.93			−0.572841			−0.286421	+	0.958104i	$0.592465\pi$
$194$	1010.68	+	3110.57i	0.374036	+	1.15116i
$195$	1211.78	−	2851.99i	0.445013	−	1.04736i
$196$	−1562.47	+	4808.79i	−0.569413	+	1.75247i
$197$	−96.3752	+	296.613i	−0.0348551	+	0.107273i	−0.966970	−	0.254889i	$-0.917961\pi$
$197$	−96.3752	+	296.613i	−0.0348551	+	0.107273i	0.932115	+	0.362162i	$0.117961\pi$
$198$	−1288.71	+	936.301i	−0.462548	+	0.336061i
$199$	−1453.74			−0.517855			−0.258927	−	0.965897i	$-0.583369\pi$
$199$	−1453.74			−0.517855			−0.258927	+	0.965897i	$0.583369\pi$
$200$	−7984.73	−	1413.72i	−2.82303	−	0.499825i
$201$	4430.38			1.55470
$202$	2694.32	−	1957.54i	0.938474	−	0.681842i
$203$	299.510	−	921.798i	0.103554	−	0.318707i
$204$	−72.1093	+	221.930i	−0.0247483	+	0.0761676i
$205$	39.8682	+	3.50215i	0.0135830	+	0.00119317i
$206$	−2499.64	−	7693.09i	−0.845427	−	2.60196i
$207$	864.224			0.290182
$208$	−2497.59	−	7686.78i	−0.832579	−	2.56242i
$209$	−1413.60	−	1027.04i	−0.467849	−	0.339912i
$210$	2707.39	+	2355.17i	0.889657	+	0.773917i
$211$	−2131.43	+	1548.57i	−0.695420	+	0.505252i	−0.878437	−	0.477858i	$-0.841413\pi$
$211$	−2131.43	+	1548.57i	−0.695420	+	0.505252i	0.183018	+	0.983110i	$0.441413\pi$
$212$	−2660.57	−	1933.02i	−0.861928	−	0.626227i
$213$	−3438.27	−	2498.05i	−1.10604	−	0.803585i
$214$	−1872.07	+	1360.14i	−0.598001	+	0.434473i
$215$	−92.4446	+	55.5020i	−0.0293240	+	0.0176056i
$216$	4830.13	+	3509.30i	1.52152	+	1.10545i
$217$	493.309	+	1518.25i	0.154323	+	0.474956i
$218$	9365.97			2.90983
$219$	93.7294	+	288.469i	0.0289207	+	0.0890089i
$220$	4149.27	+	3609.47i	1.27156	+	1.10614i
$221$	−25.1442	+	77.3858i	−0.00765330	+	0.0235544i
$222$	−4027.11	+	12394.2i	−1.21749	+	3.74704i
$223$	−2828.58	+	2055.08i	−0.849396	+	0.617123i	−0.924980	−	0.380017i	$-0.875918\pi$
$223$	−2828.58	+	2055.08i	−0.849396	+	0.617123i	0.0755831	+	0.997140i	$0.475918\pi$
$224$	4358.76			1.30014
$225$	−1385.01	+	674.310i	−0.410374	+	0.199795i
$226$	−4886.60			−1.43828
$227$	4348.31	−	3159.23i	1.27140	−	0.923724i	0.272140	−	0.962258i	$-0.412269\pi$
$227$	4348.31	−	3159.23i	1.27140	−	0.923724i	0.999257	+	0.0385335i	$0.0122686\pi$
$228$	2812.38	−	8655.61i	0.816905	−	2.51417i
$229$	−207.178	+	637.627i	−0.0597846	+	0.183998i	−0.976489	−	0.215569i	$-0.930839\pi$
$229$	−207.178	+	637.627i	−0.0597846	+	0.183998i	0.916704	+	0.399567i	$0.130839\pi$
$230$	−935.402	−	4058.18i	−0.268168	−	1.16343i
$231$	−454.404	−	1398.51i	−0.129427	−	0.398335i
$232$	6525.06			1.84651
$233$	−1442.14	−	4438.46i	−0.405485	−	1.24795i	−0.920490	−	0.390767i	$-0.872210\pi$
$233$	−1442.14	−	4438.46i	−0.405485	−	1.24795i	0.515005	−	0.857187i	$-0.327790\pi$
$234$	−2340.58	−	1700.53i	−0.653883	−	0.475073i
$235$	−1359.89	−	5899.80i	−0.377487	−	1.63771i
$236$	−2717.00	+	1974.01i	−0.749413	+	0.544480i
$237$	2390.97	+	1737.14i	0.655316	+	0.476115i
$238$	−76.2307	−	55.3849i	−0.0207618	−	0.0150843i
$239$	−5138.90	+	3733.63i	−1.39083	+	1.01050i	−0.395054	+	0.918658i	$0.629274\pi$
$239$	−5138.90	+	3733.63i	−1.39083	+	1.01050i	−0.995774	+	0.0918383i	$0.970726\pi$
$240$	−5013.62	+	11799.8i	−1.34845	+	3.17364i
$241$	−987.511	−	717.469i	−0.263947	−	0.191769i	0.447938	−	0.894064i	$-0.352158\pi$
$241$	−987.511	−	717.469i	−0.263947	−	0.191769i	−0.711885	+	0.702296i	$0.752158\pi$
$242$	1212.64	+	3732.12i	0.322113	+	0.991362i
$243$	3220.71			0.850242
$244$	−5343.35	−	16445.1i	−1.40194	−	4.31472i
$245$	2397.77	−	1439.58i	0.625257	−	0.375393i
$246$	36.8447	−	113.396i	0.00954932	−	0.0293898i
$247$	980.662	−	3018.17i	0.252624	−	0.777496i
$248$	−8694.60	+	6317.00i	−2.22624	+	1.61746i
$249$	3774.22			0.960567
$250$	4665.47	+	5773.83i	1.18028	+	1.46068i
$251$	5225.08			1.31396			0.656980	−	0.753908i	$-0.271834\pi$
$251$	5225.08			1.31396			0.656980	+	0.753908i	$0.271834\pi$
$252$	1941.89	−	1410.86i	0.485426	−	0.352682i
$253$	−527.364	+	1623.06i	−0.131048	+	0.403324i
$254$	−1690.83	+	5203.84i	−0.417685	+	1.28550i
$255$	110.659	−	66.4378i	0.0271755	−	0.0163157i
$256$	−69.9686	−	215.341i	−0.0170822	−	0.0525735i
$257$	5648.44			1.37097			0.685487	−	0.728085i	$-0.259589\pi$
$257$	5648.44			1.37097			0.685487	+	0.728085i	$0.259589\pi$
$258$	99.2666	+	305.511i	0.0239538	+	0.0737221i
$259$	−3050.11	−	2216.03i	−0.731754	−	0.531651i
$260$	−3906.00	+	9192.96i	−0.931692	+	2.19278i
$261$	1002.82	−	728.593i	0.237828	−	0.172792i
$262$	1309.74	+	951.580i	0.308839	+	0.224385i
$263$	−215.671	−	156.694i	−0.0505660	−	0.0367383i	0.562215	−	0.826991i	$-0.309949\pi$
$263$	−215.671	−	156.694i	−0.0505660	−	0.0367383i	−0.612781	+	0.790253i	$0.709949\pi$
$264$	8008.91	−	5818.81i	1.86710	−	1.35653i
$265$	408.568	+	1772.55i	0.0947099	+	0.410893i
$266$	2973.12	+	2160.10i	0.685314	+	0.497910i
$267$	−1338.74	−	4120.22i	−0.306852	−	0.944394i
$268$	−14280.7			−3.25497
$269$	−20.8315	−	64.1126i	−0.00472162	−	0.0145317i	0.948668	−	0.316274i	$-0.102432\pi$
$269$	−20.8315	−	64.1126i	−0.00472162	−	0.0145317i	−0.953390	+	0.301742i	$0.902432\pi$
$270$	−1227.59	−	5325.84i	−0.276700	−	1.20045i
$271$	−1310.75	+	4034.06i	−0.293809	+	0.904250i	0.689810	+	0.723990i	$0.257694\pi$
$271$	−1310.75	+	4034.06i	−0.293809	+	0.904250i	−0.983619	+	0.180260i	$0.942306\pi$
$272$	104.031	−	320.175i	0.0231905	−	0.0713731i
$273$	2160.66	−	1569.81i	0.479008	−	0.348020i
$274$	9630.15			2.12328
$275$	−421.232	−	3012.60i	−0.0923682	−	0.660607i
$276$	−8888.98			−1.93860
$277$	−7067.18	+	5134.61i	−1.53295	+	1.11375i	−0.578373	+	0.815773i	$0.696312\pi$
$277$	−7067.18	+	5134.61i	−1.53295	+	1.11375i	−0.954573	+	0.297977i	$0.903688\pi$
$278$	1175.20	−	3616.88i	0.253538	−	0.780310i
$279$	−630.893	+	1941.69i	−0.135378	+	0.416652i
$280$	−5272.94	−	4586.95i	−1.12542	−	0.979010i
$281$	2157.19	+	6639.13i	0.457960	+	1.40946i	0.867624	+	0.497221i	$0.165646\pi$
$281$	2157.19	+	6639.13i	0.457960	+	1.40946i	−0.409664	+	0.912237i	$0.634354\pi$
$282$	−18037.5			−3.80892
$283$	2061.43	+	6344.42i	0.433000	+	1.33264i	0.895122	+	0.445821i	$0.147088\pi$
$283$	2061.43	+	6344.42i	0.433000	+	1.33264i	−0.462122	+	0.886817i	$0.652912\pi$
$284$	11082.8	+	8052.10i	2.31564	+	1.68241i
$285$	−4315.89	+	2591.18i	−0.897021	+	0.538555i
$286$	4621.95	−	3358.04i	0.955600	−	0.694284i
$287$	27.9059	+	20.2748i	0.00573949	+	0.00416998i
$288$	4509.80	+	3276.56i	0.922717	+	0.670393i
$289$	3971.96	−	2885.80i	0.808459	−	0.587380i
$290$	−4506.71	−	3920.41i	−0.912562	−	0.793842i
$291$	−3123.86	−	2269.62i	−0.629292	−	0.457207i
$292$	−302.123	−	929.838i	−0.0605493	−	0.186351i
$293$	−4204.23			−0.838272			−0.419136	−	0.907923i	$-0.637667\pi$
$293$	−4204.23			−0.838272			−0.419136	+	0.907923i	$0.637667\pi$
$294$	−2574.72	−	7924.17i	−0.510750	−	1.57193i
$295$	1850.48	+	162.552i	0.365216	+	0.0320818i
$296$	7843.23	−	24139.0i	1.54013	−	4.74003i
$297$	−692.097	+	2130.06i	−0.135217	+	0.416156i
