LMFDB - Embedded newform 120.4.b.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(11,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("120.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.b (of order $2$, degree $1$, 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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	120.11
Dual form			120.4.b.a.11.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.03621 - 1.96312i) q^{2} +(5.02993 + 1.30378i) q^{3} +(0.292289 - 7.99466i) q^{4} +5.00000 q^{5} +(12.8015 - 7.21960i) q^{6} -8.16056i q^{7} +(-15.0993 - 16.8526i) q^{8} +(23.6003 + 13.1158i) q^{9} +O(q^{10})$	\(q+(2.03621 - 1.96312i) q^{2} +(5.02993 + 1.30378i) q^{3} +(0.292289 - 7.99466i) q^{4} +5.00000 q^{5} +(12.8015 - 7.21960i) q^{6} -8.16056i q^{7} +(-15.0993 - 16.8526i) q^{8} +(23.6003 + 13.1158i) q^{9} +(10.1810 - 9.81562i) q^{10} +16.0096i q^{11} +(11.8935 - 39.8315i) q^{12} -41.4411i q^{13} +(-16.0202 - 16.6166i) q^{14} +(25.1496 + 6.51890i) q^{15} +(-63.8291 - 4.67350i) q^{16} +83.3315i q^{17} +(73.8032 - 19.6238i) q^{18} +54.9691 q^{19} +(1.46144 - 39.9733i) q^{20} +(10.6396 - 41.0470i) q^{21} +(31.4288 + 32.5989i) q^{22} -66.4506 q^{23} +(-53.9765 - 104.453i) q^{24} +25.0000 q^{25} +(-81.3541 - 84.3828i) q^{26} +(101.608 + 96.7413i) q^{27} +(-65.2409 - 2.38524i) q^{28} -153.913 q^{29} +(64.0073 - 36.0980i) q^{30} -11.4551i q^{31} +(-139.144 + 115.788i) q^{32} +(-20.8730 + 80.5271i) q^{33} +(163.590 + 169.680i) q^{34} -40.8028i q^{35} +(111.755 - 184.843i) q^{36} +245.472i q^{37} +(111.929 - 107.911i) q^{38} +(54.0301 - 208.446i) q^{39} +(-75.4967 - 84.2629i) q^{40} -14.3614i q^{41} +(-58.9160 - 104.467i) q^{42} -485.435 q^{43} +(127.991 + 4.67943i) q^{44} +(118.002 + 65.5791i) q^{45} +(-135.307 + 130.451i) q^{46} +70.6298 q^{47} +(-314.963 - 106.726i) q^{48} +276.405 q^{49} +(50.9052 - 49.0781i) q^{50} +(-108.646 + 419.151i) q^{51} +(-331.308 - 12.1128i) q^{52} +514.271 q^{53} +(396.810 - 2.48319i) q^{54} +80.0480i q^{55} +(-137.527 + 123.219i) q^{56} +(276.491 + 71.6676i) q^{57} +(-313.398 + 302.150i) q^{58} +488.922i q^{59} +(59.4673 - 199.157i) q^{60} +886.970i q^{61} +(-22.4878 - 23.3250i) q^{62} +(107.033 - 192.592i) q^{63} +(-56.0196 + 508.926i) q^{64} -207.206i q^{65} +(115.583 + 204.946i) q^{66} -780.508 q^{67} +(666.207 + 24.3569i) q^{68} +(-334.242 - 86.6369i) q^{69} +(-80.1010 - 83.0830i) q^{70} -520.694 q^{71} +(-135.314 - 595.767i) q^{72} +490.267 q^{73} +(481.893 + 499.833i) q^{74} +(125.748 + 32.5945i) q^{75} +(16.0669 - 439.459i) q^{76} +130.647 q^{77} +(-299.189 - 530.507i) q^{78} -1158.28i q^{79} +(-319.146 - 23.3675i) q^{80} +(384.950 + 619.075i) q^{81} +(-28.1933 - 29.2429i) q^{82} -1106.27i q^{83} +(-325.047 - 97.0573i) q^{84} +416.657i q^{85} +(-988.447 + 952.969i) q^{86} +(-774.170 - 200.668i) q^{87} +(269.803 - 241.734i) q^{88} -1245.71i q^{89} +(369.016 - 98.1190i) q^{90} -338.183 q^{91} +(-19.4228 + 531.250i) q^{92} +(14.9349 - 57.6184i) q^{93} +(143.817 - 138.655i) q^{94} +274.846 q^{95} +(-850.847 + 400.993i) q^{96} +296.653 q^{97} +(562.819 - 542.618i) q^{98} +(-209.979 + 377.832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	2.03621	−	1.96312i	0.719908	−	0.694069i
$2$	2.03621	−	1.96312i	0.719908	−	0.694069i
$3$	5.02993	+	1.30378i	0.968010	+	0.250912i
$3$	5.02993	+	1.30378i	0.968010	+	0.250912i
$4$	0.292289	−	7.99466i	0.0365361	−	0.999332i
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	12.8015	−	7.21960i	0.871029	−	0.491232i
$7$		−	8.16056i		−	0.440629i	−0.975429	−	0.220314i	$-0.929292\pi$
$7$		−	8.16056i		−	0.440629i	0.975429	−	0.220314i	$-0.0707083\pi$
$8$	−15.0993	−	16.8526i	−0.667303	−	0.744786i
$9$	23.6003	+	13.1158i	0.874086	+	0.485771i
$10$	10.1810	−	9.81562i	0.321953	−	0.310397i
$11$			16.0096i			0.438825i	0.975632	+	0.219413i	$0.0704141\pi$
$11$			16.0096i			0.438825i	−0.975632	+	0.219413i	$0.929586\pi$
$12$	11.8935	−	39.8315i	0.286112	−	0.958196i
$13$		−	41.4411i		−	0.884131i	−0.896983	−	0.442066i	$-0.854246\pi$
$13$		−	41.4411i		−	0.884131i	0.896983	−	0.442066i	$-0.145754\pi$
$14$	−16.0202	−	16.6166i	−0.305827	−	0.317212i
$15$	25.1496	+	6.51890i	0.432907	+	0.112211i
$16$	−63.8291	−	4.67350i	−0.997330	−	0.0730234i
$17$			83.3315i			1.18887i	0.804142	+	0.594437i	$0.202625\pi$
$17$			83.3315i			1.18887i	−0.804142	+	0.594437i	$0.797375\pi$
$18$	73.8032	−	19.6238i	0.966421	−	0.256965i
$19$	54.9691			0.663725			0.331863	−	0.943328i	$-0.392323\pi$
$19$	54.9691			0.663725			0.331863	+	0.943328i	$0.392323\pi$
$20$	1.46144	−	39.9733i	0.0163394	−	0.446915i
$21$	10.6396	−	41.0470i	0.110559	−	0.426533i
$22$	31.4288	+	32.5989i	0.304575	+	0.315914i
$23$	−66.4506			−0.602431			−0.301215	−	0.953556i	$-0.597392\pi$
$23$	−66.4506			−0.602431			−0.301215	+	0.953556i	$0.597392\pi$
$24$	−53.9765	−	104.453i	−0.459080	−	0.888395i
$25$	25.0000			0.200000
$26$	−81.3541	−	84.3828i	−0.613648	−	0.636493i
$27$	101.608	+	96.7413i	0.724238	+	0.689551i
$28$	−65.2409	−	2.38524i	−0.440335	−	0.0160989i
$29$	−153.913			−0.985548			−0.492774	−	0.870157i	$-0.664017\pi$
$29$	−153.913			−0.985548			−0.492774	+	0.870157i	$0.664017\pi$
$30$	64.0073	−	36.0980i	0.389536	−	0.219686i
$31$		−	11.4551i		−	0.0663677i	−0.999449	−	0.0331839i	$-0.989435\pi$
$31$		−	11.4551i		−	0.0663677i	0.999449	−	0.0331839i	$-0.0105647\pi$
$32$	−139.144	+	115.788i	−0.768670	+	0.639646i
$33$	−20.8730	+	80.5271i	−0.110107	+	0.424787i
$34$	163.590	+	169.680i	0.825161	+	0.855880i
$35$		−	40.8028i		−	0.197055i
$36$	111.755	−	184.843i	0.517383	−	0.855754i
$37$			245.472i			1.09069i	0.838213	+	0.545344i	$0.183601\pi$
$37$			245.472i			1.09069i	−0.838213	+	0.545344i	$0.816399\pi$
$38$	111.929	−	107.911i	0.477821	−	0.460671i
$39$	54.0301	−	208.446i	0.221839	−	0.855847i
$40$	−75.4967	−	84.2629i	−0.298427	−	0.333079i
$41$		−	14.3614i		−	0.0547044i	−0.999626	−	0.0273522i	$-0.991292\pi$
$41$		−	14.3614i		−	0.0547044i	0.999626	−	0.0273522i	$-0.00870756\pi$
$42$	−58.9160	−	104.467i	−0.216451	−	0.383800i
$43$	−485.435			−1.72158			−0.860792	−	0.508956i	$-0.830032\pi$
$43$	−485.435			−1.72158			−0.860792	+	0.508956i	$0.830032\pi$
$44$	127.991	+	4.67943i	0.438532	+	0.0160330i
$45$	118.002	+	65.5791i	0.390903	+	0.217244i
$46$	−135.307	+	130.451i	−0.433695	+	0.418129i
$47$	70.6298			0.219200			0.109600	−	0.993976i	$-0.465043\pi$
$47$	70.6298			0.219200			0.109600	+	0.993976i	$0.465043\pi$
$48$	−314.963	−	106.726i	−0.947103	−	0.320930i
$49$	276.405			0.805846
$50$	50.9052	−	49.0781i	0.143982	−	0.138814i
$51$	−108.646	+	419.151i	−0.298303	+	1.15084i
$52$	−331.308	−	12.1128i	−0.883541	−	0.0323027i
$53$	514.271			1.33284			0.666420	−	0.745577i	$-0.267826\pi$
$53$	514.271			1.33284			0.666420	+	0.745577i	$0.267826\pi$
$54$	396.810	−	2.48319i	0.999980	−	0.00625777i
$55$			80.0480i			0.196249i
$56$	−137.527	+	123.219i	−0.328174	+	0.294033i
$57$	276.491	+	71.6676i	0.642493	+	0.166537i
$58$	−313.398	+	302.150i	−0.709504	+	0.684038i
$59$			488.922i			1.07885i	0.842033	+	0.539426i	$0.181359\pi$
$59$			488.922i			1.07885i	−0.842033	+	0.539426i	$0.818641\pi$
$60$	59.4673	−	199.157i	0.127953	−	0.428518i
$61$			886.970i			1.86172i	0.365378	+	0.930859i	$0.380940\pi$
$61$			886.970i			1.86172i	−0.365378	+	0.930859i	$0.619060\pi$
$62$	−22.4878	−	23.3250i	−0.0460638	−	0.0477787i
$63$	107.033	−	192.592i	0.214045	−	0.385147i
$64$	−56.0196	+	508.926i	−0.109413	+	0.993996i
$65$		−	207.206i		−	0.395395i
$66$	115.583	+	204.946i	0.215565	+	0.382229i
$67$	−780.508			−1.42320			−0.711599	−	0.702586i	$-0.752029\pi$
$67$	−780.508			−1.42320			−0.711599	+	0.702586i	$0.752029\pi$
$68$	666.207	+	24.3569i	1.18808	+	0.0434368i
$69$	−334.242	−	86.6369i	−0.583159	−	0.151157i
$70$	−80.1010	−	83.0830i	−0.136770	−	0.141862i
$71$	−520.694			−0.870352			−0.435176	−	0.900345i	$-0.643314\pi$
$71$	−520.694			−0.870352			−0.435176	+	0.900345i	$0.643314\pi$
$72$	−135.314	−	595.767i	−0.221484	−	0.975164i
$73$	490.267			0.786046			0.393023	−	0.919529i	$-0.371429\pi$
$73$	490.267			0.786046			0.393023	+	0.919529i	$0.371429\pi$
$74$	481.893	+	499.833i	0.757012	+	0.785195i
$75$	125.748	+	32.5945i	0.193602	+	0.0501825i
