LMFDB - Embedded newform 120.4.b.b.11.6

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			11.6
Character	$\chi$	$=$	120.11
Dual form			120.4.b.b.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03621 + 1.96312i) q^{2} +(5.02993 - 1.30378i) q^{3} +(0.292289 - 7.99466i) q^{4} -5.00000 q^{5} +(-7.68250 + 12.5291i) q^{6} -8.16056i q^{7} +(15.0993 + 16.8526i) q^{8} +(23.6003 - 13.1158i) q^{9} +O(q^{10})$	\(q+(-2.03621 + 1.96312i) q^{2} +(5.02993 - 1.30378i) q^{3} +(0.292289 - 7.99466i) q^{4} -5.00000 q^{5} +(-7.68250 + 12.5291i) 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} +(-8.95308 - 40.5936i) 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} +(-22.3072 + 73.0369i) 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} +(97.9207 + 65.0811i) 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} +(38.4125 - 62.6457i) 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} +(-97.9585 - 192.510i) 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} +(102.245 + 62.6935i) 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} +(-327.149 + 59.7118i) 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} +(-16.9794 + 396.454i) 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} +(44.7654 + 202.968i) 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} +(200.586 + 122.994i) 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} +(577.385 + 199.686i) 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} +(519.222 + 318.371i) 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} +(-331.267 + 73.0622i) 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} +(111.536 - 365.185i) 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} +(548.922 - 763.820i) 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} + 11 q^{6} - 21 q^{8}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 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 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * 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
$6$	−7.68250	+	12.5291i	−0.522728	+	0.852500i
$7$		−	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	$-0.929586\pi$
$11$		−	16.0096i		−	0.438825i	0.975632	−	0.219413i	$-0.0704141\pi$
$12$	−8.95308	−	40.5936i	−0.215378	−	0.976531i
$13$		−	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	$-0.797375\pi$
$17$		−	83.3315i		−	1.18887i	0.804142	−	0.594437i	$-0.202625\pi$
$18$	−22.3072	+	73.0369i	−0.292103	+	0.956387i
$19$	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	$-0.402608\pi$
$23$	66.4506			0.602431			0.301215	+	0.953556i	$0.402608\pi$
$24$	97.9207	+	65.0811i	0.832832	+	0.553526i
$25$	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	$-0.335983\pi$
$29$	153.913			0.985548			0.492774	+	0.870157i	$0.335983\pi$
$30$	38.4125	−	62.6457i	0.233771	−	0.381249i
$31$		−	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
$36$	−97.9585	−	192.510i	−0.453511	−	0.891250i
$37$			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	$0.00870756\pi$
$41$			14.3614i			0.0547044i	−0.999626	+	0.0273522i	$0.991292\pi$
$42$	102.245	+	62.6935i	0.375636	+	0.230329i
$43$	−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	$-0.534957\pi$
$47$	−70.6298			−0.219200			−0.109600	+	0.993976i	$0.534957\pi$
$48$	−327.149	+	59.7118i	−0.983748	+	0.179555i
$49$	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	$-0.732174\pi$
$53$	−514.271			−1.33284			−0.666420	+	0.745577i	$0.732174\pi$
$54$	−16.9794	+	396.454i	−0.0427890	+	0.999084i
$55$			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	$-0.818641\pi$
$59$		−	488.922i		−	1.07885i	0.842033	−	0.539426i	$-0.181359\pi$
$60$	44.7654	+	202.968i	0.0963198	+	0.436718i
$61$			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
$66$	200.586	+	122.994i	0.374098	+	0.229386i
$67$	−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	$-0.356686\pi$
$71$	520.694			0.870352			0.435176	+	0.900345i	$0.356686\pi$
$72$	577.385	+	199.686i	0.945076	+	0.326850i
$73$	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
$78$	519.222	+	318.371i	0.753721	+	0.462160i