$298$	3118.11	−	2265.44i	0.606132	−	0.440380i
$299$	−3099.54			−0.599502
$300$	14245.5	−	6935.61i	2.74156	−	1.33476i
$301$	−92.9323			−0.0177958
$302$	13112.0	−	9526.46i	2.49839	−	1.81519i
$303$	−1215.00	+	3739.37i	−0.230362	+	0.708981i
$304$	−4057.39	+	12487.4i	−0.765484	+	2.35592i
$305$	−3740.16	+	8802.65i	−0.702167	+	1.65258i
$306$	−37.2385	−	114.608i	−0.00695680	−	0.0214108i
$307$	1361.03			0.253024			0.126512	−	0.991965i	$-0.459622\pi$
$307$	1361.03			0.253024			0.126512	+	0.991965i	$0.459622\pi$
$308$	1464.70	+	4507.90i	0.270972	+	0.833965i
$309$	7725.96	+	5613.24i	1.42238	+	1.03342i
$310$	9800.55	+	860.912i	1.79559	+	0.157731i
$311$	−1990.40	+	1446.11i	−0.362911	+	0.263670i	−0.754265	−	0.656570i	$-0.772007\pi$
$311$	−1990.40	+	1446.11i	−0.362911	+	0.263670i	0.391354	+	0.920240i	$0.372007\pi$
$312$	14546.0	+	10568.3i	2.63943	+	1.91766i
$313$	2333.11	+	1695.11i	0.421327	+	0.306112i	0.778171	−	0.628052i	$-0.216147\pi$
$313$	2333.11	+	1695.11i	0.421327	+	0.306112i	−0.356845	+	0.934164i	$0.616147\pi$
$314$	−9310.97	+	6764.82i	−1.67340	+	1.21580i
$315$	−1322.57	−	116.179i	−0.236566	−	0.0207807i
$316$	−7706.92	−	5599.40i	−1.37199	−	0.996807i
$317$	−2319.10	−	7137.47i	−0.410896	−	1.26461i	−0.915871	−	0.401473i	$-0.868498\pi$
$317$	−2319.10	−	7137.47i	−0.410896	−	1.26461i	0.504975	−	0.863134i	$-0.331502\pi$
$318$	5419.20			0.955641
$319$	756.398	+	2327.96i	0.132759	+	0.408591i
$320$	4108.60	−	9669.79i	0.717742	−	1.68924i
$321$	844.205	−	2598.20i	0.146788	−	0.451767i
$322$	1109.17	−	3413.67i	0.191961	−	0.590796i
$323$	106.939	−	77.6961i	0.0184219	−	0.0133843i
$324$	−18391.2			−3.15351
$325$	4967.35	−	2418.41i	0.847812	−	0.412767i
$326$	413.258			0.0702093
$327$	−8945.63	+	6499.38i	−1.51283	+	1.09913i
$328$	−71.7589	+	220.851i	−0.0120800	+	0.0371783i
$329$	1612.51	−	4962.81i	0.270215	−	0.831636i
$330$	−9027.64	−	793.017i	−1.50592	−	0.132285i
$331$	−320.055	−	985.027i	−0.0531474	−	0.163571i	0.920960	−	0.389658i	$-0.127407\pi$
$331$	−320.055	−	985.027i	−0.0531474	−	0.163571i	−0.974107	+	0.226087i	$0.927407\pi$
$332$	−12165.6			−2.01107
$333$	−1489.97	−	4585.65i	−0.245194	−	0.754630i
$334$	−543.116	−	394.597i	−0.0889760	−	0.0646448i
$335$	5959.60	+	5184.28i	0.971963	+	0.845515i
$336$	−8939.52	+	6494.94i	−1.45146	+	1.05455i
$337$	−1057.22	−	768.117i	−0.170892	−	0.124160i	0.499052	−	0.866572i	$-0.333682\pi$
$337$	−1057.22	−	768.117i	−0.170892	−	0.124160i	−0.669944	+	0.742412i	$0.733682\pi$
$338$	−1046.40	−	760.258i	−0.168393	−	0.122345i
$339$	4667.29	−	3390.98i	0.747765	−	0.543283i
$340$	−356.694	+	214.152i	−0.0568954	+	0.0341589i
$341$	−3261.62	−	2369.70i	−0.517966	−	0.376325i
$342$	1452.36	+	4469.90i	0.229633	+	0.706739i
$343$	5715.58			0.899744
$344$	−193.332	−	595.016i	−0.0303017	−	0.0932590i
$345$	3709.54	+	3226.95i	0.578884	+	0.503574i
$346$	−5316.51	+	16362.5i	−0.826061	+	2.54236i
$347$	1032.43	−	3177.49i	0.159723	−	0.491576i	−0.838886	−	0.544307i	$-0.816793\pi$
$347$	1032.43	−	3177.49i	0.159723	−	0.491576i	0.998609	+	0.0527312i	$0.0167927\pi$
$348$	−10314.5	+	7493.94i	−1.58884	+	1.15436i
$349$	10728.2			1.64546			0.822732	−	0.568429i	$-0.192449\pi$
$349$	10728.2			1.64546			0.822732	+	0.568429i	$0.192449\pi$
$350$	885.949	+	6336.20i	0.135303	+	0.967669i
$351$	−4067.75			−0.618576
$352$	−8905.52	+	6470.24i	−1.34848	+	0.979730i
$353$	2579.99	−	7940.38i	0.389005	−	1.19723i	−0.544528	−	0.838743i	$-0.683291\pi$
$353$	2579.99	−	7940.38i	0.389005	−	1.19723i	0.933533	−	0.358491i	$-0.116709\pi$
$354$	1710.14	−	5263.27i	0.256760	−	0.790225i
$355$	−1701.91	−	7383.64i	−0.254445	−	1.10390i
$356$	4315.23	+	13280.9i	0.642435	+	1.97721i
$357$	111.243			0.0164919
$358$	−2330.74	−	7173.29i	−0.344088	−	1.05899i
$359$	−8253.90	−	5996.81i	−1.21344	−	0.881614i	−0.217899	−	0.975971i	$-0.569920\pi$
$359$	−8253.90	−	5996.81i	−1.21344	−	0.881614i	−0.995538	+	0.0943571i	$0.969920\pi$
$360$	−2007.56	−	8709.67i	−0.293910	−	1.27511i
$361$	1378.24	−	1001.35i	0.200939	−	0.145990i
$362$	−1830.50	−	1329.94i	−0.265771	−	0.193094i
$363$	−3748.06	−	2723.13i	−0.541935	−	0.393739i
$364$	−6964.57	+	5060.06i	−1.00287	+	0.728624i
$365$	−211.475	+	497.718i	−0.0303264	+	0.0713746i
$366$	23051.9	+	16748.2i	3.29219	+	2.39192i
$367$	−2307.74	−	7102.49i	−0.328237	−	1.01021i	−0.969958	−	0.243272i	$-0.921779\pi$
$367$	−2307.74	−	7102.49i	−0.328237	−	1.01021i	0.641721	−	0.766938i	$-0.278221\pi$
$368$	12824.0			1.81657
$369$	13.6319	+	41.9548i	0.00192317	+	0.00591891i
$370$	−19920.4	+	11959.8i	−2.79895	+	1.68044i
$371$	−484.466	+	1491.03i	−0.0677958	+	0.208654i
$372$	6489.05	−	19971.2i	0.904413	−	2.78350i
$373$	4675.25	−	3396.77i	0.648995	−	0.471523i	−0.213934	−	0.976848i	$-0.568628\pi$
$373$	4675.25	−	3396.77i	0.648995	−	0.471523i	0.862929	+	0.505326i	$0.168628\pi$
$374$	237.964			0.0329006
$375$	−8462.76	−	2277.17i	−1.16537	−	0.313580i
$376$	35129.9			4.81831
$377$	−3596.62	+	2613.10i	−0.491341	+	0.356980i
$378$	1455.64	−	4480.00i	0.198069	−	0.609593i
$379$	−2500.18	+	7694.77i	−0.338854	+	1.04289i	0.625938	+	0.779873i	$0.284716\pi$
$379$	−2500.18	+	7694.77i	−0.338854	+	1.04289i	−0.964792	+	0.263013i	$0.915284\pi$
$380$	13911.6	−	8352.28i	1.87803	−	1.12753i
$381$	−1996.18	−	6143.62i	−0.268419	−	0.826108i
$382$	7835.04			1.04941
$383$	653.851	+	2012.35i	0.0872330	+	0.268475i	0.985152	−	0.171686i	$-0.0549213\pi$
$383$	653.851	+	2012.35i	0.0872330	+	0.268475i	−0.897919	+	0.440161i	$0.854921\pi$
$384$	−6964.14	−	5059.75i	−0.925488	−	0.672406i
$385$	1025.24	−	2412.96i	0.135717	−	0.319418i
$386$	−6600.15	+	4795.29i	−0.870307	+	0.632315i
$387$	−96.1526	−	69.8590i	−0.0126298	−	0.00917605i
$388$	10069.3	+	7315.77i	1.31750	+	0.957222i
$389$	5428.83	−	3944.27i	0.707590	−	0.514094i	−0.174805	−	0.984603i	$-0.555930\pi$
$389$	5428.83	−	3944.27i	0.707590	−	0.514094i	0.882395	+	0.470509i	$0.155930\pi$
$390$	−3696.90	−	16038.8i	−0.480000	−	2.08245i
$391$	−104.448	−	75.8857i	−0.0135093	−	0.00981510i
$392$	5014.54	+	15433.2i	0.646103	+	1.98850i
$393$	−1911.29			−0.245323
$394$	511.907	+	1575.49i	0.0654556	+	0.201452i
$395$	1183.50	+	5134.56i	0.150756	+	0.654046i
$396$	−1873.21	+	5765.16i	−0.237708	+	0.731591i
$397$	−2029.26	+	6245.42i	−0.256538	+	0.789544i	0.736984	+	0.675910i	$0.236249\pi$
$397$	−2029.26	+	6245.42i	−0.256538	+	0.789544i	−0.993523	+	0.113634i	$0.963751\pi$
$398$	−6246.99	+	4538.70i	−0.786767	+	0.571620i
$399$	−4338.66			−0.544372
$400$	−20551.9	+	10005.9i	−2.56899	+	1.25074i
$401$	−10290.4			−1.28149			−0.640744	−	0.767754i	$-0.721374\pi$
$401$	−10290.4			−1.28149			−0.640744	+	0.767754i	$0.721374\pi$
$402$	19038.1	−	13832.0i	2.36203	−	1.71612i
$403$	2262.70	−	6963.87i	0.279685	−	0.860782i
$404$	3916.36	−	12053.3i	0.482292	−	1.48434i
$405$	7675.02	+	6676.53i	0.941666	+	0.819160i
$406$	−1590.88	−	4896.23i	−0.194468	−	0.598511i