$76$	16.0669	−	439.459i	0.0242499	−	0.663282i
$77$	130.647			0.193359
$78$	−299.189	−	530.507i	−0.434313	−	0.770104i
$79$		−	1158.28i		−	1.64958i	−0.565436	−	0.824792i	$-0.691292\pi$
$79$		−	1158.28i		−	1.64958i	0.565436	−	0.824792i	$-0.308708\pi$
$80$	−319.146	−	23.3675i	−0.446020	−	0.0326571i
$81$	384.950	+	619.075i	0.528052	+	0.849212i
$82$	−28.1933	−	29.2429i	−0.0379686	−	0.0393822i
$83$		−	1106.27i		−	1.46300i	−0.681841	−	0.731501i	$-0.738820\pi$
$83$		−	1106.27i		−	1.46300i	0.681841	−	0.731501i	$-0.261180\pi$
$84$	−325.047	−	97.0573i	−0.422209	−	0.126069i
$85$			416.657i			0.531681i
$86$	−988.447	+	952.969i	−1.23938	+	1.19490i
$87$	−774.170	−	200.668i	−0.954020	−	0.247286i
$88$	269.803	−	241.734i	0.326831	−	0.292829i
$89$		−	1245.71i		−	1.48365i	−0.670593	−	0.741826i	$-0.733960\pi$
$89$		−	1245.71i		−	1.48365i	0.670593	−	0.741826i	$-0.266040\pi$
$90$	369.016	−	98.1190i	0.432196	−	0.114918i
$91$	−338.183			−0.389574
$92$	−19.4228	+	531.250i	−0.0220105	+	0.602029i
$93$	14.9349	−	57.6184i	0.0166525	−	0.0642446i
$94$	143.817	−	138.655i	0.157804	−	0.152140i
$95$	274.846			0.296827
$96$	−850.847	+	400.993i	−0.904575	+	0.426315i
$97$	296.653			0.310521			0.155261	−	0.987874i	$-0.450378\pi$
$97$	296.653			0.310521			0.155261	+	0.987874i	$0.450378\pi$
$98$	562.819	−	542.618i	0.580135	−	0.559313i
$99$	−209.979	+	377.832i	−0.213169	+	0.383571i
$100$	7.30722	−	199.866i	0.00730722	−	0.199866i
$101$	−35.5352			−0.0350088			−0.0175044	−	0.999847i	$-0.505572\pi$
$101$	−35.5352			−0.0350088			−0.0175044	+	0.999847i	$0.505572\pi$
$102$	601.620	+	1066.76i	0.584013	+	1.03554i
$103$		−	797.892i		−	0.763288i	−0.924309	−	0.381644i	$-0.875358\pi$
$103$		−	797.892i		−	0.763288i	0.924309	−	0.381644i	$-0.124642\pi$
$104$	−698.390	+	625.734i	−0.658489	+	0.589983i
$105$	53.1979	−	205.235i	0.0494436	−	0.190751i
$106$	1047.16	−	1009.58i	0.959522	−	0.925083i
$107$		−	1145.44i		−	1.03490i	−0.855714	−	0.517450i	$-0.826882\pi$
$107$		−	1145.44i		−	1.03490i	0.855714	−	0.517450i	$-0.173118\pi$
$108$	803.112	−	784.043i	0.715551	−	0.698561i
$109$			698.265i			0.613593i	0.951775	+	0.306797i	$0.0992572\pi$
$109$			698.265i			0.613593i	−0.951775	+	0.306797i	$0.900743\pi$
$110$	157.144	+	162.994i	0.136210	+	0.141281i
$111$	−320.042	+	1234.71i	−0.273667	+	1.05580i
$112$	−38.1384	+	520.882i	−0.0321762	+	0.439453i
$113$		−	1990.42i		−	1.65701i	−0.559979	−	0.828507i	$-0.689191\pi$
$113$		−	1990.42i		−	1.65701i	0.559979	−	0.828507i	$-0.310809\pi$
$114$	703.685	−	396.855i	0.578124	−	0.326043i
$115$	−332.253			−0.269415
$116$	−44.9870	+	1230.48i	−0.0360081	+	0.984890i
$117$	543.535	−	978.024i	0.429486	−	0.772806i
$118$	959.815	+	995.547i	0.748797	+	0.776674i
$119$	680.032			0.523852
$120$	−269.883	−	522.267i	−0.205307	−	0.397302i
$121$	1074.69			0.807433
$122$	1741.23	+	1806.06i	1.29216	+	1.34027i
$123$	18.7242	−	72.2370i	0.0137260	−	0.0529544i
$124$	−91.5798	−	3.34820i	−0.0663234	−	0.00242482i
$125$	125.000			0.0894427
$126$	−160.141	−	602.275i	−0.113226	−	0.425833i
$127$		−	1499.36i		−	1.04761i	−0.851839	−	0.523804i	$-0.824512\pi$
$127$		−	1499.36i		−	1.04761i	0.851839	−	0.523804i	$-0.175488\pi$
$128$	885.018	+	1146.25i	0.611135	+	0.791527i
$129$	−2441.70	−	632.900i	−1.66651	−	0.431967i
$130$	−406.770	−	421.914i	−0.274432	−	0.284648i
$131$		−	1403.74i		−	0.936225i	−0.883669	−	0.468112i	$-0.844934\pi$
$131$		−	1403.74i		−	0.936225i	0.883669	−	0.468112i	$-0.155066\pi$
$132$	637.686	+	190.410i	0.420480	+	0.125553i
$133$		−	448.579i		−	0.292457i
$134$	−1589.28	+	1532.23i	−1.02457	+	0.987798i
$135$	508.039	+	483.706i	0.323889	+	0.308376i
$136$	1404.35	−	1258.25i	0.885457	−	0.793339i
$137$			719.755i			0.448853i	0.974491	+	0.224426i	$0.0720509\pi$
$137$			719.755i			0.448853i	−0.974491	+	0.224426i	$0.927949\pi$
$138$	−850.665	+	479.747i	−0.524735	+	0.295933i
$139$	410.342			0.250394			0.125197	−	0.992132i	$-0.460044\pi$
$139$	410.342			0.250394			0.125197	+	0.992132i	$0.460044\pi$
$140$	−326.205	−	11.9262i	−0.196924	−	0.00719963i
$141$	355.263	+	92.0857i	0.212188	+	0.0550001i
$142$	−1060.24	+	1022.19i	−0.626573	+	0.604084i
$143$	663.456			0.387979
$144$	−1445.09	−	947.468i	−0.836280	−	0.548303i
$145$	−769.564			−0.440750
$146$	998.285	−	962.454i	0.565881	−	0.545571i
$147$	1390.30	+	360.371i	0.780067	+	0.202197i
$148$	1962.47	+	71.7488i	1.08996	+	0.0398495i
$149$	−3420.11			−1.88045			−0.940223	−	0.340560i	$-0.889383\pi$
$149$	−3420.11			−1.88045			−0.940223	+	0.340560i	$0.889383\pi$
$150$	320.036	−	180.490i	0.174206	−	0.0982463i
$151$			2784.06i			1.50042i	0.661200	+	0.750209i	$0.270047\pi$
$151$			2784.06i			1.50042i	−0.661200	+	0.750209i	$0.729953\pi$
$152$	−829.998	−	926.372i	−0.442906	−	0.494334i
$153$	−1092.96	+	1966.65i	−0.577521	+	1.03918i
$154$	266.025	−	256.477i	0.139201	−	0.134205i
$155$		−	57.2756i		−	0.0296806i
$156$	−1650.66	−	492.879i	−0.847171	−	0.252961i
$157$		−	3488.39i		−	1.77327i	−0.462468	−	0.886636i	$-0.653036\pi$
$157$		−	3488.39i		−	1.77327i	0.462468	−	0.886636i	$-0.346964\pi$
$158$	−2273.86	−	2358.51i	−1.14493	−	1.18755i
$159$	2586.74	+	670.495i	1.29020	+	0.334426i
$160$	−695.720	+	578.941i	−0.343760	+	0.286058i
$161$			542.274i			0.265448i
$162$	1999.16	+	504.862i	0.969561	+	0.244850i
$163$	894.104			0.429642			0.214821	−	0.976653i	$-0.431083\pi$
$163$	894.104			0.429642			0.214821	+	0.976653i	$0.431083\pi$
$164$	−114.815	−	4.19769i	−0.0546679	−	0.00199869i
$165$	−104.365	+	402.636i	−0.0492412	+	0.189971i
$166$	−2171.75	−	2252.60i	−1.01542	−	1.05323i
$167$	−3541.69			−1.64110			−0.820551	−	0.571574i	$-0.806333\pi$
$167$	−3541.69			−1.64110			−0.820551	+	0.571574i	$0.806333\pi$
$168$	−852.399	+	440.479i	−0.391453	+	0.202284i
$169$	479.632			0.218312
$170$	817.950	+	848.401i	0.369023	+	0.382761i
$171$	1297.29	+	720.966i	0.580153	+	0.322419i
$172$	−141.887	+	3880.89i	−0.0629000	+	1.72044i
$173$	1559.15			0.685202			0.342601	−	0.939481i	$-0.388692\pi$
$173$	1559.15			0.685202			0.342601	+	0.939481i	$0.388692\pi$
$174$	−1970.31	+	1111.19i	−0.858441	+	0.484132i
$175$		−	204.014i		−	0.0881258i
$176$	74.8208	−	1021.88i	0.0320445	−	0.437654i
$177$	−637.447	+	2459.24i	−0.270697	+	1.04434i
$178$	−2445.48	−	2536.52i	−1.02976	−	1.06809i
$179$			3375.49i			1.40947i	0.709469	+	0.704737i	$0.248935\pi$
$179$			3375.49i			1.40947i	−0.709469	+	0.704737i	$0.751065\pi$
$180$	558.773	−	924.214i	0.231381	−	0.382705i
$181$			3698.76i			1.51893i	0.650546	+	0.759467i	$0.274540\pi$
$181$			3698.76i			1.51893i	−0.650546	+	0.759467i	$0.725460\pi$
$182$	−688.611	+	663.895i	−0.280457	+	0.270391i
$183$	−1156.41	+	4461.39i	−0.467128	+	1.80216i
$184$	1003.36	+	1119.86i	0.402004	+	0.448682i
$185$			1227.36i			0.487770i
$186$	−82.7014	−	146.642i	−0.0326019	−	0.0578082i
$187$	−1334.10			−0.521708
$188$	20.6443	−	564.661i	0.00800873	−	0.219054i
$189$	789.463	−	829.176i	0.303836	−	0.319120i
$190$	559.643	−	539.556i	0.213688	−	0.206018i
$191$	3722.29			1.41013			0.705067	−	0.709141i	$-0.250917\pi$
$191$	3722.29			1.41013			0.705067	+	0.709141i	$0.250917\pi$
$192$	−945.302	+	2486.82i	−0.355319	+	0.934745i
$193$	1473.15			0.549427			0.274713	−	0.961526i	$-0.411417\pi$
$193$	1473.15			0.549427			0.274713	+	0.961526i	$0.411417\pi$
$194$	604.048	−	582.367i	0.223547	−	0.215523i
$195$	270.150	−	1042.23i	0.0992096	−	0.382747i
$196$	80.7901	−	2209.77i	0.0294425	−	0.805308i
$197$	54.1531			0.0195850			0.00979251	−	0.999952i	$-0.496883\pi$
$197$	54.1531			0.0195850			0.00979251	+	0.999952i	$0.496883\pi$
$198$	314.169	+	1181.56i	0.112763	+	0.424090i
$199$		−	718.678i		−	0.256009i	−0.991774	−	0.128004i	$-0.959143\pi$
$199$		−	718.678i		−	0.256009i	0.991774	−	0.128004i	$-0.0408571\pi$
$200$	−377.484	−	421.315i	−0.133461	−	0.148957i
$201$	−3925.90	−	1017.61i	−1.37767	−	0.357098i
$202$	−72.3571	+	69.7601i	−0.0252031	+	0.0242985i
$203$			1256.01i			0.434261i
$204$	3319.22	+	991.100i	1.13917	+	0.340151i
$205$		−	71.8072i		−	0.0244646i
$206$	−1566.36	−	1624.67i	−0.529774	−	0.549497i
$207$	−1568.26	−	871.555i	−0.526576	−	0.292644i
$208$	−193.675	+	2645.15i	−0.0645623	+	0.881771i
$209$			880.034i			0.291259i
$210$	−294.580	−	522.335i	−0.0967998	−	0.171641i