$79$		−	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	$0.261180\pi$
$83$			1106.27i			1.46300i	−0.681841	+	0.731501i	$0.738820\pi$
$84$	−331.267	+	73.0622i	−0.430288	+	0.0949016i
$85$			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	$0.266040\pi$
$89$			1245.71i			1.48365i	−0.670593	+	0.741826i	$0.733960\pi$
$90$	111.536	−	365.185i	0.130632	−	0.427709i
$91$	−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
$96$	548.922	−	763.820i	0.583585	−	0.812052i
$97$	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	$-0.494428\pi$
$101$	35.5352			0.0350088			0.0175044	+	0.999847i	$0.494428\pi$
$102$	1044.07	+	640.194i	1.01351	+	0.621457i
$103$		−	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	$0.173118\pi$
$107$			1145.44i			1.03490i	−0.855714	+	0.517450i	$0.826882\pi$
$108$	−743.715	−	840.595i	−0.662629	−	0.748948i
$109$			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	$0.310809\pi$
$113$			1990.42i			1.65701i	−0.559979	+	0.828507i	$0.689191\pi$
$114$	−422.300	+	688.716i	−0.346948	+	0.565826i
$115$	−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
$120$	−489.603	−	325.405i	−0.372454	−	0.247544i
$121$	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
$126$	596.022	+	182.039i	0.421412	+	0.128709i
$127$		−	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	$0.155066\pi$
$131$			1403.74i			0.936225i	−0.883669	+	0.468112i	$0.844934\pi$
$132$	−649.888	+	143.335i	−0.428526	+	0.0945131i
$133$		−	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	$-0.927949\pi$
$137$		−	719.755i		−	0.448853i	0.974491	−	0.224426i	$-0.0720509\pi$
$138$	−510.507	+	832.569i	−0.314907	+	0.513572i
$139$	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
$144$	−1567.68	+	726.876i	−0.907225	+	0.420646i
$145$	−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	$-0.110617\pi$
$149$	3420.11			1.88045			0.940223	+	0.340560i	$0.110617\pi$
$150$	−192.062	+	313.228i	−0.104546	+	0.170500i
$151$			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
$156$	−1682.25	+	371.026i	−0.863381	+	0.190422i
$157$		−	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
$162$	431.483	+	2016.27i	0.209263	+	0.977860i
$163$	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	$-0.193667\pi$
$167$	3541.69			1.64110			0.820551	+	0.571574i	$0.193667\pi$
$168$	531.098	−	799.087i	0.243899	−	0.366970i
$169$	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	$-0.611308\pi$
$173$	−1559.15			−0.685202			−0.342601	+	0.939481i	$0.611308\pi$
$174$	−1182.43	+	1928.39i	−0.515173	+	0.840179i
$175$		−	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	$-0.751065\pi$
$179$		−	3375.49i		−	1.40947i	0.709469	−	0.704737i	$-0.248935\pi$
$180$	489.792	+	962.551i	0.202816	+	0.398579i
$181$			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
$186$	143.523	+	88.0039i	0.0565785	+	0.0346923i
$187$	−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	$-0.749083\pi$
$191$	−3722.29			−1.41013			−0.705067	+	0.709141i	$0.749083\pi$
$192$	381.753	+	2632.90i	0.143493	+	0.989651i
$193$	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	$-0.503117\pi$
$197$	−54.1531			−0.0195850			−0.00979251	+	0.999952i	$0.503117\pi$
$198$	1169.29	+	357.129i	0.419687	+	0.128182i
$199$		−	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
$204$	−3382.73	+	746.074i	−1.16097	+	0.256057i
$205$		−	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
$210$	−511.224	−	313.467i	−0.167990	−	0.103006i
$211$	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
$216$	3164.55	+	251.624i	0.996854	+	0.0792630i
$217$	−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
$222$	−3075.56	−	1885.84i	−0.929810	−	0.570132i
$223$		−	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	$0.101861\pi$
$227$			2151.74i			0.629145i	−0.949234	+	0.314572i	$0.898139\pi$
$228$	−492.143	−	2231.40i	−0.142952	−	0.648148i
$229$		−	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	$-0.884785\pi$
$233$		−	2518.83i		−	0.708215i	0.935205	−	0.354107i	$-0.115215\pi$
$234$	3026.73	+	924.434i	0.845571	+	0.258257i
$235$	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	$-0.588937\pi$