$407$	9521.30			1.15959
$408$	231.425	+	712.253i	0.0280815	+	0.0864260i
$409$	−5384.48	−	3912.06i	−0.650967	−	0.472955i	0.212633	−	0.977132i	$-0.431796\pi$
$409$	−5384.48	−	3912.06i	−0.650967	−	0.472955i	−0.863600	+	0.504177i	$0.831796\pi$
$410$	182.255	−	109.422i	0.0219535	−	0.0131805i
$411$	−9197.96	+	6682.71i	−1.10390	+	0.802028i
$412$	−24903.5	−	18093.4i	−2.97793	−	2.16359i
$413$	1295.25	+	941.053i	0.154322	+	0.112121i
$414$	3713.73	−	2698.18i	0.440869	−	0.320310i
$415$	5076.95	+	4416.46i	0.600524	+	0.522399i
$416$	−16174.4	−	11751.4i	−1.90629	−	1.38500i
$417$	1387.43	+	4270.07i	0.162932	+	0.501454i
$418$	−9280.97			−1.08600
$419$	1348.17	+	4149.23i	0.157189	+	0.483778i	0.998376	−	0.0569662i	$-0.0181427\pi$
$419$	1348.17	+	4149.23i	0.157189	+	0.483778i	−0.841187	+	0.540744i	$0.818143\pi$
$420$	13603.3	+	1194.96i	1.58041	+	0.138828i
$421$	2611.17	−	8036.36i	0.302282	−	0.930329i	−0.678395	−	0.734697i	$-0.737324\pi$
$421$	2611.17	−	8036.36i	0.302282	−	0.930329i	0.980677	−	0.195632i	$-0.0626757\pi$
$422$	−4324.35	+	13309.0i	−0.498830	+	1.53524i
$423$	5399.03	−	3922.62i	0.620590	−	0.450885i
$424$	−10554.5			−1.20889
$425$	226.598	+	40.1198i	0.0258627	+	0.00457905i
$426$	−22574.0			−2.56740
$427$	−6668.88	+	4845.22i	−0.755807	+	0.549126i
$428$	−2721.17	+	8374.90i	−0.307319	+	0.945832i
$429$	−2084.25	+	6414.67i	−0.234566	+	0.721919i
$430$	−223.969	+	527.122i	−0.0251180	+	0.0591164i
$431$	−123.883	−	381.273i	−0.0138451	−	0.0426109i	0.943895	−	0.330245i	$-0.107131\pi$
$431$	−123.883	−	381.273i	−0.0138451	−	0.0426109i	−0.957740	+	0.287634i	$0.907131\pi$
$432$	16829.9			1.87437
$433$	−3996.84	−	12301.0i	−0.443594	−	1.36524i	−0.884019	−	0.467451i	$-0.845172\pi$
$433$	−3996.84	−	12301.0i	−0.443594	−	1.36524i	0.440425	−	0.897789i	$-0.354828\pi$
$434$	6859.93	+	4984.03i	0.758727	+	0.551247i
$435$	7024.96	+	617.095i	0.774301	+	0.0680171i
$436$	28834.9	−	20949.8i	3.16730	−	2.30118i
$437$	4073.62	+	2959.66i	0.445922	+	0.323981i
$438$	1303.40	+	946.973i	0.142189	+	0.103306i
$439$	−4561.58	+	3314.18i	−0.495928	+	0.360313i	−0.807460	−	0.589923i	$-0.799158\pi$
$439$	−4561.58	+	3314.18i	−0.495928	+	0.360313i	0.311531	+	0.950236i	$0.399158\pi$
$440$	17582.3	+	1544.48i	1.90501	+	0.167342i
$441$	2493.95	+	1811.96i	0.269296	+	0.195655i
$442$	133.556	+	411.042i	0.0143724	+	0.0442337i
$443$	−2827.26			−0.303221			−0.151611	−	0.988440i	$-0.548446\pi$
$443$	−2827.26			−0.303221			−0.151611	+	0.988440i	$0.548446\pi$
$444$	15325.1	+	47165.7i	1.63805	+	5.04140i
$445$	3020.51	−	7108.93i	0.321766	−	0.757293i
$446$	−5738.76	+	17662.1i	−0.609278	+	1.87517i
$447$	−1406.10	+	4327.53i	−0.148784	+	0.457909i
$448$	7325.82	−	5322.52i	0.772572	−	0.561306i
$449$	−14913.8			−1.56754			−0.783769	−	0.621052i	$-0.786706\pi$
$449$	−14913.8			−1.56754			−0.783769	+	0.621052i	$0.786706\pi$
$450$	−3846.39	+	7221.75i	−0.402935	+	0.756526i
$451$	−87.1118			−0.00909520
$452$	−15044.3	+	10930.3i	−1.56554	+	1.13743i
$453$	−5912.83	+	18197.8i	−0.613265	+	1.88744i
$454$	8822.07	−	27151.5i	0.911983	−	2.80679i
$455$	4743.39	+	416.675i	0.488733	+	0.0429319i
$456$	−9025.95	−	27779.0i	−0.926927	−	2.85279i
$457$	6570.60			0.672559			0.336280	−	0.941762i	$-0.390831\pi$
$457$	6570.60			0.672559			0.336280	+	0.941762i	$0.390831\pi$
$458$	1100.45	+	3386.82i	0.112272	+	0.345537i
$459$	−137.074	−	99.5901i	−0.0139391	−	0.0101274i
$460$	−11957.1	−	10401.6i	−1.21197	−	1.05430i
$461$	11261.5	−	8181.99i	1.13775	−	0.826623i	0.150945	−	0.988542i	$-0.451768\pi$
$461$	11261.5	−	8181.99i	1.13775	−	0.826623i	0.986804	+	0.161919i	$0.0517683\pi$
$462$	−6318.93	−	4590.97i	−0.636327	−	0.462319i
$463$	9396.58	+	6827.02i	0.943188	+	0.685266i	0.949186	−	0.314716i	$-0.101909\pi$
$463$	9396.58	+	6827.02i	0.943188	+	0.685266i	−0.00599770	+	0.999982i	$0.501909\pi$
$464$	14880.7	−	10811.4i	1.48883	−	1.08170i
$465$	−9958.12	+	5978.68i	−0.993112	+	0.596246i
$466$	−20054.4	−	14570.4i	−1.99357	−	1.44841i
$467$	−1752.46	−	5393.52i	−0.173649	−	0.534437i	0.825920	−	0.563787i	$-0.190656\pi$
$467$	−1752.46	−	5393.52i	−0.173649	−	0.534437i	−0.999569	+	0.0293500i	$0.990656\pi$
$468$	−11009.7			−1.08744
$469$	2103.75	+	6474.69i	0.207127	+	0.637470i
$470$	−24263.4	−	21106.8i	−2.38125	−	2.07146i
$471$	4198.75	−	12922.4i	0.410761	−	1.26419i
$472$	−3330.68	+	10250.8i	−0.324803	+	0.999641i
$473$	189.873	−	137.951i	0.0184574	−	0.0134101i
$474$	15697.9			1.52116
$475$	−8837.69	−	1564.74i	−0.853687	−	0.151147i
$476$	−358.575			−0.0345279
$477$	−1622.09	+	1178.52i	−0.155703	+	0.113125i
$478$	−10426.1	+	32088.2i	−0.997652	+	3.07046i
$479$	2337.30	−	7193.47i	0.222952	−	0.686175i	−0.775541	−	0.631297i	$-0.782523\pi$
$479$	2337.30	−	7193.47i	0.222952	−	0.686175i	0.998493	−	0.0548782i	$-0.0174770\pi$
$480$	7123.15	+	30903.3i	0.677345	+	2.93862i
$481$	5343.77	+	16446.4i	0.506559	+	1.55903i
$482$	−6483.51			−0.612688
$483$	1309.48	+	4030.16i	0.123361	+	0.379666i
$484$	12081.3	+	8777.60i	1.13461	+	0.824342i
$485$	−1546.28	−	6708.44i	−0.144769	−	0.628072i
$486$	13840.0	−	10055.3i	1.29176	−	0.938516i
$487$	−3743.14	−	2719.55i	−0.348291	−	0.253049i	0.399860	−	0.916576i	$-0.369059\pi$
$487$	−3743.14	−	2719.55i	−0.348291	−	0.253049i	−0.748152	+	0.663527i	$0.769059\pi$
$488$	−44896.0	−	32618.9i	−4.16465	−	3.02579i
$489$	−394.711	+	286.774i	−0.0365019	+	0.0265202i
$490$	5809.17	−	13672.2i	0.535575	−	1.26050i
$491$	14224.2	+	10334.5i	1.30739	+	0.949874i	0.999999	−	0.00170911i	$-0.000544026\pi$
$491$	14224.2	+	10334.5i	1.30739	+	0.949874i	0.307391	+	0.951583i	$0.400544\pi$
$492$	−140.211	−	431.526i	−0.0128480	−	0.0395421i
$493$	−185.174			−0.0169165
$494$	−5208.89	−	16031.3i	−0.474411	−	1.46009i
$495$	2874.64	−	1725.88i	0.261021	−	0.156712i
$496$	−9361.68	+	28812.3i	−0.847484	+	2.60829i
$497$	2018.07	−	6210.99i	0.182139	−	0.560565i
$498$	16218.5	−	11783.4i	1.45937	−	1.06030i
$499$	−2983.65			−0.267669			−0.133834	−	0.991004i	$-0.542729\pi$
$499$	−2983.65			−0.267669			−0.133834	+	0.991004i	$0.542729\pi$
$500$	27278.4	+	7340.10i	2.43986	+	0.656519i
$501$	792.566			0.0706771
$502$	22453.1	−	16313.1i	1.99628	−	1.45038i
$503$	1756.75	−	5406.72i	0.155725	−	0.479272i	−0.842509	−	0.538683i	$-0.818922\pi$
$503$	1756.75	−	5406.72i	0.155725	−	0.479272i	0.998234	+	0.0594106i	$0.0189221\pi$
$504$	2380.50	−	7326.41i	0.210388	−	0.647509i
$505$	−6010.06	+	3608.33i	−0.529592	+	0.317957i
$506$	2801.15	+	8621.05i	0.246099	+	0.757416i
$507$	1527.01			0.133761
$508$	6434.40	+	19803.0i	0.561969	+	1.72956i
$509$	−4078.11	−	2962.92i	−0.355126	−	0.258014i	0.395890	−	0.918298i	$-0.370436\pi$
$509$	−4078.11	−	2962.92i	−0.355126	−	0.258014i	−0.751016	+	0.660284i	$0.770436\pi$
$510$	268.098	−	630.982i	0.0232776	−	0.0547850i
$511$	−377.070	+	273.958i	−0.0326431	+	0.0237166i