$211$	169.468			0.0552922			0.0276461	−	0.999618i	$-0.491199\pi$
$211$	169.468			0.0552922			0.0276461	+	0.999618i	$0.491199\pi$
$212$	150.316	−	4111.42i	0.0486968	−	1.33195i
$213$	−2619.05	−	678.870i	−0.842509	−	0.218382i
$214$	−2248.65	−	2332.36i	−0.718291	−	0.745032i
$215$	−2427.18			−0.769916
$216$	96.1307	−	3173.08i	0.0302818	−	0.999541i
$217$	−93.4802			−0.0292435
$218$	1370.78	+	1421.81i	0.425876	+	0.441731i
$219$	2466.01	+	639.200i	0.760901	+	0.197229i
$220$	639.956	+	23.3971i	0.196118	+	0.00717016i
$221$	3453.35			1.05112
$222$	1772.21	+	3142.41i	0.535780	+	0.950020i
$223$		−	2719.54i		−	0.816655i	−0.912836	−	0.408327i	$-0.866112\pi$
$223$		−	2719.54i		−	0.816655i	0.912836	−	0.408327i	$-0.133888\pi$
$224$	944.897	+	1135.49i	0.281846	+	0.338698i
$225$	590.008	+	327.896i	0.174817	+	0.0971543i
$226$	−3907.43	−	4052.90i	−1.15008	−	1.19290i
$227$		−	2151.74i		−	0.629145i	−0.949234	−	0.314572i	$-0.898139\pi$
$227$		−	2151.74i		−	0.629145i	0.949234	−	0.314572i	$-0.101861\pi$
$228$	653.773	−	2189.50i	0.189900	−	0.635979i
$229$		−	599.977i		−	0.173134i	−0.996246	−	0.0865669i	$-0.972410\pi$
$229$		−	599.977i		−	0.173134i	0.996246	−	0.0865669i	$-0.0275896\pi$
$230$	−676.536	+	652.254i	−0.193954	+	0.186993i
$231$	657.146	+	170.335i	0.187173	+	0.0485162i
$232$	2323.98	+	2593.83i	0.657659	+	0.734022i
$233$			2518.83i			0.708215i	0.935205	+	0.354107i	$0.115215\pi$
$233$			2518.83i			0.708215i	−0.935205	+	0.354107i	$0.884785\pi$
$234$	−813.232	−	3058.49i	−0.227191	−	0.854442i
$235$	353.149			0.0980294
$236$	3908.77	+	142.906i	1.07813	+	0.0394170i
$237$	1510.15	−	5826.08i	0.413901	−	1.59681i
$238$	1384.69	−	1334.99i	0.377126	−	0.363590i
$239$	2037.95			0.551566			0.275783	−	0.961220i	$-0.411063\pi$
$239$	2037.95			0.551566			0.275783	+	0.961220i	$0.411063\pi$
$240$	−1574.81	−	533.632i	−0.423557	−	0.143524i
$241$	488.201			0.130489			0.0652443	−	0.997869i	$-0.479217\pi$
$241$	488.201			0.130489			0.0652443	+	0.997869i	$0.479217\pi$
$242$	2188.30	−	2109.76i	0.581277	−	0.560414i
$243$	1129.13	+	3615.79i	0.298082	+	0.954540i
$244$	7091.02	+	259.251i	1.86048	+	0.0680199i
$245$	1382.03			0.360385
$246$	−103.684	−	183.847i	−0.0268725	−	0.0476491i
$247$		−	2277.98i		−	0.586820i
$248$	−193.048	+	172.965i	−0.0494298	+	0.0442874i
$249$	1442.33	−	5564.47i	0.367085	−	1.41620i
$250$	254.526	−	245.390i	0.0643906	−	0.0620794i
$251$			501.010i			0.125990i	0.998014	+	0.0629949i	$0.0200652\pi$
$251$			501.010i			0.125990i	−0.998014	+	0.0629949i	$0.979935\pi$
$252$	−1508.42	−	911.981i	−0.377070	−	0.227974i
$253$		−	1063.85i		−	0.264362i
$254$	−2943.42	−	3053.00i	−0.727113	−	0.754182i
$255$	−543.229	+	2095.76i	−0.133405	+	0.514672i
$256$	4052.32	+	596.611i	0.989335	+	0.145657i
$257$			2191.97i			0.532028i	0.963969	+	0.266014i	$0.0857067\pi$
$257$			2191.97i			0.532028i	−0.963969	+	0.266014i	$0.914293\pi$
$258$	−6214.28	+	3504.65i	−1.49955	+	0.845697i
$259$	2003.19			0.480588
$260$	−1656.54	−	60.5639i	−0.395131	−	0.0144462i
$261$	−3632.39	−	2018.69i	−0.861453	−	0.478751i
$262$	−2755.72	−	2858.31i	−0.649805	−	0.673996i
$263$	1631.60			0.382542			0.191271	−	0.981537i	$-0.438739\pi$
$263$	1631.60			0.382542			0.191271	+	0.981537i	$0.438739\pi$
$264$	1672.26	−	864.143i	0.389850	−	0.201456i
$265$	2571.35			0.596064
$266$	−880.616	−	913.400i	−0.202985	−	0.210542i
$267$	1624.13	−	6265.83i	0.372267	−	1.43619i
$268$	−228.134	+	6239.90i	−0.0519981	+	1.42225i
$269$	−3168.95			−0.718269			−0.359134	−	0.933286i	$-0.616928\pi$
$269$	−3168.95			−0.718269			−0.359134	+	0.933286i	$0.616928\pi$
$270$	1984.05	−	12.4160i	0.447205	−	0.00279856i
$271$			3969.78i			0.889840i	0.895570	+	0.444920i	$0.146768\pi$
$271$			3969.78i			0.889840i	−0.895570	+	0.444920i	$0.853232\pi$
$272$	389.450	−	5318.98i	0.0868156	−	1.18570i
$273$	−1701.04	−	440.916i	−0.377111	−	0.0977489i
$274$	1412.97	+	1465.57i	0.311535	+	0.323133i
$275$			400.240i			0.0877650i
$276$	−790.328	+	2646.82i	−0.172363	+	0.577247i
$277$			2205.23i			0.478338i	0.970978	+	0.239169i	$0.0768750\pi$
$277$			2205.23i			0.478338i	−0.970978	+	0.239169i	$0.923125\pi$
$278$	835.543	−	805.553i	0.180261	−	0.173791i
$279$	150.243	−	270.344i	0.0322396	−	0.0580111i
$280$	−687.633	+	616.096i	−0.146764	+	0.131496i
$281$		−	1327.90i		−	0.281907i	−0.990016	−	0.140953i	$-0.954983\pi$
$281$		−	1327.90i		−	0.281907i	0.990016	−	0.140953i	$-0.0450168\pi$
$282$	904.165	−	509.919i	0.190930	−	0.107678i
$283$	−1387.82			−0.291510			−0.145755	−	0.989321i	$-0.546561\pi$
$283$	−1387.82			−0.291510			−0.145755	+	0.989321i	$0.546561\pi$
$284$	−152.193	+	4162.77i	−0.0317993	+	0.869771i
$285$	1382.45	+	358.338i	0.287331	+	0.0744776i
$286$	1350.93	−	1302.45i	0.279309	−	0.269284i
$287$	−117.197			−0.0241043
$288$	−4802.50	+	907.651i	−0.982605	+	0.185708i
$289$	−2031.14			−0.413421
$290$	−1566.99	+	1510.75i	−0.317300	+	0.305911i
$291$	1492.14	+	386.770i	0.300588	+	0.0779137i
$292$	143.299	−	3919.52i	0.0287191	−	0.785522i
$293$	−9165.11			−1.82741			−0.913705	−	0.406378i	$-0.866792\pi$
$293$	−9165.11			−1.82741			−0.913705	+	0.406378i	$0.866792\pi$
$294$	3538.39	−	1995.54i	0.701915	−	0.395857i
$295$			2444.61i			0.482477i
$296$	4136.85	−	3706.47i	0.812329	−	0.727819i
$297$	−1548.79	+	1626.70i	−0.302592	+	0.317814i
$298$	−6964.06	+	6714.10i	−1.35375	+	1.30516i
$299$			2753.79i			0.532628i
$300$	297.337	−	995.787i	0.0572224	−	0.191639i
$301$			3961.42i			0.758580i
$302$	5465.45	+	5668.92i	1.04139	+	1.08016i
$303$	−178.740	−	46.3301i	−0.0338888	−	0.00878414i
$304$	−3508.63	−	256.898i	−0.661953	−	0.0484675i
$305$			4434.85i			0.832586i
$306$	1635.28	+	6150.13i	0.305499	+	1.14895i
$307$	−2559.22			−0.475773			−0.237887	−	0.971293i	$-0.576455\pi$
$307$	−2559.22			−0.475773			−0.237887	+	0.971293i	$0.576455\pi$
$308$	38.1867	−	1044.48i	0.00706458	−	0.193230i
$309$	1040.28	−	4013.34i	0.191518	−	0.738870i
$310$	−112.439	−	116.625i	−0.0206004	−	0.0213673i
$311$	−369.625			−0.0673938			−0.0336969	−	0.999432i	$-0.510728\pi$
$311$	−369.625			−0.0673938			−0.0336969	+	0.999432i	$0.510728\pi$
$312$	−4328.67	+	2236.85i	−0.785458	+	0.405887i
$313$	−5370.45			−0.969828			−0.484914	−	0.874562i	$-0.661149\pi$
$313$	−5370.45			−0.969828			−0.484914	+	0.874562i	$0.661149\pi$
$314$	−6848.14	−	7103.09i	−1.23077	−	1.27659i
$315$	535.163	−	962.959i	0.0957238	−	0.172243i
$316$	−9260.09	−	338.553i	−1.64848	−	0.0602694i
$317$	11272.7			1.99728			0.998640	−	0.0521440i	$-0.0166055\pi$
$317$	11272.7			1.99728			0.998640	+	0.0521440i	$0.0166055\pi$
$318$	6583.41	−	3712.83i	1.16094	−	0.654733i
$319$		−	2464.08i		−	0.432483i
$320$	−280.098	+	2544.63i	−0.0489311	+	0.444529i
$321$	1493.41	−	5761.50i	0.259669	−	1.00179i
$322$	1064.55	+	1104.18i	0.184240	+	0.191099i
$323$			4580.66i			0.789086i
$324$	5061.81	−	2896.60i	0.867938	−	0.496673i
$325$		−	1036.03i		−	0.176826i
$326$	1820.58	−	1755.24i	0.309303	−	0.298201i
$327$	−910.384	+	3512.22i	−0.153958	+	0.593964i
$328$	−242.027	+	216.848i	−0.0407431	+	0.0365044i
$329$		−	576.379i		−	0.0965860i
$330$	577.915	+	1024.73i	0.0964035	+	0.170938i
$331$	−2828.03			−0.469616			−0.234808	−	0.972042i	$-0.575446\pi$
$331$	−2828.03			−0.469616			−0.234808	+	0.972042i	$0.575446\pi$
$332$	−8844.26	−	323.351i	−1.46202	−	0.0534523i
$333$	−3219.57	+	5793.23i	−0.529825	+	0.953354i
$334$	−7211.61	+	6952.77i	−1.18144	+	1.13904i
$335$	−3902.54			−0.636473
$336$	−870.948	+	2570.27i	−0.141411	+	0.417321i
$337$	3642.70			0.588815			0.294407	−	0.955680i	$-0.404878\pi$
$337$	3642.70			0.588815			0.294407	+	0.955680i	$0.404878\pi$
$338$	976.631	−	941.578i	0.157165	−	0.151524i
$339$	2595.06	−	10011.6i	0.415766	−	1.60401i
$340$	3331.03	+	121.784i	0.531326	+	0.0194255i
$341$	183.392			0.0291238
$342$	4056.89	−	1078.70i	0.641438	−	0.170554i
$343$		−	5054.69i		−	0.795708i
$344$	7329.75	+	8180.84i	1.14882	+	1.28221i
$345$	−1671.21	−	433.185i	−0.260797	−	0.0675996i
$346$	3174.75	−	3060.80i	0.493282	−	0.475577i
$347$		−	4927.62i		−	0.762331i	−0.924507	−	0.381165i	$-0.875523\pi$
$347$		−	4927.62i		−	0.762331i	0.924507	−	0.381165i	$-0.124477\pi$
$348$	−1830.56	+	6130.57i	−0.281977	+	0.944348i
$349$			2431.57i			0.372948i	0.982460	+	0.186474i	$0.0597060\pi$