$239$	−2037.95			−0.551566			−0.275783	+	0.961220i	$0.588937\pi$
$240$	1635.75	−	298.559i	0.439945	−	0.0802995i
$241$	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
$246$	−179.936	−	110.332i	−0.0466355	−	0.0285955i
$247$		−	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	$-0.979935\pi$
$251$		−	501.010i		−	0.125990i	0.998014	−	0.0629949i	$-0.0200652\pi$
$252$	−1570.99	+	799.396i	−0.392711	+	0.199830i
$253$		−	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	$-0.914293\pi$
$257$		−	2191.97i		−	0.532028i	0.963969	−	0.266014i	$-0.0857067\pi$
$258$	3729.35	−	6082.08i	0.899920	−	1.46765i
$259$	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	$-0.561261\pi$
$263$	−1631.60			−0.382542			−0.191271	+	0.981537i	$0.561261\pi$
$264$	1041.92	−	1567.67i	0.242901	−	0.365468i
$265$	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	$-0.383072\pi$
$269$	3168.95			0.718269			0.359134	+	0.933286i	$0.383072\pi$
$270$	84.8970	−	1982.27i	0.0191358	−	0.446804i
$271$			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
$276$	−594.938	−	2697.47i	−0.129750	−	0.588292i
$277$			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	$0.0450168\pi$
$281$			1327.90i			0.281907i	−0.990016	+	0.140953i	$0.954983\pi$
$282$	542.614	−	884.931i	0.114582	−	0.186868i
$283$	−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
$288$	1765.19	−	4557.63i	0.361162	−	0.932503i
$289$	−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	$-0.133208\pi$
$293$	9165.11			1.82741			0.913705	+	0.406378i	$0.133208\pi$
$294$	−2123.48	+	3463.12i	−0.421238	+	0.686984i
$295$			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
$300$	−223.827	−	1014.84i	−0.0430755	−	0.195306i
$301$			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
$306$	6086.28	+	1858.89i	1.13702	+	0.347273i
$307$	−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	$-0.489272\pi$
$311$	369.625			0.0673938			0.0336969	+	0.999432i	$0.489272\pi$
$312$	2697.03	−	4057.94i	0.489389	−	0.736333i
$313$	−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	$-0.983395\pi$
$317$	−11272.7			−1.99728			−0.998640	+	0.0521440i	$0.983395\pi$
$318$	3950.88	−	6443.37i	0.696712	−	1.13625i
$319$		−	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
$324$	−4836.78	−	3258.49i	−0.829352	−	0.558727i
$325$		−	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
$330$	−1002.93	−	614.969i	−0.167302	−	0.102585i
$331$	−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
$336$	487.281	+	2669.72i	0.0791172	+	0.433468i
$337$	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
$342$	−1226.21	+	4014.77i	−0.193876	+	0.634778i
$343$		−	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	$0.124477\pi$
$347$			4927.62i			0.762331i	−0.924507	+	0.381165i	$0.875523\pi$
$348$	−1377.99	−	6247.88i	−0.212265	−	0.962418i
$349$			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	$0.231443\pi$
$353$			8817.03i			1.32941i	−0.747104	+	0.664707i	$0.768557\pi$
$354$	6125.77	+	3756.14i	0.919721	+	0.563946i
$355$	−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	$-0.490463\pi$
$359$	407.550			0.0599155			0.0299577	+	0.999551i	$0.490463\pi$
$360$	−2886.93	−	998.430i	−0.422651	−	0.146172i
$361$	−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
$366$	−11113.0	−	6814.14i	−1.58711	−	0.973172i
$367$			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
$372$	−465.005	+	102.559i	−0.0648102	+	0.0142941i
$373$			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
$378$	3235.29	+	138.561i	0.440225	+	0.0188541i
$379$	−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	$-0.672585\pi$
$383$	−7735.52			−1.03203			−0.516014	+	0.856580i	$0.672585\pi$
$384$	−5946.03	−	4611.70i	−0.790188	−	0.612864i
$385$	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	$-0.265721\pi$
$389$	10301.3			1.34267			0.671335	+	0.741154i	$0.265721\pi$
$390$	−2596.11	−	1591.86i	−0.337074	−	0.206684i
$391$		−	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
$396$	−3082.01	+	1568.28i	−0.391103	+	0.199012i
$397$			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	$0.0671325\pi$