$512$	−9857.45	−	7161.86i	−0.850863	−	0.618188i
$513$	5346.10	+	3884.17i	0.460110	+	0.334289i
$514$	24272.4	−	17634.9i	2.08290	−	1.51331i
$515$	3824.28	+	16591.4i	0.327219	+	1.41962i
$516$	988.978	+	718.535i	0.0843747	+	0.0613018i
$517$	4072.32	+	12533.3i	0.346423	+	1.06618i
$518$	−20025.5			−1.69859
$519$	−6276.64	−	19317.5i	−0.530855	−	1.63380i
$520$	7200.11	+	31237.2i	0.607203	+	2.63432i
$521$	5057.33	−	15564.9i	0.425270	−	1.30885i	−0.477466	−	0.878650i	$-0.658445\pi$
$521$	5057.33	−	15564.9i	0.425270	−	1.30885i	0.902736	−	0.430196i	$-0.141555\pi$
$522$	2034.58	−	6261.79i	0.170596	−	0.525040i
$523$	−2132.73	+	1549.52i	−0.178313	+	0.129552i	−0.673362	−	0.739313i	$-0.735150\pi$
$523$	−2132.73	+	1549.52i	−0.178313	+	0.129552i	0.495048	+	0.868865i	$0.335150\pi$
$524$	6160.77			0.513615
$525$	−5243.10	−	5437.04i	−0.435862	−	0.451985i
$526$	−1415.99			−0.117377
$527$	246.743	−	179.270i	0.0203953	−	0.0148180i
$528$	8623.38	−	26540.0i	0.710766	−	2.18751i
$529$	−2240.08	+	6894.26i	−0.184111	+	0.566636i
$530$	7289.72	+	6341.37i	0.597444	+	0.519719i
$531$	632.724	+	1947.33i	0.0517098	+	0.159146i
$532$	13985.0			1.13971
$533$	−48.8910	−	150.471i	−0.00397318	−	0.0122282i
$534$	−18616.5	−	13525.7i	−1.50864	−	1.09609i
$535$	4175.92	−	2507.15i	0.337459	−	0.202604i
$536$	−37078.8	+	26939.3i	−2.98799	+	2.17090i
$537$	7203.94	+	5233.97i	0.578907	+	0.420600i
$538$	−289.681	−	210.466i	−0.0232138	−	0.0168658i
$539$	−4924.81	+	3578.09i	−0.393556	+	0.285935i
$540$	−15692.2	−	13650.7i	−1.25053	−	1.08784i
$541$	−9369.11	−	6807.06i	−0.744565	−	0.540958i	0.149573	−	0.988751i	$-0.452210\pi$
$541$	−9369.11	−	6807.06i	−0.744565	−	0.540958i	−0.894137	+	0.447793i	$0.852210\pi$
$542$	6962.16	+	21427.3i	0.551754	+	1.69812i
$543$	2671.24			0.211112
$544$	−257.334	−	791.992i	−0.0202814	−	0.0624198i
$545$	−19638.7	−	1725.13i	−1.54354	−	0.135590i
$546$	4383.67	−	13491.5i	0.343596	−	1.05748i
$547$	1752.01	−	5392.13i	0.136948	−	0.421483i	−0.858940	−	0.512076i	$-0.828876\pi$
$547$	1752.01	−	5392.13i	0.136948	−	0.421483i	0.995888	+	0.0905938i	$0.0288765\pi$
$548$	29648.2	−	21540.7i	2.31115	−	1.67915i
$549$	−10542.2			−0.819546
$550$	−11215.7	−	11630.6i	−0.869526	−	0.901690i
$551$	7222.10			0.558388
$552$	−23079.6	+	16768.3i	−1.77959	+	1.29295i
$553$	−1403.36	+	4319.10i	−0.107915	+	0.332128i
$554$	−14338.3	+	44128.7i	−1.09959	+	3.38420i
$555$	10727.0	−	25246.6i	0.820426	−	1.93091i
$556$	−4472.17	−	13763.9i	−0.341119	−	1.04986i
$557$	−4968.53			−0.377959			−0.188980	−	0.981981i	$-0.560518\pi$
$557$	−4968.53			−0.377959			−0.188980	+	0.981981i	$0.560518\pi$
$558$	3351.06	+	10313.5i	0.254232	+	0.782446i
$559$	344.852	+	250.549i	0.0260924	+	0.0189573i
$560$	−19625.3	−	1723.95i	−1.48093	−	0.130090i
$561$	−227.284	+	165.132i	−0.0171051	+	0.0124276i
$562$	29997.7	+	21794.6i	2.25156	+	1.63586i
$563$	−8731.04	−	6343.47i	−0.653587	−	0.474859i	0.210904	−	0.977507i	$-0.432359\pi$
$563$	−8731.04	−	6343.47i	−0.653587	−	0.474859i	−0.864491	+	0.502648i	$0.832359\pi$
$564$	−55531.7	+	40346.1i	−4.14593	+	3.01220i
$565$	10246.3	+	900.067i	0.762946	+	0.0670197i
$566$	28666.1	+	20827.1i	2.12885	+	1.54670i
$567$	2709.30	+	8338.37i	0.200670	+	0.617599i
$568$	43965.3			3.24778
$569$	−876.580	−	2697.84i	−0.0645838	−	0.198768i	0.913558	−	0.406709i	$-0.133324\pi$
$569$	−876.580	−	2697.84i	−0.0645838	−	0.198768i	−0.978141	+	0.207941i	$0.933324\pi$
$570$	−10456.3	+	24609.3i	−0.768358	+	1.80837i
$571$	2021.34	−	6221.03i	0.148144	−	0.455941i	−0.849258	−	0.527978i	$-0.822950\pi$
$571$	2021.34	−	6221.03i	0.148144	−	0.455941i	0.997402	+	0.0720377i	$0.0229502\pi$
$572$	6718.28	−	20676.7i	0.491093	−	1.51143i
$573$	−7483.41	+	5437.01i	−0.545591	+	0.396395i
$574$	183.216			0.0133228
$575$	1213.88	+	8681.55i	0.0880390	+	0.629645i
$576$	11580.7			0.837725
$577$	4388.86	−	3188.69i	0.316656	−	0.230064i	−0.418091	−	0.908405i	$-0.637301\pi$
$577$	4388.86	−	3188.69i	0.316656	−	0.230064i	0.734747	+	0.678341i	$0.237301\pi$
$578$	8058.52	−	24801.6i	0.579914	−	1.78479i
$579$	2976.31	−	9160.15i	0.213629	−	0.657484i
$580$	−22643.9	−	1989.11i	−1.62110	−	0.142403i
$581$	1792.18	+	5515.75i	0.127972	+	0.393859i
$582$	−20509.7			−1.46075
$583$	−1223.50	−	3765.53i	−0.0869159	−	0.267500i
$584$	−2538.50	−	1844.33i	−0.179870	−	0.130683i
$585$	4594.54	+	3996.81i	0.324719	+	0.282475i
$586$	−18066.3	+	13126.0i	−1.27357	+	0.925304i
$587$	16859.9	+	12249.4i	1.18549	+	0.861310i	0.992780	−	0.119946i	$-0.0382720\pi$
$587$	16859.9	+	12249.4i	1.18549	+	0.861310i	0.192711	+	0.981256i	$0.438272\pi$
$588$	−25651.5	−	18636.9i	−1.79907	−	1.30710i
$589$	−9623.39	+	6991.80i	−0.673217	+	0.489121i
$590$	8459.32	−	5078.82i	0.590279	−	0.354393i
$591$	−1582.22	−	1149.55i	−0.110125	−	0.0800105i
$592$	−22109.3	−	68045.4i	−1.53494	−	4.72407i
$593$	−8301.64			−0.574886			−0.287443	−	0.957798i	$-0.592805\pi$
$593$	−8301.64			−0.574886			−0.287443	+	0.957798i	$0.592805\pi$
$594$	3676.15	+	11314.0i	0.253929	+	0.781515i
$595$	149.640	+	130.173i	0.0103103	+	0.00896902i
$596$	4532.36	−	13949.2i	0.311498	−	0.958691i
$597$	2817.06	−	8670.02i	0.193123	−	0.594372i
$598$	−13319.3	+	9677.03i	−0.910813	+	0.661744i
$599$	22052.7			1.50426			0.752129	−	0.659016i	$-0.229027\pi$
$599$	22052.7			1.50426			0.752129	+	0.659016i	$0.229027\pi$
$600$	23904.1	−	44880.9i	1.62647	−	3.05376i
$601$	−4849.47			−0.329141			−0.164571	−	0.986365i	$-0.552624\pi$
$601$	−4849.47			−0.329141			−0.164571	+	0.986365i	$0.552624\pi$
$602$	−399.347	+	290.142i	−0.0270368	+	0.0196434i
$603$	−2690.49	+	8280.49i	−0.181700	+	0.559217i
$604$	19059.1	−	58658.0i	1.28395	−	3.95159i
$605$	−1855.26	−	8048.92i	−0.124673	−	0.540884i
$606$	6453.57	+	19862.1i	0.432605	+	1.33142i
$607$	−23938.2			−1.60070			−0.800348	−	0.599536i	$-0.795352\pi$
$607$	−23938.2			−1.60070			−0.800348	+	0.599536i	$0.795352\pi$
$608$	10036.4	+	30888.9i	0.669458	+	2.06038i
$609$	4917.15	+	3572.52i	0.327180	+	0.237710i
$610$	11410.5	+	49503.7i	0.757371	+	3.28581i
$611$	−19363.6	+	14068.5i	−1.28211	+	0.931507i
$612$	−371.001	−	269.548i	−0.0245046	−	0.0178036i
$613$	19265.9	+	13997.5i	1.26940	+	0.922275i	0.999179	−	0.0405223i	$-0.0129022\pi$
$613$	19265.9	+	13997.5i	1.26940	+	0.922275i	0.270224	+	0.962797i	$0.412902\pi$
$614$	5848.60	−	4249.26i	0.384414	−	0.279293i
$615$	−98.1431	+	230.985i	−0.00643498	+	0.0151450i
$616$	12306.8	+	8941.40i	0.804959	+	0.584837i
$617$	8.51935	+	26.2199i	0.000555877	+	0.00171081i	0.951334	−	0.308161i	$-0.0997137\pi$
$617$	8.51935	+	26.2199i	0.000555877	+	0.00171081i	−0.950778	+	0.309872i	$0.899714\pi$
$618$	50724.8			3.30170
$619$	7240.90	+	22285.2i	0.470172	+	1.44704i	0.852360	+	0.522956i	$0.175171\pi$
$619$	7240.90	+	22285.2i	0.470172	+	1.44704i	−0.382188	+	0.924085i	$0.624829\pi$
$620$	32098.5	−	19271.4i	2.07921	−	1.24832i