$349$			2431.57i			0.372948i	−0.982460	+	0.186474i	$0.940294\pi$
$350$	−400.505	−	415.415i	−0.0611654	−	0.0634425i
$351$	4009.07	−	4210.74i	0.609653	−	0.640321i
$352$	−1853.72	−	2227.64i	−0.280693	−	0.337312i
$353$		−	8817.03i		−	1.32941i	−0.747104	−	0.664707i	$-0.768557\pi$
$353$		−	8817.03i		−	1.32941i	0.747104	−	0.664707i	$-0.231443\pi$
$354$	3529.82	+	6258.92i	0.529966	+	0.939711i
$355$	−2603.47			−0.389233
$356$	−9959.03	−	364.107i	−1.48266	−	0.0542068i
$357$	3420.51	+	886.611i	0.507094	+	0.131441i
$358$	6626.50	+	6873.19i	0.978272	+	1.01469i
$359$	−407.550			−0.0599155			−0.0299577	−	0.999551i	$-0.509537\pi$
$359$	−407.550			−0.0599155			−0.0299577	+	0.999551i	$0.509537\pi$
$360$	−676.568	−	2978.83i	−0.0990508	−	0.436107i
$361$	−3837.40			−0.559469
$362$	7261.13	+	7531.45i	1.05424	+	1.09349i
$363$	5405.63	+	1401.16i	0.781603	+	0.202595i
$364$	−98.8471	+	2703.66i	−0.0142335	+	0.389314i
$365$	2451.33			0.351531
$366$	6403.57	+	11354.5i	0.914535	+	1.62161i
$367$			10422.5i			1.48243i	0.671268	+	0.741215i	$0.265750\pi$
$367$			10422.5i			1.48243i	−0.671268	+	0.741215i	$0.734250\pi$
$368$	4241.48	+	310.557i	0.600822	+	0.0439915i
$369$	188.362	−	338.935i	0.0265738	−	0.0478163i
$370$	2409.46	+	2499.17i	0.338546	+	0.351150i
$371$		−	4196.74i		−	0.587288i
$372$	−456.274	−	136.241i	−0.0635933	−	0.0189886i
$373$			137.913i			0.0191444i	0.999954	+	0.00957222i	$0.00304698\pi$
$373$			137.913i			0.0191444i	−0.999954	+	0.00957222i	$0.996953\pi$
$374$	−2716.51	+	2619.01i	−0.375582	+	0.362101i
$375$	628.741	+	162.972i	0.0865814	+	0.0224423i
$376$	−1066.46	−	1190.30i	−0.146273	−	0.163257i
$377$			6378.32i			0.871353i
$378$	−20.2642	−	3238.19i	−0.00275735	−	0.440620i
$379$	−13519.4			−1.83231			−0.916156	−	0.400821i	$-0.868725\pi$
$379$	−13519.4			−1.83231			−0.916156	+	0.400821i	$0.868725\pi$
$380$	80.3343	−	2197.30i	0.0108449	−	0.296629i
$381$	1954.83	−	7541.65i	0.262858	−	1.01410i
$382$	7579.36	−	7307.32i	1.01517	−	0.978730i
$383$	7735.52			1.03203			0.516014	−	0.856580i	$-0.327415\pi$
$383$	7735.52			1.03203			0.516014	+	0.856580i	$0.327415\pi$
$384$	2957.11	+	6919.44i	0.392980	+	0.919547i
$385$	653.237			0.0864728
$386$	2999.63	−	2891.97i	0.395537	−	0.381340i
$387$	−11456.4	−	6366.88i	−1.50481	−	0.836297i
$388$	86.7084	−	2371.64i	0.0113452	−	0.310314i
$389$	−10301.3			−1.34267			−0.671335	−	0.741154i	$-0.734279\pi$
$389$	−10301.3			−1.34267			−0.671335	+	0.741154i	$0.734279\pi$
$390$	−1495.94	−	2652.53i	−0.194231	−	0.344401i
$391$		−	5537.43i		−	0.716214i
$392$	−4173.54	−	4658.14i	−0.537744	−	0.600183i
$393$	1830.17	−	7060.72i	0.234910	−	0.906275i
$394$	110.267	−	106.309i	0.0140994	−	0.0135934i
$395$		−	5791.42i		−	0.737717i
$396$	2959.26	+	1789.15i	0.375526	+	0.227041i
$397$			9705.75i			1.22700i	0.789696	+	0.613498i	$0.210238\pi$
$397$			9705.75i			1.22700i	−0.789696	+	0.613498i	$0.789762\pi$
$398$	−1410.85	−	1463.38i	−0.177688	−	0.184303i
$399$	584.848	−	2256.32i	0.0733810	−	0.283101i
$400$	−1595.73	−	116.837i	−0.199466	−	0.0146047i
$401$		−	3362.05i		−	0.418686i	−0.977842	−	0.209343i	$-0.932868\pi$
$401$		−	3362.05i		−	0.418686i	0.977842	−	0.209343i	$-0.0671325\pi$
$402$	−9991.64	+	5634.96i	−1.23965	+	0.699120i
$403$	−474.713			−0.0586778
$404$	−10.3865	+	284.092i	−0.00127908	+	0.0349854i
$405$	1924.75	+	3095.38i	0.236152	+	0.379779i
$406$	2465.71	+	2557.51i	0.301407	+	0.312628i
$407$	−3929.92			−0.478621
$408$	8704.27	−	4497.95i	1.05619	−	0.545788i
$409$	3469.99			0.419511			0.209755	−	0.977754i	$-0.432733\pi$
$409$	3469.99			0.419511			0.209755	+	0.977754i	$0.432733\pi$
$410$	−140.966	−	146.214i	−0.0169801	−	0.0176122i
$411$	−938.402	+	3620.32i	−0.112623	+	0.434494i
$412$	−6378.87	−	233.215i	−0.762778	−	0.0278876i
$413$	3989.88			0.475373
$414$	−4904.26	+	1304.01i	−0.582202	+	0.154804i
$415$		−	5531.36i		−	0.654274i
$416$	4798.40	+	5766.29i	0.565531	+	0.679605i
$417$	2063.99	+	534.996i	0.242384	+	0.0628270i
$418$	1727.61	+	1791.93i	0.202154	+	0.209680i
$419$			12636.7i			1.47338i	0.676233	+	0.736688i	$0.263611\pi$
$419$			12636.7i			1.47338i	−0.676233	+	0.736688i	$0.736389\pi$
$420$	−1625.24	−	485.287i	−0.188818	−	0.0563799i
$421$			3868.31i			0.447814i	0.974610	+	0.223907i	$0.0718812\pi$
$421$			3868.31i			0.447814i	−0.974610	+	0.223907i	$0.928119\pi$
$422$	345.072	−	332.686i	0.0398053	−	0.0383766i
$423$	1666.89	+	926.369i	0.191600	+	0.106481i
$424$	−7765.15	−	8666.79i	−0.889408	−	0.992681i
$425$			2083.29i			0.237775i
$426$	−6665.64	+	3759.20i	−0.758102	+	0.427544i
$427$	7238.17			0.820327
$428$	−9157.43	−	334.800i	−1.03421	−	0.0378112i
$429$	3337.13	+	865.000i	0.375567	+	0.0973487i
$430$	−4942.23	+	4764.85i	−0.554269	+	0.534375i
$431$	−9156.14			−1.02328			−0.511642	−	0.859199i	$-0.670963\pi$
$431$	−9156.14			−1.02328			−0.511642	+	0.859199i	$0.670963\pi$
$432$	−6033.41	−	6649.77i	−0.671951	−	0.740596i
$433$	7684.27			0.852846			0.426423	−	0.904524i	$-0.359773\pi$
$433$	7684.27			0.852846			0.426423	+	0.904524i	$0.359773\pi$
$434$	−190.345	+	183.513i	−0.0210527	+	0.0202970i
$435$	−3870.85	−	1003.34i	−0.426651	−	0.110590i
$436$	5582.39	+	204.095i	0.613184	+	0.0224183i
$437$	−3652.73			−0.399849
$438$	6276.13	−	3539.53i	0.684669	−	0.386131i
$439$			13.8081i			0.00150120i	1.00000		0.000750598i	$0.000238923\pi$
$439$			13.8081i			0.00150120i	−1.00000		0.000750598i	$0.999761\pi$
$440$	1349.02	−	1208.67i	0.146163	−	0.130957i
$441$	6523.25	+	3625.28i	0.704379	+	0.391457i
$442$	7031.74	−	6779.36i	0.756710	−	0.729550i
$443$			7170.53i			0.769034i	0.923118	+	0.384517i	$0.125632\pi$
$443$			7170.53i			0.769034i	−0.923118	+	0.384517i	$0.874368\pi$
$444$	9777.53	+	2919.52i	1.04509	+	0.312059i
$445$		−	6228.55i		−	0.663509i
$446$	−5338.80	−	5537.55i	−0.566815	−	0.587916i
$447$	−17202.9	−	4459.07i	−1.82029	−	0.471827i
$448$	4153.12	+	457.151i	0.437983	+	0.0482106i
$449$		−	538.402i		−	0.0565897i	−0.999600	−	0.0282948i	$-0.990992\pi$
$449$		−	538.402i		−	0.0565897i	0.999600	−	0.0282948i	$-0.00900773\pi$
$450$	1845.08	−	490.595i	0.193284	−	0.0513930i
$451$	229.921			0.0240057
$452$	−15912.7	−	581.776i	−1.65591	−	0.0605408i
$453$	−3629.79	+	14003.6i	−0.376474	+	1.45242i
$454$	−4224.13	−	4381.39i	−0.436670	−	0.452926i
$455$	−1690.91			−0.174223
$456$	−2967.04	−	5741.72i	−0.304703	−	0.589650i
$457$	14128.6			1.44619			0.723093	−	0.690751i	$-0.242720\pi$
$457$	14128.6			1.44619			0.723093	+	0.690751i	$0.242720\pi$
$458$	−1177.83	−	1221.68i	−0.120167	−	0.124640i
$459$	−8061.59	+	8467.12i	−0.819789	+	0.861027i
$460$	−97.1138	+	2656.25i	−0.00984338	+	0.269235i
$461$	259.782			0.0262457			0.0131228	−	0.999914i	$-0.495823\pi$
$461$	259.782			0.0262457			0.0131228	+	0.999914i	$0.495823\pi$
$462$	1672.48	−	943.222i	0.168421	−	0.0949841i
$463$		−	16415.6i		−	1.64772i	−0.566792	−	0.823861i	$-0.691816\pi$
$463$		−	16415.6i		−	1.64772i	0.566792	−	0.823861i	$-0.308184\pi$
$464$	9824.12	+	719.311i	0.982916	+	0.0719680i
$465$	74.6747	−	288.092i	0.00744722	−	0.0287311i
$466$	4944.78	+	5128.86i	0.491550	+	0.509850i
$467$			8220.54i			0.814564i	0.913302	+	0.407282i	$0.133523\pi$
$467$			8220.54i			0.814564i	−0.913302	+	0.407282i	$0.866477\pi$
$468$	−7660.10	−	4631.24i	−0.756599	−	0.457434i
$469$			6369.38i			0.627102i
$470$	719.085	−	693.276i	0.0705722	−	0.0680392i
$471$	4548.09	−	17546.3i	0.444936	−	1.71654i
$472$	8239.60	−	7382.40i	0.803514	−	0.719921i
$473$		−	7771.62i		−	0.755475i
$474$	−8362.35	−	14827.7i	−0.810328	−	1.43684i
$475$	1374.23			0.132745
$476$	198.766	−	5436.62i	0.0191395	−	0.523502i
$477$	12136.9	+	6745.08i	1.16502	+	0.647455i
$478$	4149.70	−	4000.76i	0.397077	−	0.382825i
$479$	1872.05			0.178573			0.0892864	−	0.996006i	$-0.471541\pi$
$479$	1872.05			0.178573			0.0892864	+	0.996006i	$0.471541\pi$
$480$	−4254.23	+	2004.97i	−0.404538	+	0.190654i
$481$	10172.7			0.964310
$482$	994.078	−	958.399i	0.0939399	−	0.0905682i
$483$	−707.006	+	2727.60i	−0.0666043	+	0.256957i
$484$	314.121	−	8591.80i	0.0295004	−	0.806893i
$485$	1483.27			0.138869
$486$	9397.40	+	5145.88i	0.877109	+	0.480292i
$487$			2708.04i			0.251978i	0.992032	+	0.125989i	$0.0402103\pi$