$621$	1994.45	−	6138.28i	0.128880	−	0.396651i
$622$	−4038.23	+	12428.4i	−0.260319	+	0.801179i
$623$	5385.71	−	3912.95i	0.346347	−	0.251636i
$624$	50683.2			3.25153
$625$	−8719.15	−	12966.0i	−0.558026	−	0.829824i
$626$	15318.1			0.978007
$627$	8864.45	−	6440.40i	0.564612	−	0.410215i
$628$	−13534.0	+	41653.5i	−0.859980	+	2.64675i
$629$	−222.583	+	685.039i	−0.0141096	+	0.0434249i
$630$	−6046.03	+	3629.93i	−0.382349	+	0.229555i
$631$	662.358	+	2038.53i	0.0417877	+	0.128609i	0.969774	−	0.244005i	$-0.0784614\pi$
$631$	662.358	+	2038.53i	0.0417877	+	0.128609i	−0.927986	+	0.372614i	$0.878461\pi$
$632$	−30573.3			−1.92427
$633$	−5105.30	−	15712.5i	−0.320565	−	0.986597i
$634$	−32249.4	−	23430.5i	−2.02017	−	1.46774i
$635$	4503.86	−	10600.1i	0.281465	−	0.662441i
$636$	16684.0	−	12121.7i	1.04020	−	0.755747i
$637$	−8944.56	−	6498.60i	−0.556352	−	0.404213i
$638$	10518.4	+	7642.10i	0.652710	+	0.474222i
$639$	6756.92	−	4909.19i	0.418309	−	0.303920i
$640$	−3447.18	−	14955.4i	−0.212909	−	0.923694i
$641$	−16852.6	−	12244.1i	−1.03844	−	0.754469i	−0.0684575	−	0.997654i	$-0.521808\pi$
$641$	−16852.6	−	12244.1i	−1.03844	−	0.754469i	−0.969980	+	0.243185i	$0.921808\pi$
$642$	−4484.08	−	13800.6i	−0.275658	−	0.848389i
$643$	−29336.6			−1.79926			−0.899628	−	0.436657i	$-0.856162\pi$
$643$	−29336.6			−1.79926			−0.899628	+	0.436657i	$0.856162\pi$
$644$	−4220.91	−	12990.6i	−0.258272	−	0.794879i
$645$	−151.871	−	658.885i	−0.00927121	−	0.0402226i
$646$	216.964	−	667.748i	0.0132142	−	0.0406690i
$647$	−2452.54	+	7548.13i	−0.149025	+	0.458652i	−0.997507	−	0.0705732i	$-0.977517\pi$
$647$	−2452.54	+	7548.13i	−0.149025	+	0.458652i	0.848482	+	0.529225i	$0.177517\pi$
$648$	−47751.6	+	34693.6i	−2.89485	+	2.10323i
$649$	−4043.28			−0.244550
$650$	13795.1	−	25900.8i	0.832444	−	1.56294i
$651$	−10010.7			−0.602686
$652$	1272.29	−	924.374i	0.0764215	−	0.0555234i
$653$	−3363.18	+	10350.8i	−0.201549	+	0.620304i	0.798288	+	0.602275i	$0.205739\pi$
$653$	−3363.18	+	10350.8i	−0.201549	+	0.620304i	−0.999837	+	0.0180290i	$0.994261\pi$
$654$	−18149.4	+	55858.0i	−1.08516	+	3.33979i
$655$	−2571.01	−	2236.53i	−0.153370	−	0.133417i
$656$	202.281	+	622.558i	0.0120393	+	0.0370530i
$657$	−596.076			−0.0353960
$658$	−8565.03	−	26360.5i	−0.507447	−	1.56176i
$659$	23268.1	+	16905.3i	1.37541	+	0.999295i	0.997292	+	0.0735377i	$0.0234289\pi$
$659$	23268.1	+	16905.3i	1.37541	+	0.999295i	0.378119	+	0.925757i	$0.376571\pi$
$660$	−29567.1	+	17751.5i	−1.74378	+	1.04694i
$661$	4489.07	−	3261.50i	0.264152	−	0.191918i	−0.447823	−	0.894122i	$-0.647801\pi$
$661$	4489.07	−	3261.50i	0.264152	−	0.191918i	0.711976	+	0.702204i	$0.247801\pi$
$662$	−4450.67	−	3233.60i	−0.261299	−	0.189845i
$663$	−412.799	−	299.916i	−0.0241807	−	0.0175683i
$664$	−31587.2	+	22949.4i	−1.84612	+	1.34128i
$665$	−5836.21	−	5076.95i	−0.340329	−	0.296053i
$666$	−20719.4	−	15053.5i	−1.20550	−	0.875845i
$667$	−2179.75	−	6708.57i	−0.126537	−	0.389441i
$668$	−2554.72			−0.147972
$669$	−6775.15	−	20851.8i	−0.391543	−	1.20505i
$670$	41795.2	+	3671.43i	2.40999	+	0.211701i
$671$	6433.04	−	19798.9i	0.370111	−	1.13909i
$672$	−8446.39	+	25995.3i	−0.484861	+	1.49225i
$673$	8913.64	−	6476.14i	0.510543	−	0.370931i	−0.302487	−	0.953154i	$-0.597817\pi$
$673$	8913.64	−	6476.14i	0.510543	−	0.370931i	0.813030	+	0.582222i	$0.197817\pi$
$674$	−6941.20			−0.396684
$675$	1593.06	+	11393.4i	0.0908401	+	0.649678i
$676$	−4922.10			−0.280047
$677$	3876.03	−	2816.10i	0.220041	−	0.159869i	−0.472304	−	0.881436i	$-0.656578\pi$
$677$	3876.03	−	2816.10i	0.220041	−	0.159869i	0.692345	+	0.721566i	$0.256578\pi$
$678$	9469.24	−	29143.3i	0.536378	−	1.65080i
$679$	1833.53	−	5643.02i	0.103629	−	0.318938i
$680$	−522.150	+	1228.90i	−0.0294464	+	0.0693035i
$681$	10415.3	+	32054.9i	0.586071	+	1.80374i
$682$	−21414.2			−1.20233
$683$	3369.89	+	10371.5i	0.188793	+	0.581044i	0.999993	−	0.00372404i	$-0.00118540\pi$
$683$	3369.89	+	10371.5i	0.188793	+	0.581044i	−0.811200	+	0.584768i	$0.801185\pi$
$684$	14469.6	+	10512.8i	0.808860	+	0.587671i
$685$	−20192.7	−	1773.79i	−1.12631	−	0.0989386i
$686$	24560.9	−	17844.5i	1.36696	−	0.993158i
$687$	−3401.30	−	2471.19i	−0.188890	−	0.137237i
$688$	−1426.79	−	1036.62i	−0.0790636	−	0.0574431i
$689$	5817.64	−	4226.76i	0.321675	−	0.233711i
$690$	26015.3	+	2285.27i	1.43534	+	0.126085i
$691$	17991.6	+	13071.6i	0.990494	+	0.719636i	0.960029	−	0.279900i	$-0.0903012\pi$
$691$	17991.6	+	13071.6i	0.990494	+	0.719636i	0.0304648	+	0.999536i	$0.490301\pi$
$692$	20231.8	+	62267.1i	1.11141	+	3.42058i
$693$	2889.81			0.158405
$694$	−5483.86	−	16877.6i	−0.299949	−	0.923148i
$695$	−3130.37	+	7367.48i	−0.170851	+	0.402107i
$696$	−12644.3	+	38915.0i	−0.688620	+	2.11935i
$697$	2.03644	−	6.26753i	0.000110668	−	0.000340602i
$698$	46101.0	−	33494.3i	2.49992	−	1.81630i
$699$	29265.2			1.58357
$700$	16900.4	+	17525.5i	0.912534	+	0.946288i
$701$	−23186.1			−1.24925			−0.624626	−	0.780924i	$-0.714749\pi$
$701$	−23186.1			−1.24925			−0.624626	+	0.780924i	$0.714749\pi$
$702$	−17479.8	+	12699.8i	−0.939792	+	0.682799i
$703$	8681.07	−	26717.6i	0.465737	−	1.43339i
$704$	−7066.75	+	21749.2i	−0.378321	+	1.16435i
$705$	37821.2	+	3322.34i	2.02047	+	0.177484i
$706$	−13703.9	−	42176.1i	−0.730526	−	2.24833i
$707$	−6041.76			−0.321392
$708$	−6507.88	−	20029.2i	−0.345454	−	1.06320i
$709$	6798.49	+	4939.39i	0.360117	+	0.261640i	0.753101	−	0.657905i	$-0.228557\pi$
$709$	6798.49	+	4939.39i	0.360117	+	0.261640i	−0.392984	+	0.919545i	$0.628557\pi$
$710$	−30365.8	−	26415.3i	−1.60508	−	1.39627i
$711$	−4698.74	+	3413.84i	−0.247843	+	0.180069i
$712$	36257.5	+	26342.6i	1.90844	+	1.38656i
$713$	9399.15	+	6828.88i	0.493690	+	0.358687i
$714$	478.031	−	347.310i	0.0250558	−	0.0182041i
$715$	−10309.9	+	6189.88i	−0.539256	+	0.323760i
$716$	−23220.8	−	16870.9i	−1.21202	−	0.880581i
$717$	−12309.0	−	37883.1i	−0.641125	−	1.97318i
$718$	−54191.0			−2.81670
$719$	−2318.10	−	7134.38i	−0.120237	−	0.370052i	0.872766	−	0.488139i	$-0.162324\pi$
$719$	−2318.10	−	7134.38i	−0.120237	−	0.370052i	−0.993003	+	0.118087i	$0.962324\pi$
$720$	−19009.4	−	16536.4i	−0.983944	−	0.855938i
$721$	−4534.70	+	13956.4i	−0.234232	+	0.720891i
$722$	2796.24	−	8605.94i	0.144135	−	0.443601i
$723$	6192.53	−	4499.14i	0.318538	−	0.231431i
$724$	−8610.36			−0.441991
$725$	8727.63	+	9050.46i	0.447084	+	0.463622i
$726$	−24607.9			−1.25797
$727$	−2031.25	+	1475.79i	−0.103624	+	0.0752876i	−0.638391	−	0.769712i	$-0.720400\pi$
$727$	−2031.25	+	1475.79i	−0.103624	+	0.0752876i	0.534766	+	0.845000i	$0.320400\pi$
$728$	−8537.65	+	26276.2i	−0.434652	+	1.33772i
$729$	1350.34	−	4155.92i	0.0686044	−	0.211143i
$730$	645.169	+	2799.03i	0.0327106	+	0.141913i
$731$	5.48656	+	16.8859i	0.000277603	+	0.000854375i
$732$	108432.			5.47508
$733$	−688.054	−	2117.61i	−0.0346710	−	0.106706i	0.932223	−	0.361884i	$-0.117866\pi$