$487$			2708.04i			0.251978i	−0.992032	+	0.125989i	$0.959790\pi$
$488$	14947.7	−	13392.7i	1.38658	−	1.24233i
$489$	4497.28	+	1165.71i	0.415898	+	0.107803i
$490$	2814.09	−	2713.09i	0.259444	−	0.250132i
$491$			6462.29i			0.593969i	0.954882	+	0.296985i	$0.0959810\pi$
$491$			6462.29i			0.593969i	−0.954882	+	0.296985i	$0.904019\pi$
$492$	−572.037	−	170.807i	−0.0524175	−	0.0156516i
$493$		−	12825.8i		−	1.17169i
$494$	−4471.96	−	4638.45i	−0.407294	−	0.422457i
$495$	−1049.90	+	1889.16i	−0.0953319	+	0.171538i
$496$	−53.5355	+	731.170i	−0.00484640	+	0.0661906i
$497$			4249.15i			0.383502i
$498$	−7986.84	−	14161.9i	−0.718673	−	1.27432i
$499$	10668.0			0.957043			0.478522	−	0.878076i	$-0.341173\pi$
$499$	10668.0			0.957043			0.478522	+	0.878076i	$0.341173\pi$
$500$	36.5361	−	999.332i	0.00326789	−	0.0893830i
$501$	−17814.4	−	4617.58i	−1.58860	−	0.411773i
$502$	983.544	+	1020.16i	0.0874457	+	0.0907012i
$503$	12001.4			1.06385			0.531924	−	0.846792i	$-0.321469\pi$
$503$	12001.4			1.06385			0.531924	+	0.846792i	$0.321469\pi$
$504$	−4861.79	+	1104.24i	−0.429685	+	0.0975924i
$505$	−177.676			−0.0156564
$506$	−2088.46	−	2166.22i	−0.183485	−	0.190316i
$507$	2412.51	+	625.335i	0.211328	+	0.0547773i
$508$	−11986.8	−	438.245i	−1.04691	−	0.0382755i
$509$	14792.6			1.28816			0.644079	−	0.764959i	$-0.277241\pi$
$509$	14792.6			1.28816			0.644079	+	0.764959i	$0.277241\pi$
$510$	3008.10	+	5333.82i	0.261178	+	0.463109i
$511$		−	4000.85i		−	0.346355i
$512$	9422.58	−	6740.38i	0.813327	−	0.581807i
$513$	5585.29	+	5317.78i	0.480695	+	0.457672i
$514$	4303.10	+	4463.30i	0.369264	+	0.383011i
$515$		−	3989.46i		−	0.341353i
$516$	−5773.50	+	19335.6i	−0.492566	+	1.64962i
$517$			1130.76i			0.0961906i
$518$	4078.92	−	3932.52i	0.345980	−	0.333561i
$519$	7842.40	+	2032.79i	0.663282	+	0.171926i
$520$	−3491.95	+	3128.67i	−0.294485	+	0.263849i
$521$			16252.9i			1.36671i	0.730088	+	0.683353i	$0.239479\pi$
$521$			16252.9i			1.36671i	−0.730088	+	0.683353i	$0.760521\pi$
$522$	−11359.2	+	3020.35i	−0.952454	+	0.253251i
$523$	−1771.09			−0.148077			−0.0740385	−	0.997255i	$-0.523589\pi$
$523$	−1771.09			−0.148077			−0.0740385	+	0.997255i	$0.523589\pi$
$524$	−11222.4	−	410.298i	−0.935600	−	0.0342060i
$525$	265.989	−	1026.18i	0.0221119	−	0.0853066i
$526$	3322.27	−	3203.03i	0.275396	−	0.265511i
$527$	954.572			0.0789029
$528$	1708.65	−	5042.43i	0.140832	−	0.415613i
$529$	−7751.32			−0.637077
$530$	5235.81	−	5047.88i	0.429111	−	0.413710i
$531$	−6412.62	+	11538.7i	−0.524075	+	0.943009i
$532$	−3586.23	−	131.115i	−0.292261	−	0.0106852i
$533$	−595.154			−0.0483659
$534$	−8993.53	−	15946.9i	−0.728817	−	1.29230i
$535$		−	5727.22i		−	0.462821i
$536$	11785.2	+	13153.6i	0.949704	+	1.05998i
$537$	−4400.89	+	16978.5i	−0.353654	+	1.36438i
$538$	−6452.64	+	6221.04i	−0.517088	+	0.498528i
$539$			4425.14i			0.353626i
$540$	4015.56	−	3920.21i	0.320004	−	0.312406i
$541$		−	9682.68i		−	0.769484i	−0.923024	−	0.384742i	$-0.874290\pi$
$541$		−	9682.68i		−	0.769484i	0.923024	−	0.384742i	$-0.125710\pi$
$542$	7793.16	+	8083.29i	0.617611	+	0.640603i
$543$	−4822.37	+	18604.5i	−0.381119	+	1.47034i
$544$	−9648.81	−	11595.1i	−0.760458	−	0.913851i
$545$			3491.33i			0.274407i
$546$	−4329.23	+	2441.55i	−0.339330	+	0.191371i
$547$	−4085.62			−0.319357			−0.159679	−	0.987169i	$-0.551046\pi$
$547$	−4085.62			−0.319357			−0.159679	+	0.987169i	$0.551046\pi$
$548$	5754.20	+	210.376i	0.448553	+	0.0163993i
$549$	−11633.3	+	20932.8i	−0.904370	+	1.62730i
$550$	785.721	+	814.972i	0.0609150	+	0.0631828i
$551$	−8460.45			−0.654133
$552$	3586.77	+	6941.00i	0.276564	+	0.535197i
$553$	−9452.25			−0.726854
$554$	4329.14	+	4490.31i	0.331999	+	0.344359i
$555$	−1600.21	+	6173.54i	−0.122388	+	0.472166i
$556$	119.938	−	3280.55i	0.00914843	−	0.250227i
$557$	4855.83			0.369386			0.184693	−	0.982796i	$-0.440871\pi$
$557$	4855.83			0.369386			0.184693	+	0.982796i	$0.440871\pi$
$558$	−224.793	−	845.424i	−0.0170542	−	0.0641392i
$559$			20117.0i			1.52211i
$560$	−190.692	+	2604.41i	−0.0143896	+	0.196529i
$561$	−6710.44	−	1739.38i	−0.505018	−	0.130903i
$562$	−2606.83	−	2703.88i	−0.195663	−	0.202947i
$563$		−	23820.6i		−	1.78316i	−0.452867	−	0.891578i	$-0.649599\pi$
$563$		−	23820.6i		−	1.78316i	0.452867	−	0.891578i	$-0.350401\pi$
$564$	840.033	−	2813.29i	0.0627159	−	0.210037i
$565$		−	9952.08i		−	0.741039i
$566$	−2825.89	+	2724.46i	−0.209860	+	0.202328i
$567$	5052.00	−	3141.41i	0.374187	−	0.232675i
$568$	7862.13	+	8775.04i	0.580788	+	0.648226i
$569$		−	20135.5i		−	1.48352i	−0.670664	−	0.741761i	$-0.733991\pi$
$569$		−	20135.5i		−	1.48352i	0.670664	−	0.741761i	$-0.266009\pi$
$570$	3518.42	−	1984.28i	0.258545	−	0.145811i
$571$	10810.5			0.792302			0.396151	−	0.918185i	$-0.370346\pi$
$571$	10810.5			0.792302			0.396151	+	0.918185i	$0.370346\pi$
$572$	193.921	−	5304.10i	0.0141752	−	0.387720i
$573$	18722.8	+	4853.05i	1.36502	+	0.353820i
$574$	−238.638	+	230.073i	−0.0173529	+	0.0167301i
$575$	−1661.26			−0.120486
$576$	−7997.07	+	11276.1i	−0.578492	+	0.815688i
$577$	−20510.1			−1.47980			−0.739902	−	0.672715i	$-0.765128\pi$
$577$	−20510.1			−1.47980			−0.739902	+	0.672715i	$0.765128\pi$
$578$	−4135.82	+	3987.38i	−0.297625	+	0.286943i
$579$	7409.82	+	1920.66i	0.531851	+	0.137858i
$580$	−224.935	+	6152.40i	−0.0161033	+	0.440456i
$581$	−9027.80			−0.644641
$582$	3797.59	−	2141.72i	0.270473	−	0.152538i
$583$			8233.27i			0.584883i
$584$	−7402.71	−	8262.26i	−0.524531	−	0.585437i
$585$	2717.67	−	4890.12i	0.192072	−	0.345610i
$586$	−18662.1	+	17992.2i	−1.31557	+	1.26835i
$587$		−	11542.2i		−	0.811582i	−0.913966	−	0.405791i	$-0.866996\pi$
$587$		−	11542.2i		−	0.811582i	0.913966	−	0.405791i	$-0.133004\pi$
$588$	3287.42	−	11009.6i	0.230562	−	0.772159i
$589$		−	629.678i		−	0.0440500i
$590$	4799.07	+	4977.74i	0.334872	+	0.347339i
$591$	272.386	+	70.6037i	0.0189585	+	0.00491413i
$592$	1147.22	−	15668.3i	0.0796457	−	1.08778i
$593$			7779.03i			0.538695i	0.963043	+	0.269348i	$0.0868081\pi$
$593$			7779.03i			0.538695i	−0.963043	+	0.269348i	$0.913192\pi$
$594$	39.7549	+	6352.76i	0.00274607	+	0.438816i
$595$	3400.16			0.234274
$596$	−999.660	+	27342.6i	−0.0687041	+	1.87919i
$597$	936.997	−	3614.90i	0.0642358	−	0.247819i
$598$	5406.03	+	5607.29i	0.369680	+	0.383443i
$599$	18156.7			1.23850			0.619250	−	0.785194i	$-0.287437\pi$
$599$	18156.7			1.23850			0.619250	+	0.785194i	$0.287437\pi$
$600$	−1349.41	−	2611.34i	−0.0918160	−	0.177679i
$601$	−15937.9			−1.08173			−0.540867	−	0.841108i	$-0.681904\pi$
$601$	−15937.9			−1.08173			−0.540867	+	0.841108i	$0.681904\pi$
$602$	7776.76	+	8066.28i	0.526507	+	0.546108i
$603$	−18420.2	−	10237.0i	−1.24400	−	0.691349i
$604$	22257.6	+	813.748i	1.49942	+	0.0548194i
$605$	5373.46			0.361095
$606$	−454.903	+	256.550i	−0.0304937	+	0.0171974i
$607$			22506.3i			1.50495i	0.658622	+	0.752474i	$0.271140\pi$
$607$			22506.3i			1.50495i	−0.658622	+	0.752474i	$0.728860\pi$
$608$	−7648.63	+	6364.78i	−0.510186	+	0.424549i
$609$	−1637.57	+	6317.66i	−0.108961	+	0.420369i
$610$	8706.16	+	9030.28i	0.577872	+	0.599386i
$611$		−	2926.98i		−	0.193802i
$612$	15403.2	+	9312.68i	1.01738	+	0.615103i
$613$		−	8616.21i		−	0.567709i	−0.958867	−	0.283854i	$-0.908387\pi$
$613$		−	8616.21i		−	0.567709i	0.958867	−	0.283854i	$-0.0916132\pi$
$614$	−5211.10	+	5024.07i	−0.342513	+	0.330220i
$615$	93.6208	−	361.185i	0.00613846	−	0.0236819i
$616$	−1972.69	−	2201.75i	−0.129029	−	0.144011i
$617$		−	16425.9i		−	1.07177i	−0.844292	−	0.535884i	$-0.819978\pi$
$617$		−	16425.9i		−	1.07177i	0.844292	−	0.535884i	$-0.180022\pi$
$618$	−5760.46	−	10214.2i	−0.374951	−	0.664846i
$619$	17346.1			1.12633			0.563166	−	0.826343i	$-0.309583\pi$
$619$	17346.1			1.12633			0.563166	+	0.826343i	$0.309583\pi$
$620$	−457.899	−	16.7410i	−0.0296607	−	0.00108441i
$621$	−6751.89	−	6428.51i	−0.436303	−	0.415406i
$622$	−752.633	+	725.619i	−0.0485174	+	0.0467760i
$623$	−10165.7			−0.653740
$624$	−4422.87	+	13052.4i	−0.283744	+	0.837363i
$625$	625.000			0.0400000
$626$	−10935.4	+	10542.9i	−0.698187	+	0.673127i
$627$	−1147.37	+	4426.50i	−0.0730806	+	0.281942i
$628$	−27888.5	−	1019.62i	−1.77209	−	0.0647884i
$629$	−20455.6			−1.29669