$733$	−688.054	−	2117.61i	−0.0346710	−	0.106706i	−0.966894	+	0.255177i	$0.917866\pi$
$734$	−32091.3	−	23315.7i	−1.61378	−	1.17248i
$735$	3939.15	+	17089.8i	0.197684	+	0.857640i
$736$	25663.4	−	18645.6i	1.28528	−	0.933811i
$737$	−13909.4	−	10105.8i	−0.695197	−	0.505090i
$738$	189.565	+	137.727i	0.00945527	+	0.00686966i
$739$	6654.13	−	4834.51i	0.331226	−	0.240650i	−0.409724	−	0.912209i	$-0.634375\pi$
$739$	6654.13	−	4834.51i	0.331226	−	0.240650i	0.740951	+	0.671559i	$0.234375\pi$
$740$	−34576.9	+	81378.5i	−1.71767	+	4.04261i
$741$	16099.8	+	11697.2i	0.798167	+	0.579902i
$742$	2573.29	+	7919.78i	0.127316	+	0.391839i
$743$	−449.577			−0.0221984			−0.0110992	−	0.999938i	$-0.503533\pi$
$743$	−449.577			−0.0221984			−0.0110992	+	0.999938i	$0.503533\pi$
$744$	−20825.7	−	64095.0i	−1.02622	−	3.15838i
$745$	−6955.37	+	4175.88i	−0.342047	+	0.205359i
$746$	9485.39	−	29193.0i	0.465529	−	1.43275i
$747$	−2292.02	+	7054.10i	−0.112263	+	0.345510i
$748$	732.617	−	532.277i	0.0358117	−	0.0260187i
$749$	4197.95			0.204793
$750$	−43475.5	+	16636.0i	−2.11667	+	0.809950i
$751$	4588.83			0.222968			0.111484	−	0.993766i	$-0.464440\pi$
$751$	4588.83			0.222968			0.111484	+	0.993766i	$0.464440\pi$
$752$	80115.0	−	58206.9i	3.88496	−	2.82259i
$753$	−10125.1	+	31162.0i	−0.490014	+	1.50811i
$754$	−7297.02	+	22457.9i	−0.352443	+	1.08471i
$755$	−29248.2	+	17560.1i	−1.40987	+	0.846460i
$756$	−5539.39	−	17048.5i	−0.266489	−	0.820169i
$757$	3857.39			0.185204			0.0926019	−	0.995703i	$-0.470482\pi$
$757$	3857.39			0.185204			0.0926019	+	0.995703i	$0.470482\pi$
$758$	13280.0	+	40871.6i	0.636346	+	1.95847i
$759$	−8657.89	−	6290.33i	−0.414047	−	0.300823i
$760$	20364.7	−	47929.2i	0.971979	−	2.28760i
$761$	1652.00	−	1200.25i	0.0786924	−	0.0571734i	−0.547743	−	0.836646i	$-0.684513\pi$
$761$	1652.00	−	1200.25i	0.0786924	−	0.0571734i	0.626436	+	0.779473i	$0.284513\pi$
$762$	−27758.8	−	20168.0i	−1.31968	−	0.958804i
$763$	−13746.2	−	9987.19i	−0.652222	−	0.473867i
$764$	24121.7	−	17525.4i	1.14227	−	0.829904i
$765$	56.9724	+	247.171i	0.00269260	+	0.0116817i
$766$	9092.43	+	6606.03i	0.428881	+	0.311600i
$767$	−2269.27	−	6984.08i	−0.106830	−	0.328788i
$768$	1419.86			0.0667121
$769$	2316.48	+	7129.41i	0.108628	+	0.334321i	0.990565	−	0.137046i	$-0.0437607\pi$
$769$	2316.48	+	7129.41i	0.108628	+	0.334321i	−0.881937	+	0.471367i	$0.843761\pi$
$770$	−3127.81	−	13569.8i	−0.146388	−	0.635094i
$771$	−10945.5	+	33686.9i	−0.511276	+	1.57355i
$772$	−9593.70	+	29526.4i	−0.447260	+	1.37653i
$773$	−9488.89	+	6894.08i	−0.441516	+	0.320780i	−0.786237	−	0.617925i	$-0.787973\pi$
$773$	−9488.89	+	6894.08i	−0.441516	+	0.320780i	0.344721	+	0.938705i	$0.387973\pi$
$774$	−631.291			−0.0293169
$775$	−20391.4	−	3610.35i	−0.945135	−	0.167339i
$776$	39944.8			1.84786
$777$	19126.7	−	13896.4i	0.883099	−	0.641609i
$778$	11014.3	−	33898.5i	0.507560	−	1.56211i
$779$	−79.4245	+	244.443i	−0.00365299	+	0.0112427i
$780$	−47257.1	−	41109.2i	−2.16933	−	1.88711i
$781$	5096.54	+	15685.5i	0.233506	+	0.718659i
$782$	−685.751			−0.0313586
$783$	−2860.63	−	8804.13i	−0.130563	−	0.401831i
$784$	37007.2	+	26887.3i	1.68582	+	1.22482i
$785$	20769.4	−	12469.6i	0.944321	−	0.566953i
$786$	−8213.16	+	5967.21i	−0.372715	+	0.270793i
$787$	−6670.93	−	4846.71i	−0.302151	−	0.219526i	0.426370	−	0.904549i	$-0.359792\pi$
$787$	−6670.93	−	4846.71i	−0.302151	−	0.219526i	−0.728521	+	0.685023i	$0.759792\pi$
$788$	5100.05	+	3705.40i	0.230561	+	0.167512i
$789$	1352.44	−	982.606i	0.0610243	−	0.0443368i
$790$	21116.3	+	18369.1i	0.950991	+	0.827272i
$791$	7171.93	+	5210.71i	0.322382	+	0.234225i
$792$	6011.82	+	18502.5i	0.269723	+	0.830123i
$793$	37809.7			1.69314
$794$	10778.6	+	33173.2i	0.481762	+	1.48271i
$795$	−11363.1	−	998.168i	−0.506926	−	0.0445300i
$796$	−9080.37	+	27946.5i	−0.404328	+	1.24439i
$797$	−4254.84	+	13095.1i	−0.189102	+	0.581996i	−0.999995	−	0.00319879i	$-0.998982\pi$
$797$	−4254.84	+	13095.1i	−0.189102	+	0.581996i	0.810893	+	0.585194i	$0.198982\pi$
$798$	−18644.0	+	13545.6i	−0.827055	+	0.600890i
$799$	−996.948			−0.0441420
$800$	−26580.2	+	49905.4i	−1.17469	+	2.20553i
$801$	8513.78			0.375555
$802$	−44219.6	+	32127.4i	−1.94694	+	1.41454i
$803$	363.736	−	1119.46i	0.0159850	−	0.0491968i
$804$	27673.1	−	85169.0i	1.21387	−	3.73592i
$805$	−2954.49	+	6953.54i	−0.129357	+	0.304447i
$806$	−12018.6	−	36989.3i	−0.525231	−	1.61649i
$807$	422.730			0.0184397
$808$	−12569.0	−	38683.5i	−0.547248	−	1.68426i
$809$	29901.2	+	21724.5i	1.29947	+	0.944119i	0.999950	−	0.00997139i	$-0.00317405\pi$
$809$	29901.2	+	21724.5i	1.29947	+	0.944119i	0.299518	+	0.954091i	$0.403174\pi$
$810$	53825.6	+	4728.21i	2.33486	+	0.205102i
$811$	11900.0	−	8645.89i	0.515249	−	0.374351i	−0.299562	−	0.954077i	$-0.596841\pi$
$811$	11900.0	−	8645.89i	0.515249	−	0.374351i	0.814811	+	0.579726i	$0.196841\pi$
$812$	−15849.7	−	11515.5i	−0.684994	−	0.497677i
$813$	−21518.9	−	15634.4i	−0.928291	−	0.674443i
$814$	40914.7	−	29726.3i	1.76174	−	1.27998i
$815$	−866.525	−	76.1184i	−0.0372430	−	0.00327155i
$816$	1707.91	+	1240.87i	0.0732707	+	0.0532343i
$817$	−213.985	−	658.577i	−0.00916325	−	0.0282016i
$818$	−35351.8			−1.51106
$819$	1621.89	+	4991.65i	0.0691981	+	0.212970i
$820$	316.350	−	744.544i	0.0134724	−	0.0317081i
$821$	−11760.0	+	36193.6i	−0.499911	+	1.53857i	0.309249	+	0.950981i	$0.399922\pi$
$821$	−11760.0	+	36193.6i	−0.499911	+	1.53857i	−0.809160	+	0.587588i	$0.800078\pi$
$822$	−18661.3	+	57433.6i	−0.791834	+	2.43701i
$823$	3323.08	−	2414.36i	0.140748	−	0.102259i	−0.515183	−	0.857080i	$-0.672276\pi$
$823$	3323.08	−	2414.36i	0.140748	−	0.102259i	0.655931	+	0.754821i	$0.272276\pi$
$824$	−98792.0			−4.17668
$825$	18783.2	+	3325.62i	0.792664	+	0.140343i
$826$	8503.95			0.358221
$827$	13578.9	−	9865.62i	0.570959	−	0.414826i	−0.264494	−	0.964387i	$-0.585205\pi$
$827$	13578.9	−	9865.62i	0.570959	−	0.414826i	0.835453	+	0.549561i	$0.185205\pi$
$828$	5398.12	−	16613.7i	0.226567	−	0.697302i
$829$	−3997.64	+	12303.5i	−0.167483	+	0.515461i	−0.999211	−	0.0397237i	$-0.987352\pi$
$829$	−3997.64	+	12303.5i	−0.167483	+	0.515461i	0.831727	+	0.555184i	$0.187352\pi$
$830$	35605.1	+	3127.67i	1.48900	+	0.130799i
$831$	−16927.7	−	52098.0i	−0.706636	−	2.17480i
$832$	−41534.3			−1.73070
$833$	−142.307	−	437.977i	−0.00591915	−	0.0182173i
$834$	19293.5	+	14017.6i	0.801056	+	0.582001i
$835$	1066.13	+	927.433i	0.0441857	+	0.0384373i
$836$	−28573.2	+	20759.7i	−1.18209	+	0.858837i
$837$	12335.2	+	8962.02i	0.509397	+	0.370099i
$838$	18747.5	+	13620.9i	0.772819	+	0.561486i
$839$	−34205.0	+	24851.4i	−1.40750	+	1.02261i	−0.413815	+	0.910361i	$0.635804\pi$
$839$	−34205.0	+	24851.4i	−1.40750	+	1.02261i	−0.993681	+	0.112244i	$0.964196\pi$
$840$	37574.1	−	22558.8i	1.54337	−	0.926612i
$841$	11546.1	+	8388.71i	0.473413	+	0.343955i