$630$	−800.706	−	3011.38i	−0.0506363	−	0.190438i
$631$			17840.3i			1.12553i	0.826616	+	0.562766i	$0.190263\pi$
$631$			17840.3i			1.12553i	−0.826616	+	0.562766i	$0.809737\pi$
$632$	−19520.1	+	17489.3i	−1.22859	+	1.10077i
$633$	852.411	+	220.949i	0.0535234	+	0.0138735i
$634$	22953.6	−	22129.7i	1.43786	−	1.38625i
$635$		−	7496.78i		−	0.468505i
$636$	6116.46	−	20484.2i	0.381342	−	1.27712i
$637$		−	11454.5i		−	0.712474i
$638$	−4837.30	−	5017.38i	−0.300173	−	0.311348i
$639$	−12288.5	−	6829.33i	−0.760762	−	0.422792i
$640$	4425.09	+	5731.26i	0.273308	+	0.353981i
$641$			7593.09i			0.467877i	0.972251	+	0.233939i	$0.0751614\pi$
$641$			7593.09i			0.467877i	−0.972251	+	0.233939i	$0.924839\pi$
$642$	−8269.65	−	14663.3i	−0.508375	−	0.901427i
$643$	10822.0			0.663727			0.331863	−	0.943327i	$-0.392323\pi$
$643$	10822.0			0.663727			0.331863	+	0.943327i	$0.392323\pi$
$644$	4335.30	+	158.501i	0.265271	+	0.00969845i
$645$	−12208.5	−	3164.50i	−0.745286	−	0.193182i
$646$	8992.40	+	9327.18i	0.547680	+	0.568069i
$647$	460.162			0.0279611			0.0139805	−	0.999902i	$-0.495550\pi$
$647$	460.162			0.0279611			0.0139805	+	0.999902i	$0.495550\pi$
$648$	4620.53	−	15835.0i	0.280110	−	0.959968i
$649$	−7827.45			−0.473427
$650$	−2033.85	−	2109.57i	−0.122730	−	0.127299i
$651$	−470.199	−	121.878i	−0.0283080	−	0.00733757i
$652$	261.337	−	7148.06i	0.0156974	−	0.429355i
$653$	5795.47			0.347312			0.173656	−	0.984806i	$-0.444442\pi$
$653$	5795.47			0.347312			0.173656	+	0.984806i	$0.444442\pi$
$654$	5041.20	+	8938.81i	0.301417	+	0.534458i
$655$		−	7018.71i		−	0.418692i
$656$	−67.1182	+	916.678i	−0.00399470	+	0.0545583i
$657$	11570.5	+	6430.25i	0.687072	+	0.381839i
$658$	−1131.50	−	1173.63i	−0.0670374	−	0.0695331i
$659$		−	18954.8i		−	1.12044i	−0.828343	−	0.560222i	$-0.810716\pi$
$659$		−	18954.8i		−	1.12044i	0.828343	−	0.560222i	$-0.189284\pi$
$660$	3188.43	+	952.048i	0.188045	+	0.0561491i
$661$		−	9477.84i		−	0.557708i	−0.960333	−	0.278854i	$-0.910045\pi$
$661$		−	9477.84i		−	0.557708i	0.960333	−	0.278854i	$-0.0899546\pi$
$662$	−5758.47	+	5551.78i	−0.338080	+	0.325946i
$663$	17370.1	+	4502.41i	1.01749	+	0.263739i
$664$	−18643.5	+	16704.0i	−1.08962	+	0.976265i
$665$		−	2242.89i		−	0.130791i
$666$	4817.10	+	18116.6i	0.280269	+	1.05406i
$667$	10227.6			0.593724
$668$	−1035.20	+	28314.6i	−0.0599594	+	1.64001i
$669$	3545.68	−	13679.1i	0.204909	−	0.790530i
$670$	−7946.39	+	7661.17i	−0.458203	+	0.441757i
$671$	−14200.0			−0.816969
$672$	3272.33	+	6943.39i	0.187847	+	0.398582i
$673$	−27039.5			−1.54873			−0.774367	−	0.632737i	$-0.781931\pi$
$673$	−27039.5			−1.54873			−0.774367	+	0.632737i	$0.781931\pi$
$674$	7417.30	−	7151.07i	0.423893	−	0.408678i
$675$	2540.19	+	2418.53i	0.144848	+	0.137910i
$676$	140.191	−	3834.50i	0.00797628	−	0.218167i
$677$	−28999.0			−1.64627			−0.823133	−	0.567849i	$-0.807776\pi$
$677$	−28999.0			−1.64627			−0.823133	+	0.567849i	$0.807776\pi$
$678$	−14370.0	−	25480.2i	−0.813978	−	1.44331i
$679$		−	2420.86i		−	0.136825i
$680$	7021.76	−	6291.26i	0.395988	−	0.354792i
$681$	2805.39	−	10823.1i	0.157860	−	0.609018i
$682$	373.424	−	360.021i	0.0209665	−	0.0202140i
$683$			8541.52i			0.478524i	0.970955	+	0.239262i	$0.0769055\pi$
$683$			8541.52i			0.478524i	−0.970955	+	0.239262i	$0.923094\pi$
$684$	6143.06	−	10160.7i	0.343400	−	0.567986i
$685$			3598.78i			0.200733i
$686$	−9922.99	−	10292.4i	−0.552276	−	0.572837i
$687$	782.238	−	3017.84i	0.0434414	−	0.167595i
$688$	30984.9	+	2268.68i	1.71699	+	0.125716i
$689$		−	21312.0i		−	1.17840i
$690$	−4253.32	+	2398.73i	−0.234668	+	0.132345i
$691$	10911.4			0.600710			0.300355	−	0.953827i	$-0.402895\pi$
$691$	10911.4			0.600710			0.300355	+	0.953827i	$0.402895\pi$
$692$	455.722	−	12464.9i	0.0250346	−	0.684744i
$693$	3083.32	+	1713.55i	0.169012	+	0.0939283i
$694$	−9673.54	−	10033.7i	−0.529110	−	0.548808i
$695$	2051.71			0.111980
$696$	8307.68	+	16076.7i	0.452445	+	0.875556i
$697$	1196.76			0.0650366
$698$	4773.47	+	4951.18i	0.258852	+	0.268488i
$699$	−3284.00	+	12669.5i	−0.177700	+	0.685559i
$700$	−1631.02	−	59.6310i	−0.0880669	−	0.00321977i
$701$	36601.7			1.97208			0.986040	−	0.166507i	$-0.0532490\pi$
$701$	36601.7			1.97208			0.986040	+	0.166507i	$0.0532490\pi$
$702$	−102.906	−	16444.2i	−0.00553269	−	0.884114i
$703$			13493.4i			0.723917i
$704$	−8147.70	−	896.851i	−0.436191	−	0.0480133i
$705$	1776.31	+	460.429i	0.0948934	+	0.0245968i
$706$	−17308.9	−	17953.3i	−0.922705	−	0.957056i
$707$			289.987i			0.0154259i
$708$	19474.5	+	5814.98i	1.03375	+	0.308673i
$709$			2489.39i			0.131863i	0.997824	+	0.0659316i	$0.0210019\pi$
$709$			2489.39i			0.131863i	−0.997824	+	0.0659316i	$0.978998\pi$
$710$	−5301.20	+	5110.93i	−0.280212	+	0.270155i
$711$	15191.9	−	27335.9i	0.801321	−	1.44188i
$712$	−20993.4	+	18809.4i	−1.10500	+	0.990045i
$713$			761.200i			0.0399820i
$714$	8705.40	−	4909.56i	0.456290	−	0.257333i
$715$	3317.28			0.173509
$716$	26985.9	+	986.617i	1.40853	+	0.0514967i
$717$	10250.8	+	2657.04i	0.533921	+	0.138395i
$718$	−829.856	+	800.070i	−0.0431336	+	0.0415855i
$719$	24728.1			1.28262			0.641309	−	0.767283i	$-0.278392\pi$
$719$	24728.1			1.28262			0.641309	+	0.767283i	$0.278392\pi$
$720$	−7225.46	−	4737.34i	−0.373996	−	0.245209i
$721$	−6511.25			−0.336327
$722$	−7813.74	+	7533.28i	−0.402766	+	0.388310i
$723$	2455.61	+	636.506i	0.126314	+	0.0327412i
$724$	29570.3	+	1081.11i	1.51792	+	0.0554959i
$725$	−3847.82			−0.197110
$726$	13757.6	−	7758.85i	0.703297	−	0.396636i
$727$			16184.4i			0.825648i	0.910811	+	0.412824i	$0.135458\pi$
$727$			16184.4i			0.825648i	−0.910811	+	0.412824i	$0.864542\pi$
$728$	5106.34	+	5699.26i	0.259964	+	0.290149i
$729$	965.258	+	19659.3i	0.0490402	+	0.998797i
$730$	4991.43	−	4812.27i	0.253070	−	0.243987i
$731$		−	40452.0i		−	2.04675i
$732$	35329.3	+	10549.1i	1.78389	+	0.532660i
$733$		−	22066.1i		−	1.11191i	−0.831213	−	0.555954i	$-0.812353\pi$
$733$		−	22066.1i		−	1.11191i	0.831213	−	0.555954i	$-0.187647\pi$
$734$	20460.7	+	21222.4i	1.02891	+	1.06721i
$735$	6951.49	+	1801.86i	0.348857	+	0.0904252i
$736$	9246.21	−	7694.20i	0.463070	−	0.385342i
$737$		−	12495.6i		−	0.624535i
$738$	−281.826	−	1059.92i	−0.0140571	−	0.0528675i
$739$	15057.3			0.749516			0.374758	−	0.927123i	$-0.377726\pi$
$739$	15057.3			0.749516			0.374758	+	0.927123i	$0.377726\pi$
$740$	9812.34	+	358.744i	0.487444	+	0.0178212i
$741$	2969.99	−	11458.1i	0.147240	−	0.568048i
$742$	−8238.71	−	8545.43i	−0.407618	−	0.422793i
$743$	−29887.3			−1.47572			−0.737860	−	0.674954i	$-0.764164\pi$
$743$	−29887.3			−1.47572			−0.737860	+	0.674954i	$0.764164\pi$
$744$	−1196.53	+	618.308i	−0.0589608	+	0.0304681i
$745$	−17100.6			−0.840961
$746$	270.741	+	280.820i	0.0132876	+	0.0137822i
$747$	14509.7	−	26108.4i	0.710684	−	1.27879i
$748$	−389.944	+	10665.7i	−0.0190612	+	0.521359i
$749$	−9347.46			−0.456006
$750$	1600.18	−	902.450i	0.0779072	−	0.0439371i
$751$			7576.72i			0.368147i	0.982912	+	0.184074i	$0.0589285\pi$
$751$			7576.72i			0.368147i	−0.982912	+	0.184074i	$0.941072\pi$
$752$	−4508.24	−	330.088i	−0.218615	−	0.0160068i
$753$	−653.206	+	2520.04i	−0.0316124	+	0.121959i
$754$	12521.4	+	12987.6i	0.604779	+	0.627294i
$755$			13920.3i			0.671008i
$756$	−6398.23	−	6553.85i	−0.307806	−	0.315292i
$757$			11996.2i			0.575972i	0.957635	+	0.287986i	$0.0929857\pi$
$757$			11996.2i			0.575972i	−0.957635	+	0.287986i	$0.907014\pi$
$758$	−27528.4	+	26540.3i	−1.31910	+	1.27175i
$759$	1387.02	−	5351.07i	0.0663316	−	0.255905i
$760$	−4149.99	−	4631.86i	−0.198074	−	0.221073i
$761$		−	3634.83i		−	0.173144i	−0.996246	−	0.0865719i	$-0.972409\pi$
$761$		−	3634.83i		−	0.173144i	0.996246	−	0.0865719i	$-0.0275912\pi$
$762$	−10824.8	−	19193.9i	−0.514619	−	0.912497i
$763$	5698.24			0.270367
$764$	1087.98	−	29758.4i	0.0515208	−	1.40919i
$765$	−5464.81	+	9833.25i	−0.258275	+	0.464735i
$766$	15751.1	−	15185.8i	0.742965	−	0.716298i
$767$	20261.5			0.953846
$768$	19605.0	+	8284.23i	0.921139	+	0.389234i
$769$	2008.75			0.0941967			0.0470983	−	0.998890i	$-0.485003\pi$
$769$	2008.75			0.0941967			0.0470983	+	0.998890i	$0.485003\pi$
$770$	1330.13	−	1282.38i	0.0622525	−	0.0600181i
$771$	−2857.84	+	11025.4i	−0.133492	+	0.515008i