$842$	−13869.5	−	42686.0i	−0.567666	−	1.74710i
$843$	−43775.5			−1.78850
$844$	16456.2	+	50646.9i	0.671144	+	2.06557i
$845$	2054.09	+	1786.86i	0.0836245	+	0.0727453i
$846$	10953.8	−	33712.4i	0.445154	−	1.37004i
$847$	2199.90	−	6770.60i	0.0892438	−	0.274664i
$848$	−24069.9	+	17487.8i	−0.974720	+	0.708176i
$849$	−41832.3			−1.69103
$850$	1098.99	−	535.056i	0.0443471	−	0.0215909i
$851$	−27437.9			−1.10524
$852$	−69498.3	+	50493.5i	−2.79457	+	2.03037i
$853$	8807.70	−	27107.3i	0.353540	−	1.08809i	−0.603310	−	0.797506i	$-0.706152\pi$
$853$	8807.70	−	27107.3i	0.353540	−	1.08809i	0.956851	−	0.290579i	$-0.0938480\pi$
$854$	−13530.2	+	41641.6i	−0.542146	+	1.66855i
$855$	−2222.01	−	9640.07i	−0.0888786	−	0.385595i
$856$	8733.23	+	26878.1i	0.348710	+	1.07322i
$857$	4999.42			0.199273			0.0996366	−	0.995024i	$-0.468232\pi$
$857$	4999.42			0.199273			0.0996366	+	0.995024i	$0.468232\pi$
$858$	11070.7	+	34072.2i	0.440499	+	1.35572i
$859$	−20283.7	−	14737.0i	−0.805669	−	0.585353i	0.106902	−	0.994270i	$-0.465907\pi$
$859$	−20283.7	−	14737.0i	−0.805669	−	0.585353i	−0.912572	+	0.408916i	$0.865907\pi$
$860$	489.535	+	2123.82i	0.0194105	+	0.0842111i
$861$	−174.994	+	127.140i	−0.00692656	+	0.00503244i
$862$	−1722.72	−	1251.63i	−0.0680695	−	0.0494554i
$863$	−3644.26	−	2647.71i	−0.143745	−	0.104437i	0.513588	−	0.858037i	$-0.328316\pi$
$863$	−3644.26	−	2647.71i	−0.143745	−	0.104437i	−0.657334	+	0.753600i	$0.728316\pi$
$864$	33679.9	−	24469.9i	1.32617	−	0.963522i
$865$	14161.6	−	33329.9i	0.556656	−	1.31012i
$866$	−55579.9	−	40381.2i	−2.18093	−	1.58454i
$867$	9513.83	+	29280.6i	0.372672	+	1.14697i
$868$	32267.9			1.26180
$869$	−3544.12	−	10907.7i	−0.138350	−	0.425797i
$870$	32114.1	−	19280.7i	1.25146	−	0.751354i
$871$	9649.46	−	29698.0i	0.375384	−	1.15531i
$872$	35347.8	−	108789.i	1.37274	−	4.22485i
$873$	6139.03	−	4460.27i	0.238001	−	0.172918i
$874$	26745.4			1.03510
$875$	−690.599	−	13449.0i	−0.0266817	−	0.519611i
$876$	6130.94			0.236467
$877$	−8221.02	+	5972.92i	−0.316538	+	0.229979i	−0.734697	−	0.678395i	$-0.762676\pi$
$877$	−8221.02	+	5972.92i	−0.316538	+	0.229979i	0.418159	+	0.908374i	$0.362676\pi$
$878$	−9254.78	+	28483.3i	−0.355733	+	1.09483i
$879$	8146.95	−	25073.7i	0.312616	−	0.962134i
$880$	42656.1	−	25610.0i	1.63402	−	0.981036i
$881$	−10338.8	−	31819.5i	−0.395372	−	1.21683i	−0.928672	−	0.370903i	$-0.879048\pi$
$881$	−10338.8	−	31819.5i	−0.395372	−	1.21683i	0.533300	−	0.845926i	$-0.320952\pi$
$882$	16374.0			0.625105
$883$	4567.13	+	14056.2i	0.174061	+	0.535706i	0.999589	−	0.0286552i	$-0.00912250\pi$
$883$	4567.13	+	14056.2i	0.174061	+	0.535706i	−0.825528	+	0.564361i	$0.809122\pi$
$884$	1330.60	+	966.734i	0.0506253	+	0.0367814i
$885$	−4555.30	+	10721.1i	−0.173022	+	0.407216i
$886$	−12149.2	+	8826.93i	−0.460678	+	0.334702i
$887$	12478.8	+	9066.41i	0.472377	+	0.343202i	0.798367	−	0.602171i	$-0.205698\pi$
$887$	12478.8	+	9066.41i	0.472377	+	0.343202i	−0.325990	+	0.945373i	$0.605698\pi$
$888$	128765.	+	93553.0i	4.86606	+	3.53540i
$889$	8030.58	−	5834.56i	0.302966	−	0.220118i
$890$	−9214.97	−	39978.6i	−0.347064	−	1.50571i
$891$	−17913.1	−	13014.7i	−0.673527	−	0.489346i
$892$	21838.7	+	67212.5i	0.819745	+	2.52292i
$893$	38882.6			1.45706
$894$	7468.65	+	22986.2i	0.279406	+	0.859924i
$895$	3565.88	+	15470.4i	0.133178	+	0.577785i
$896$	4087.56	−	12580.2i	0.152406	−	0.469057i
$897$	6006.29	−	18485.4i	0.223572	−	0.688084i
$898$	−64087.2	+	46562.1i	−2.38153	+	1.73028i
$899$	16663.7			0.618203
$900$	4311.75	+	30837.1i	0.159694	+	1.14212i
$901$	299.525			0.0110750
$902$	−374.335	+	271.970i	−0.0138182	+	0.0100395i
$903$	180.084	−	554.242i	0.00663657	−	0.0204253i
$904$	−18442.3	+	56759.7i	−0.678521	+	2.08827i
$905$	3593.27	+	3125.80i	0.131983	+	0.114812i
$906$	31406.6	+	96659.6i	1.15167	+	3.54448i
$907$	43594.8			1.59596			0.797982	−	0.602681i	$-0.205901\pi$
$907$	43594.8			1.59596			0.797982	+	0.602681i	$0.205901\pi$
$908$	−33572.1	−	103324.i	−1.22701	−	3.77636i
$909$	−6251.13	−	4541.71i	−0.228093	−	0.165719i
$910$	21684.1	−	13018.7i	0.789913	−	0.474249i
$911$	42130.2	−	30609.4i	1.53220	−	1.11321i	0.577205	−	0.816599i	$-0.304143\pi$
$911$	42130.2	−	30609.4i	1.53220	−	1.11321i	0.954998	−	0.296612i	$-0.0958568\pi$
$912$	−66611.3	−	48395.9i	−2.41855	−	1.75718i
$913$	−11849.4	−	8609.06i	−0.429525	−	0.312068i
$914$	28235.0	−	20514.0i	1.02181	−	0.742386i
$915$	−45250.7	−	39363.8i	−1.63491	−	1.42222i
$916$	10963.6	+	7965.50i	0.395466	+	0.287323i
$917$	−907.572	−	2793.22i	−0.0326834	−	0.100589i
$918$	−899.960			−0.0323563
$919$	4485.22	+	13804.1i	0.160994	+	0.495490i	0.998719	−	0.0506033i	$-0.0161144\pi$
$919$	4485.22	+	13804.1i	0.160994	+	0.495490i	−0.837724	+	0.546093i	$0.816114\pi$
$920$	−50667.6	−	4450.81i	−1.81572	−	0.159499i
$921$	−2637.41	+	8117.11i	−0.0943600	+	0.290410i
$922$	22848.0	−	70318.9i	0.816116	−	2.51175i
$923$	−24233.7	+	17606.8i	−0.864206	+	0.627882i
$924$	−29723.1			−1.05824
$925$	43972.3	−	21408.4i	1.56303	−	0.760978i
$926$	61693.3			2.18938
$927$	−15183.1	+	11031.2i	−0.537949	+	0.390843i
$928$	14059.8	−	43271.6i	0.497345	−	1.53067i
$929$	8814.66	−	27128.7i	0.311302	−	0.958089i	−0.665948	−	0.745998i	$-0.731973\pi$
$929$	8814.66	−	27128.7i	0.311302	−	0.958089i	0.977250	−	0.212091i	$-0.0680273\pi$
$930$	−24125.9	+	56781.5i	−0.850666	+	2.00209i
$931$	5550.21	+	17081.8i	0.195382	+	0.601324i
$932$	−94332.2			−3.31540
$933$	−4767.51	−	14672.9i	−0.167290	−	0.514865i
$934$	−24369.6	−	17705.6i	−0.853746	−	0.620283i
$935$	−498.966	−	43.8308i	−0.0174524	−	0.00153307i
$936$	−28585.8	+	20768.8i	−0.998245	+	0.725267i
$937$	−22316.8	−	16214.1i	−0.778077	−	0.565306i	0.126324	−	0.991989i	$-0.459682\pi$
$937$	−22316.8	−	16214.1i	−0.778077	−	0.565306i	−0.904401	+	0.426683i	$0.859682\pi$
$938$	29254.7	+	21254.8i	1.01834	+	0.739866i
$939$	−14630.6	+	10629.7i	−0.508468	+	0.369423i
$940$	−121911.	−	10709.1i	−4.23011	−	0.371586i
$941$	2094.39	+	1521.66i	0.0725560	+	0.0527150i	0.623472	−	0.781846i	$-0.285722\pi$
$941$	2094.39	+	1521.66i	0.0725560	+	0.0527150i	−0.550916	+	0.834561i	$0.685722\pi$
$942$	−22302.1	−	68638.8i	−0.771382	−	2.37407i
$943$	251.034			0.00866892
$944$	9388.85	+	28895.9i	0.323709	+	0.996273i
$945$	−3877.38	+	9125.61i	−0.133472	+	0.314134i
$946$	385.224	−	1185.60i	0.0132397	−	0.0407475i
$947$	−7157.52	+	22028.6i	−0.245605	+	0.755895i	0.749931	+	0.661516i	$0.230087\pi$
$947$	−7157.52	+	22028.6i	−0.245605	+	0.755895i	−0.995536	+	0.0943789i	$0.969913\pi$
$948$	48328.9	−	35113.0i	1.65575	−	1.20297i
$949$	2137.83			0.0731263
$950$	−42862.4	+	20868.1i	−1.46383	+	0.712683i
$951$	47061.3			1.60470
$952$	−931.016	+	676.423i	−0.0316958	+	0.0230284i
$953$	−13151.0	+	40474.6i	−0.447012	+	1.37576i	0.433250	+	0.901274i	$0.357367\pi$
$953$	−13151.0	+	40474.6i	−0.447012	+	1.37576i	−0.880262	+	0.474488i	$0.842633\pi$