$772$	430.584	−	11777.3i	0.0200739	−	0.549060i
$773$	−19241.3			−0.895291			−0.447646	−	0.894211i	$-0.647737\pi$
$773$	−19241.3			−0.895291			−0.447646	+	0.894211i	$0.647737\pi$
$774$	−35826.6	+	9526.08i	−1.66378	+	0.442387i
$775$		−	286.378i		−	0.0132735i
$776$	−4479.27	−	4999.38i	−0.207212	−	0.231272i
$777$	10075.9	+	2611.72i	0.465214	+	0.120586i
$778$	−20975.7	+	20222.8i	−0.966600	+	0.931906i
$779$		−	789.436i		−	0.0363087i
$780$	−8253.31	−	2464.39i	−0.378866	−	0.113127i
$781$		−	8336.10i		−	0.381932i
$782$	−10870.7	−	11275.4i	−0.497102	−	0.515609i
$783$	−15638.7	−	14889.7i	−0.713771	−	0.679585i
$784$	−17642.7	−	1291.78i	−0.803695	−	0.0588456i
$785$		−	17441.9i		−	0.793031i
$786$	−10134.5	−	17969.9i	−0.459903	−	0.815479i
$787$	−24750.5			−1.12104			−0.560521	−	0.828140i	$-0.689399\pi$
$787$	−24750.5			−1.12104			−0.560521	+	0.828140i	$0.689399\pi$
$788$	15.8283	−	432.936i	0.000715560	−	0.0195719i
$789$	8206.82	+	2127.24i	0.370305	+	0.0959847i
$790$	−11369.3	−	11792.5i	−0.512026	−	0.531088i
$791$	−16242.9			−0.730128
$792$	9537.99	−	2166.32i	0.427926	−	0.0971929i
$793$	36757.0			1.64600
$794$	19053.6	+	19762.9i	0.851620	+	0.883325i
$795$	12933.7	+	3352.48i	0.576996	+	0.149560i
$796$	−5745.58	−	210.061i	−0.255838	−	0.00935356i
$797$	3787.61			0.168336			0.0841682	−	0.996452i	$-0.473177\pi$
$797$	3787.61			0.168336			0.0841682	+	0.996452i	$0.473177\pi$
$798$	−3238.56	−	5742.46i	−0.143664	−	0.254738i
$799$			5885.69i			0.260602i
$800$	−3478.60	+	2894.71i	−0.153734	+	0.127929i
$801$	16338.5	−	29399.2i	0.720716	−	1.29684i
$802$	−6600.13	−	6845.84i	−0.290597	−	0.301415i
$803$			7848.97i			0.344937i
$804$	−9282.94	+	31088.8i	−0.407194	+	1.36370i
$805$			2711.37i			0.118712i
$806$	−966.615	+	931.921i	−0.0422426	+	0.0407264i
$807$	−15939.6	−	4131.61i	−0.695291	−	0.180223i
$808$	536.559	+	598.861i	0.0233615	+	0.0260741i
$809$			8671.52i			0.376853i	0.982087	+	0.188427i	$0.0603388\pi$
$809$			8671.52i			0.376853i	−0.982087	+	0.188427i	$0.939661\pi$
$810$	9995.80	+	2524.31i	0.433601	+	0.109500i
$811$	−26638.8			−1.15341			−0.576705	−	0.816952i	$-0.695662\pi$
$811$	−26638.8			−1.15341			−0.576705	+	0.816952i	$0.695662\pi$
$812$	10041.4	+	367.119i	0.433971	+	0.0158662i
$813$	−5175.71	+	19967.7i	−0.223272	+	0.861374i
$814$	−8002.13	+	7714.91i	−0.344563	+	0.332196i
$815$	4470.52			0.192142
$816$	8893.68	−	26246.3i	0.381545	−	1.12599i
$817$	−26683.9			−1.14266
$818$	7065.62	−	6812.01i	0.302009	−	0.291169i
$819$	−7981.22	−	4435.55i	−0.340521	−	0.189244i
$820$	−574.074	−	20.9884i	−0.0244482	−	0.000893839i
$821$	10070.8			0.428102			0.214051	−	0.976822i	$-0.431334\pi$
$821$	10070.8			0.428102			0.214051	+	0.976822i	$0.431334\pi$
$822$	5196.35	+	9213.92i	0.220491	+	0.390964i
$823$		−	19497.7i		−	0.825817i	−0.910773	−	0.412908i	$-0.864513\pi$
$823$		−	19497.7i		−	0.825817i	0.910773	−	0.412908i	$-0.135487\pi$
$824$	−13446.5	+	12047.6i	−0.568486	+	0.509344i
$825$	−521.825	+	2013.18i	−0.0220213	+	0.0849574i
$826$	8124.22	−	7832.63i	0.342225	−	0.329942i
$827$			40613.3i			1.70770i	0.520523	+	0.853848i	$0.325737\pi$
$827$			40613.3i			1.70770i	−0.520523	+	0.853848i	$0.674263\pi$
$828$	−7426.17	+	12282.9i	−0.311687	+	0.515533i
$829$		−	13046.2i		−	0.546576i	−0.961932	−	0.273288i	$-0.911889\pi$
$829$		−	13046.2i		−	0.546576i	0.961932	−	0.273288i	$-0.0881112\pi$
$830$	−10858.7	−	11263.0i	−0.454111	−	0.471017i
$831$	−2875.14	+	11092.2i	−0.120021	+	0.463036i
$832$	21090.5	+	2321.51i	0.878823	+	0.0967356i
$833$			23033.3i			0.958050i
$834$	5252.98	−	2962.51i	0.218101	−	0.123002i
$835$	−17708.4			−0.733923
$836$	7035.57	+	257.224i	0.291065	+	0.0106415i
$837$	1108.18	−	1163.93i	0.0457639	−	0.0480660i
$838$	24807.5	+	25731.0i	1.02262	+	1.06070i
$839$	−19242.7			−0.791812			−0.395906	−	0.918291i	$-0.629569\pi$
$839$	−19242.7			−0.791812			−0.395906	+	0.918291i	$0.629569\pi$
$840$	−4262.00	+	2202.39i	−0.175063	+	0.0904641i
$841$	−699.862			−0.0286958
$842$	7593.97	+	7876.68i	0.310814	+	0.322385i
$843$	1731.29	−	6679.23i	0.0707339	−	0.272889i
$844$	49.5336	−	1354.84i	0.00202016	−	0.0552553i
$845$	2398.16			0.0976323
$846$	5212.71	−	1386.03i	0.211840	−	0.0563269i
$847$		−	8770.10i		−	0.355778i
$848$	−32825.4	−	2403.44i	−1.32928	−	0.0973285i
$849$	−6980.62	−	1809.41i	−0.282184	−	0.0731434i
$850$	4089.75	+	4242.01i	0.165032	+	0.171176i
$851$		−	16311.8i		−	0.657064i
$852$	−6192.85	+	20740.0i	−0.249018	+	0.833968i
$853$		−	5866.99i		−	0.235500i	−0.993043	−	0.117750i	$-0.962432\pi$
$853$		−	5866.99i		−	0.235500i	0.993043	−	0.117750i	$-0.0375682\pi$
$854$	14738.4	−	14209.4i	0.590560	−	0.569364i
$855$	6486.44	+	3604.83i	0.259452	+	0.144190i
$856$	−19303.7	+	17295.4i	−0.770779	+	0.690591i
$857$		−	24816.7i		−	0.989174i	−0.869128	−	0.494587i	$-0.835319\pi$
$857$		−	24816.7i		−	0.989174i	0.869128	−	0.494587i	$-0.164681\pi$
$858$	8493.20	−	4789.89i	0.337941	−	0.190588i
$859$	−34929.6			−1.38741			−0.693704	−	0.720261i	$-0.744022\pi$
$859$	−34929.6			−1.38741			−0.693704	+	0.720261i	$0.744022\pi$
$860$	−709.436	+	19404.4i	−0.0281297	+	0.769402i
$861$	−589.494	−	152.800i	−0.0233332	−	0.00604808i
$862$	−18643.8	+	17974.6i	−0.736671	+	0.710230i
$863$	2720.77			0.107319			0.0536594	−	0.998559i	$-0.482911\pi$
$863$	2720.77			0.107319			0.0536594	+	0.998559i	$0.482911\pi$
$864$	−25339.6	−	1695.99i	−0.997768	−	0.0667809i
$865$	7795.74			0.306432
$866$	15646.8	−	15085.2i	0.613971	−	0.591934i
$867$	−10216.5	−	2648.16i	−0.400196	−	0.103733i
$868$	−27.3232	+	747.342i	−0.00106845	+	0.0292240i
$869$	18543.7			0.723879
$870$	−9851.54	+	5555.94i	−0.383906	+	0.216511i
$871$			32345.1i			1.25829i
$872$	11767.6	−	10543.3i	0.456996	−	0.409453i
$873$	7001.11	+	3890.85i	0.271422	+	0.150842i
$874$	−7437.72	+	7170.76i	−0.287854	+	0.277523i
$875$		−	1020.07i		−	0.0394110i
$876$	5830.97	−	19528.0i	0.224897	−	0.753187i
$877$			24974.9i			0.961621i	0.876825	+	0.480811i	$0.159658\pi$
$877$			24974.9i			0.961621i	−0.876825	+	0.480811i	$0.840342\pi$
$878$	27.1070	+	28.1162i	0.00104193	+	0.00108072i
$879$	−46099.8	−	11949.3i	−1.76895	−	0.458520i
$880$	374.104	−	5109.39i	0.0143307	−	0.195725i
$881$			46146.6i			1.76472i	0.470575	+	0.882360i	$0.344047\pi$
$881$			46146.6i			1.76472i	−0.470575	+	0.882360i	$0.655953\pi$
$882$	20399.6	−	5424.12i	0.778786	−	0.207074i
$883$	11741.8			0.447502			0.223751	−	0.974646i	$-0.428170\pi$
$883$	11741.8			0.447502			0.223751	+	0.974646i	$0.428170\pi$
$884$	1009.38	−	27608.4i	0.0384038	−	1.05042i
$885$	−3187.23	+	12296.2i	−0.121059	+	0.467043i
$886$	14076.6	+	14600.7i	0.533763	+	0.553634i
$887$	46378.0			1.75560			0.877801	−	0.479025i	$-0.159010\pi$
$887$	46378.0			1.75560			0.877801	+	0.479025i	$0.159010\pi$
$888$	25640.5	−	13249.8i	0.968961	−	0.500712i
$889$	−12235.6			−0.461607
$890$	−12227.4	−	12682.6i	−0.460521	−	0.477666i
$891$	−9911.15	+	6162.90i	−0.372655	+	0.231723i
$892$	−21741.8	−	794.891i	−0.816109	−	0.0298374i
$893$	3882.46			0.145489
$894$	−43782.4	+	24691.8i	−1.63792	+	0.923735i
$895$			16877.4i			0.630336i
$896$	9354.07	−	7222.24i	0.348769	−	0.269284i
$897$	−3590.33	+	13851.4i	−0.133643	+	0.515589i
$898$	−1056.95	−	1096.30i	−0.0392771	−	0.0407394i
$899$			1763.09i			0.0654086i
$900$	2793.87	−	4621.07i	0.103477	−	0.171151i
$901$			42854.9i			1.58458i
$902$	468.167	−	451.363i	0.0172819	−	0.0166616i
$903$	−5164.82	+	19925.7i	−0.190337	+	0.734313i
$904$	−33543.7	+	30054.0i	−1.23412	+	1.10573i
$905$			18493.8i			0.679287i
$906$	20099.8	+	35640.0i	0.737053	+	1.30691i
$907$	48030.2			1.75834			0.879172	−	0.476504i	$-0.158096\pi$
$907$	48030.2			1.75834			0.879172	+	0.476504i	$0.158096\pi$
$908$	−17202.4	−	628.929i	−0.628725	−	0.0229865i
$909$	−838.643	−	466.074i	−0.0306007	−	0.0170063i
$910$	−3443.05	+	3319.47i	−0.125424	+	0.120923i
$911$	23856.7			0.867627			0.433813	−	0.901003i	$-0.357168\pi$
$911$	23856.7			0.867627			0.433813	+	0.901003i	$0.357168\pi$
$912$	−17313.2	−	5866.66i	−0.628616	−	0.213009i
$913$	17711.0			0.642002
$914$	28768.7	−	27736.1i	1.04112	−	1.00375i
$915$	−5782.06	+	22307.0i	−0.208906	+	0.805951i
$916$	−4796.61	−	175.367i	−0.173018	−	0.00632563i
$917$	−11455.3			−0.412528
$918$	206.928	+	33066.7i	0.00743970	+	1.18885i
$919$		−	23788.7i		−	0.853882i	−0.904279	−	0.426941i	$-0.859591\pi$
$919$		−	23788.7i		−	0.853882i	0.904279	−	0.426941i	$-0.140409\pi$
$920$	5016.80	+	5599.32i	0.179782	+	0.200657i
$921$	−12872.7	−	3336.66i	−0.460553	−	0.119377i
$922$	528.971	−	509.985i	0.0188945	−	0.0182163i
$923$			21578.1i			0.769505i
$924$	1553.85	−	5203.87i	0.0553224	−	0.185276i
$925$			6136.81i			0.218137i
$926$	−32225.8	−	33425.5i	−1.14363	−	1.18621i
$927$	10465.0	−	18830.5i	0.370783	−	0.667179i
$928$	21416.0	−	17821.3i	0.757561	−	0.630402i
$929$			11787.2i			0.416280i	0.978099	+	0.208140i	$0.0667410\pi$
$929$			11787.2i			0.416280i	−0.978099	+	0.208140i	$0.933259\pi$
$930$	−413.507	−	733.211i	−0.0145800	−	0.0258526i
$931$	15193.8			0.534861
$932$	20137.2	+	736.226i	0.707742	+	0.0258754i
$933$	−1859.18	−	481.909i	−0.0652379	−	0.0169100i
$934$	16137.9	+	16738.7i	0.565364	+	0.586412i
$935$	−6670.52			−0.233315
$936$	−24689.3	+	5607.55i	−0.862173	+	0.195821i
$937$	−3452.81			−0.120383			−0.0601913	−	0.998187i	$-0.519171\pi$
$937$	−3452.81			−0.120383			−0.0601913	+	0.998187i	$0.519171\pi$
$938$	12503.9	+	12969.4i	0.435252	+	0.451456i
$939$	−27013.0	−	7001.89i	−0.938803	−	0.243342i
$940$	103.222	−	2823.31i	0.00358161	−	0.0979640i
$941$	6824.77			0.236431			0.118215	−	0.992988i	$-0.462283\pi$
$941$	6824.77			0.236431			0.118215	+	0.992988i	$0.462283\pi$
$942$	−25184.8	−	44656.5i	−0.871088	−	1.54457i
$943$			954.326i			0.0329556i
$944$	2284.98	−	31207.5i	0.0787814	−	1.07597i
$945$	3947.31	−	4145.88i	0.135880	−	0.142715i
$946$	−15256.7	−	15824.6i	−0.524352	−	0.543872i
$947$			53603.4i			1.83936i	0.392664	+	0.919682i	$0.371553\pi$
$947$			53603.4i			1.83936i	−0.392664	+	0.919682i	$0.628447\pi$
$948$	−46136.2	−	13776.0i	−1.58063	−	0.471966i
$949$		−	20317.2i		−	0.694968i
$950$	2798.21	−	2697.78i	0.0955643	−	0.0921343i
$951$	56700.8	+	14697.1i	1.93339	+	0.501142i
$952$	−10268.0	−	11460.3i	−0.349568	−	0.390158i
$953$			48823.8i			1.65956i	0.558093	+	0.829778i	$0.311533\pi$
$953$			48823.8i			1.65956i	−0.558093	+	0.829778i	$0.688467\pi$
$954$	37954.8	−	10091.9i	1.28808	−	0.342493i
$955$	18611.5			0.630631
$956$	595.671	−	16292.7i	0.0201521	−	0.551198i
$957$	3212.62	−	12394.1i	0.108515	−	0.418648i
$958$	3811.89	−	3675.07i	0.128556	−	0.123942i
$959$	5873.61			0.197778
$960$	−4726.51	+	12434.1i	−0.158904	+	0.418031i
$961$	29659.8			0.995595
$962$	20713.7	−	19970.2i	0.694215	−	0.669298i
$963$	15023.4	−	27032.8i	0.502724	−	0.904591i
$964$	142.696	−	3903.00i	0.00476755	−	0.130402i
$965$	7365.73			0.245711
$966$	3915.00	+	6941.90i	0.130397	+	0.231213i
$967$		−	43081.5i		−	1.43269i	−0.697747	−	0.716344i	$-0.745814\pi$
$967$		−	43081.5i		−	1.43269i	0.697747	−	0.716344i	$-0.254186\pi$
$968$	−16227.2	−	18111.4i	−0.538802	−	0.601365i
$969$	−5972.17	+	23040.4i	−0.197991	+	0.763843i
$970$	3020.24	−	2911.84i	0.0999732	−	0.0963850i
$971$			23781.1i			0.785964i	0.919546	+	0.392982i	$0.128556\pi$
$971$			23781.1i			0.785964i	−0.919546	+	0.392982i	$0.871444\pi$
$972$	29237.1	−	7970.18i	0.964794	−	0.263008i
$973$		−	3348.62i		−	0.110331i
$974$	5316.22	+	5514.14i	0.174890	+	0.181401i
$975$	1350.75	−	5211.15i	0.0443679	−	0.171169i
$976$	4145.25	−	56614.5i	0.135949	−	1.85675i
$977$		−	20430.1i		−	0.669005i	−0.942395	−	0.334502i	$-0.891432\pi$
$977$		−	20430.1i		−	0.669005i	0.942395	−	0.334502i	$-0.108568\pi$
$978$	11445.8	−	6455.08i	0.374231	−	0.211054i
$979$	19943.3			0.651063
$980$	403.951	−	11048.8i	0.0131671	−	0.360145i
$981$	−9158.33	+	16479.3i	−0.298066	+	0.536333i
$982$	12686.3	+	13158.6i	0.412256	+	0.427603i
$983$	−32728.4			−1.06193			−0.530963	−	0.847395i	$-0.678170\pi$
$983$	−32728.4			−1.06193			−0.530963	+	0.847395i	$0.678170\pi$
$984$	−1500.10	+	775.181i	−0.0485991	+	0.0251137i
$985$	270.766			0.00875869
$986$	−25178.6	−	26116.0i	−0.813235	−	0.843511i
$987$	751.471	−	2899.14i	0.0242346	−	0.0934962i
$988$	−18211.7	−	665.829i	−0.586428	−	0.0214401i
$989$	32257.4			1.03714
$990$	1570.85	+	5907.80i	0.0504290	+	0.189659i
$991$		−	30927.0i		−	0.991351i	−0.868508	−	0.495675i	$-0.834921\pi$
$991$		−	30927.0i		−	0.991351i	0.868508	−	0.495675i	$-0.165079\pi$
$992$	1326.37	+	1593.91i	0.0424519	+	0.0510149i
$993$	−14224.8	−	3687.13i	−0.454593	−	0.117832i
$994$	8341.61	+	8652.16i	0.266177	+	0.276086i
$995$		−	3593.39i		−	0.114491i
$996$	−44064.4	−	13157.4i	−1.40184	−	0.418583i
$997$		−	31213.2i		−	0.991508i	−0.868463	−	0.495754i	$-0.834892\pi$
$997$		−	31213.2i		−	0.991508i	0.868463	−	0.495754i	$-0.165108\pi$
$998$	21722.2	−	20942.6i	0.688983	−	0.664254i
$999$	−23747.3	+	24941.9i	−0.752084	+	0.789917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.a.11.19	✓	24
3.2	odd	2		120.4.b.b.11.6	yes	24
4.3	odd	2		480.4.b.b.431.1		24
8.3	odd	2		120.4.b.b.11.5	yes	24
8.5	even	2		480.4.b.a.431.1		24
12.11	even	2		480.4.b.a.431.2		24
24.5	odd	2		480.4.b.b.431.2		24
24.11	even	2	inner	120.4.b.a.11.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.19	✓	24	1.1	even	1	trivial
120.4.b.a.11.20	yes	24	24.11	even	2	inner
120.4.b.b.11.5	yes	24	8.3	odd	2
120.4.b.b.11.6	yes	24	3.2	odd	2
480.4.b.a.431.1		24	8.5	even	2
480.4.b.a.431.2		24	12.11	even	2
480.4.b.b.431.1		24	4.3	odd	2
480.4.b.b.431.2		24	24.5	odd	2

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.03621 - 1.96312i) q^{2} +(5.02993 + 1.30378i) q^{3} +(0.292289 - 7.99466i) q^{4} +5.00000 q^{5} +(12.8015 - 7.21960i) q^{6} -8.16056i q^{7} +(-15.0993 - 16.8526i) q^{8} +(23.6003 + 13.1158i) q^{9} +O(q^{10})\)	\(q+(2.03621 - 1.96312i) q^{2} +(5.02993 + 1.30378i) q^{3} +(0.292289 - 7.99466i) q^{4} +5.00000 q^{5} +(12.8015 - 7.21960i) q^{6} -8.16056i q^{7} +(-15.0993 - 16.8526i) q^{8} +(23.6003 + 13.1158i) q^{9} +(10.1810 - 9.81562i) q^{10} +16.0096i q^{11} +(11.8935 - 39.8315i) q^{12} -41.4411i q^{13} +(-16.0202 - 16.6166i) q^{14} +(25.1496 + 6.51890i) q^{15} +(-63.8291 - 4.67350i) q^{16} +83.3315i q^{17} +(73.8032 - 19.6238i) q^{18} +54.9691 q^{19} +(1.46144 - 39.9733i) q^{20} +(10.6396 - 41.0470i) q^{21} +(31.4288 + 32.5989i) q^{22} -66.4506 q^{23} +(-53.9765 - 104.453i) q^{24} +25.0000 q^{25} +(-81.3541 - 84.3828i) q^{26} +(101.608 + 96.7413i) q^{27} +(-65.2409 - 2.38524i) q^{28} -153.913 q^{29} +(64.0073 - 36.0980i) q^{30} -11.4551i q^{31} +(-139.144 + 115.788i) q^{32} +(-20.8730 + 80.5271i) q^{33} +(163.590 + 169.680i) q^{34} -40.8028i q^{35} +(111.755 - 184.843i) q^{36} +245.472i q^{37} +(111.929 - 107.911i) q^{38} +(54.0301 - 208.446i) q^{39} +(-75.4967 - 84.2629i) q^{40} -14.3614i q^{41} +(-58.9160 - 104.467i) q^{42} -485.435 q^{43} +(127.991 + 4.67943i) q^{44} +(118.002 + 65.5791i) q^{45} +(-135.307 + 130.451i) q^{46} +70.6298 q^{47} +(-314.963 - 106.726i) q^{48} +276.405 q^{49} +(50.9052 - 49.0781i) q^{50} +(-108.646 + 419.151i) q^{51} +(-331.308 - 12.1128i) q^{52} +514.271 q^{53} +(396.810 - 2.48319i) q^{54} +80.0480i q^{55} +(-137.527 + 123.219i) q^{56} +(276.491 + 71.6676i) q^{57} +(-313.398 + 302.150i) q^{58} +488.922i q^{59} +(59.4673 - 199.157i) q^{60} +886.970i q^{61} +(-22.4878 - 23.3250i) q^{62} +(107.033 - 192.592i) q^{63} +(-56.0196 + 508.926i) q^{64} -207.206i q^{65} +(115.583 + 204.946i) q^{66} -780.508 q^{67} +(666.207 + 24.3569i) q^{68} +(-334.242 - 86.6369i) q^{69} +(-80.1010 - 83.0830i) q^{70} -520.694 q^{71} +(-135.314 - 595.767i) q^{72} +490.267 q^{73} +(481.893 + 499.833i) q^{74} +(125.748 + 32.5945i) q^{75} +(16.0669 - 439.459i) q^{76} +130.647 q^{77} +(-299.189 - 530.507i) q^{78} -1158.28i q^{79} +(-319.146 - 23.3675i) q^{80} +(384.950 + 619.075i) q^{81} +(-28.1933 - 29.2429i) q^{82} -1106.27i q^{83} +(-325.047 - 97.0573i) q^{84} +416.657i q^{85} +(-988.447 + 952.969i) q^{86} +(-774.170 - 200.668i) q^{87} +(269.803 - 241.734i) q^{88} -1245.71i q^{89} +(369.016 - 98.1190i) q^{90} -338.183 q^{91} +(-19.4228 + 531.250i) q^{92} +(14.9349 - 57.6184i) q^{93} +(143.817 - 138.655i) q^{94} +274.846 q^{95} +(-850.847 + 400.993i) q^{96} +296.653 q^{97} +(562.819 - 542.618i) q^{98} +(-209.979 + 377.832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Introduction

L-functions

Modular forms

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