$954$	−3290.99	+	10128.6i	−0.111687	+	0.343738i
$955$	−16428.6	−	1443.14i	−0.556668	−	0.0488995i
$956$	39676.1	+	122110.i	1.34228	+	4.13110i
$957$	−15349.5			−0.518473
$958$	−12414.8	−	38208.8i	−0.418689	−	1.28859i
$959$	−14133.9	−	10268.9i	−0.475921	−	0.345777i
$960$	49708.3	+	43241.5i	1.67118	+	1.45376i
$961$	1897.20	−	1378.40i	0.0636838	−	0.0462690i
$962$	74310.2	+	53989.6i	2.49050	+	1.80945i
$963$	4343.42	+	3155.68i	0.145342	+	0.105597i
$964$	−19960.7	+	14502.3i	−0.666899	+	0.484531i
$965$	14722.5	−	8839.14i	0.491125	−	0.294862i
$966$	18209.5	+	13230.0i	0.606503	+	0.440651i
$967$	9275.49	+	28547.0i	0.308459	+	0.949339i	0.978364	+	0.206892i	$0.0663348\pi$
$967$	9275.49	+	28547.0i	0.308459	+	0.949339i	−0.669905	+	0.742447i	$0.733665\pi$
$968$	47926.6			1.59134
$969$	256.147	+	788.339i	0.00849187	+	0.0261353i
$970$	−27589.0	−	23999.8i	−0.913225	−	0.794419i
$971$	−2208.86	+	6798.18i	−0.0730028	+	0.224680i	−0.980900	−	0.194514i	$-0.937687\pi$
$971$	−2208.86	+	6798.18i	−0.0730028	+	0.224680i	0.907897	+	0.419193i	$0.137687\pi$
$972$	20117.2	−	61914.4i	0.663848	−	2.04311i
$973$	−5581.59	+	4055.26i	−0.183903	+	0.133613i
$974$	−24575.6			−0.808474
$975$	4797.52	+	34311.3i	0.157583	+	1.12702i
$976$	−156434.			−5.13045
$977$	−37940.6	+	27565.5i	−1.24240	+	0.902658i	−0.997756	−	0.0669543i	$-0.978672\pi$
$977$	−37940.6	+	27565.5i	−1.24240	+	0.902658i	−0.244646	+	0.969612i	$0.578672\pi$
$978$	−800.810	+	2464.64i	−0.0261831	+	0.0805833i
$979$	−5195.25	+	15989.3i	−0.169603	+	0.521983i
$980$	−12697.3	−	55086.3i	−0.413877	−	1.79558i
$981$	−6714.97	−	20666.5i	−0.218545	−	0.672612i
$982$	93388.9			3.03479
$983$	18941.8	+	58296.8i	0.614597	+	1.89154i	0.407456	+	0.913225i	$0.366416\pi$
$983$	18941.8	+	58296.8i	0.614597	+	1.89154i	0.207142	+	0.978311i	$0.433584\pi$
$984$	−1178.09	−	855.930i	−0.0381667	−	0.0277297i
$985$	−783.184	−	3397.80i	−0.0253343	−	0.109911i
$986$	−795.727	+	578.130i	−0.0257009	+	0.0186728i
$987$	26473.1	+	19233.8i	0.853747	+	0.620283i
$988$	−51895.3	−	37704.2i	−1.67106	−	1.21410i
$989$	−547.165	+	397.539i	−0.0175924	+	0.0127816i
$990$	6964.49	−	16391.3i	0.223582	−	0.526211i
$991$	−12484.0	−	9070.14i	−0.400168	−	0.290739i	0.369441	−	0.929254i	$-0.379549\pi$
$991$	−12484.0	−	9070.14i	−0.400168	−	0.290739i	−0.769609	+	0.638515i	$0.779549\pi$
$992$	23157.2	+	71270.6i	0.741172	+	2.28109i
$993$	6494.83			0.207560
$994$	−10719.2	−	32990.3i	−0.342045	−	1.05270i
$995$	13934.8	−	8366.19i	0.443982	−	0.266559i
$996$	23574.5	−	72554.9i	0.749987	−	2.30822i
$997$	6645.80	−	20453.7i	0.211108	−	0.649723i	−0.788299	−	0.615292i	$-0.789038\pi$
$997$	6645.80	−	20453.7i	0.211108	−	0.649723i	0.999407	−	0.0344311i	$-0.0109619\pi$
$998$	−12821.3	+	9315.21i	−0.406664	+	0.295459i
$999$	−36008.7			−1.14041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.d.a.11.7	✓	28
3.2	odd	2		225.4.h.b.136.1		28
5.2	odd	4		125.4.e.b.74.14		56
5.3	odd	4		125.4.e.b.74.1		56
5.4	even	2		125.4.d.a.51.1		28
25.4	even	10		625.4.a.d.1.14		14
25.9	even	10		125.4.d.a.76.1		28
25.12	odd	20		125.4.e.b.49.1		56
25.13	odd	20		125.4.e.b.49.14		56
25.16	even	5	inner	25.4.d.a.16.7	yes	28
25.21	even	5		625.4.a.c.1.1		14
75.41	odd	10		225.4.h.b.91.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.7	✓	28	1.1	even	1	trivial
25.4.d.a.16.7	yes	28	25.16	even	5	inner
125.4.d.a.51.1		28	5.4	even	2
125.4.d.a.76.1		28	25.9	even	10
125.4.e.b.49.1		56	25.12	odd	20
125.4.e.b.49.14		56	25.13	odd	20
125.4.e.b.74.1		56	5.3	odd	4
125.4.e.b.74.14		56	5.2	odd	4
225.4.h.b.91.1		28	75.41	odd	10
225.4.h.b.136.1		28	3.2	odd	2
625.4.a.c.1.1		14	25.21	even	5
625.4.a.d.1.14		14	25.4	even	10

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.29718 - 3.12208i) q^{2} +(-1.93780 + 5.96393i) q^{3} +(6.24620 - 19.2238i) q^{4} +(-9.58545 + 5.75493i) q^{5} +(10.2928 + 31.6780i) q^{6} -9.63602 q^{7} +(-20.0464 - 61.6963i) q^{8} +(-9.96993 - 7.24358i) q^{9} +O(q^{10})\)	\(q+(4.29718 - 3.12208i) q^{2} +(-1.93780 + 5.96393i) q^{3} +(6.24620 - 19.2238i) q^{4} +(-9.58545 + 5.75493i) q^{5} +(10.2928 + 31.6780i) q^{6} -9.63602 q^{7} +(-20.0464 - 61.6963i) q^{8} +(-9.96993 - 7.24358i) q^{9} +(-23.2230 + 54.6565i) q^{10} +(19.6877 - 14.3039i) q^{11} +(102.546 + 74.5038i) q^{12} +(35.7572 + 25.9791i) q^{13} +(-41.4077 + 30.0844i) q^{14} +(-15.7473 - 68.3188i) q^{15} +(-147.942 - 107.486i) q^{16} +(0.568894 + 1.75088i) q^{17} -65.4576 q^{18} +(-22.1878 - 68.2870i) q^{19} +(50.7592 + 220.216i) q^{20} +(18.6727 - 57.4685i) q^{21} +(39.9434 - 122.933i) q^{22} +(-56.7348 + 41.2202i) q^{23} +406.798 q^{24} +(58.7616 - 110.327i) q^{25} +234.764 q^{26} +(-74.4571 + 54.0962i) q^{27} +(-60.1885 + 185.241i) q^{28} +(-31.0824 + 95.6617i) q^{29} +(-280.966 - 244.414i) q^{30} +(-51.1943 - 157.560i) q^{31} -452.340 q^{32} +(47.1569 + 145.134i) q^{33} +(7.91102 + 5.74769i) q^{34} +(92.3655 - 55.4546i) q^{35} +(-201.524 + 146.415i) q^{36} +(316.532 + 229.974i) q^{37} +(-308.542 - 224.169i) q^{38} +(-224.228 + 162.911i) q^{39} +(547.211 + 476.022i) q^{40} +(-2.89600 - 2.10407i) q^{41} +(-99.1818 - 305.250i) q^{42} +9.64426 q^{43} +(-152.003 - 467.818i) q^{44} +(137.253 + 12.0567i) q^{45} +(-115.107 + 354.261i) q^{46} +(-167.342 + 515.027i) q^{47} +(927.719 - 674.027i) q^{48} -250.147 q^{49} +(-91.9413 - 657.554i) q^{50} -11.5445 q^{51} +(722.765 - 525.119i) q^{52} +(50.2766 - 154.735i) q^{53} +(-151.062 + 464.922i) q^{54} +(-106.397 + 250.411i) q^{55} +(193.167 + 594.507i) q^{56} +450.254 q^{57} +(165.097 + 508.117i) q^{58} +(-134.417 - 97.6599i) q^{59} +(-1411.71 - 124.009i) q^{60} +(692.078 - 502.824i) q^{61} +(-711.905 - 517.230i) q^{62} +(96.0704 + 69.7993i) q^{63} +(-760.253 + 552.356i) q^{64} +(-492.256 - 43.2414i) q^{65} +(655.762 + 476.439i) q^{66} +(-218.322 - 671.926i) q^{67} +37.2120 q^{68} +(-135.894 - 418.239i) q^{69} +(223.777 - 526.671i) q^{70} +(-209.430 + 644.559i) q^{71} +(-247.041 + 760.316i) q^{72} +(39.1313 - 28.4306i) q^{73} +2078.19 q^{74} +(544.115 + 564.242i) q^{75} -1451.33 q^{76} +(-189.711 + 137.833i) q^{77} +(-454.925 + 1400.12i) q^{78} +(145.637 - 448.225i) q^{79} +(2036.66 + 178.907i) q^{80} +(-281.164 - 865.334i) q^{81} -19.0137 q^{82} +(-185.987 - 572.410i) q^{83} +(-988.132 - 717.920i) q^{84} +(-15.5293 - 13.5090i) q^{85} +(41.4431 - 30.1102i) q^{86} +(-510.288 - 370.746i) q^{87} +(-1277.17 - 927.915i) q^{88} +(-558.915 + 406.075i) q^{89} +(627.441 - 376.704i) q^{90} +(-344.557 - 250.335i) q^{91} +(438.034 + 1348.13i) q^{92} +1038.88 q^{93} +(888.856 + 2735.62i) q^{94} +(605.666 + 526.872i) q^{95} +(876.544 - 2697.72i) q^{96} +(-190.279 + 585.617i) q^{97} +(-1074.93 + 780.980i) q^{98} -299.896 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

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