$401$			3362.05i			0.418686i	−0.977842	+	0.209343i	$0.932868\pi$
$402$	5996.25	−	9779.09i	0.743945	−	1.21328i
$403$	−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
$408$	5423.30	−	8159.87i	0.658072	−	0.990132i
$409$	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
$414$	−1482.32	+	4853.35i	−0.175972	+	0.576157i
$415$		−	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	$-0.736389\pi$
$419$		−	12636.7i		−	1.47338i	0.676233	−	0.736688i	$-0.263611\pi$
$420$	1656.33	−	365.311i	0.192431	−	0.0424413i
$421$			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
$426$	−4000.23	+	6523.84i	−0.454957	+	0.741975i
$427$	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	$-0.329037\pi$
$431$	9156.14			1.02328			0.511642	+	0.859199i	$0.329037\pi$
$432$	−6937.65	+	5700.05i	−0.772657	+	0.634823i
$433$	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
$438$	−3766.47	+	6142.62i	−0.410888	+	0.670104i
$439$			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	$-0.874368\pi$
$443$		−	7170.53i		−	0.769034i	0.923118	−	0.384517i	$-0.125632\pi$
$444$	9964.62	−	2197.73i	1.06509	−	0.234910i
$445$		−	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	$0.00900773\pi$
$449$			538.402i			0.0565897i	−0.999600	+	0.0282948i	$0.990992\pi$
$450$	−557.679	+	1825.92i	−0.0584206	+	0.191277i
$451$	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
$456$	5382.61	+	3577.45i	0.552772	+	0.367389i
$457$	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	$-0.504177\pi$
$461$	−259.782			−0.0262457			−0.0131228	+	0.999914i	$0.504177\pi$
$462$	1003.70	−	1636.90i	0.101074	−	0.164838i
$463$		−	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	$-0.866477\pi$
$467$		−	8220.54i		−	0.814564i	0.913302	−	0.407282i	$-0.133523\pi$
$468$	−7977.84	+	4059.51i	−0.787982	+	0.400963i
$469$			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
$474$	14512.3	+	8898.52i	1.40627	+	0.862283i
$475$	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	$-0.528459\pi$
$479$	−1872.05			−0.178573			−0.0892864	+	0.996006i	$0.528459\pi$
$480$	−2744.61	+	3819.10i	−0.260987	+	0.363161i
$481$	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
$486$	4799.10	+	9579.14i	0.447925	+	0.894071i
$487$			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	$-0.904019\pi$
$491$		−	6462.29i		−	0.593969i	0.954882	−	0.296985i	$-0.0959810\pi$
$492$	582.983	−	128.579i	0.0534205	−	0.0117821i
$493$		−	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
$498$	−13860.6	−	8498.93i	−1.24721	−	0.764751i
$499$	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	$-0.678531\pi$
$503$	−12001.4			−1.06385			−0.531924	+	0.846792i	$0.678531\pi$
$504$	1629.55	−	4711.79i	0.144020	−	0.416428i
$505$	−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	$-0.722759\pi$
$509$	−14792.6			−1.28816			−0.644079	+	0.764959i	$0.722759\pi$
$510$	−5220.36	−	3200.97i	−0.453258	−	0.277924i
$511$		−	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
$516$	4346.14	+	19705.6i	0.370791	+	1.68118i
$517$			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	$-0.760521\pi$
$521$		−	16252.9i		−	1.36671i	0.730088	−	0.683353i	$-0.239479\pi$
$522$	−3433.36	+	11241.3i	−0.287881	+	0.942565i
$523$	−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
$528$	955.961	+	5237.53i	0.0787933	+	0.431693i
$529$	−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
$534$	−15607.7	−	9570.16i	−1.26481	−	0.775546i
$535$		−	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
$540$	3718.57	+	4202.98i	0.296337	+	0.334940i
$541$		−	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
$546$	2598.09	−	4237.14i	0.203641	−	0.332111i
$547$	−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
$552$	6506.89	+	4324.68i	0.501724	+	0.333461i
$553$	−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	$-0.559129\pi$
$557$	−4855.83			−0.369386			−0.184693	+	0.982796i	$0.559129\pi$
$558$	836.647	+	255.531i	0.0634732	+	0.0193862i
$559$			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	$0.350401\pi$
$563$			23820.6i			1.78316i	−0.452867	+	0.891578i	$0.649599\pi$
$564$	632.355	+	2867.12i	0.0472109	+	0.214056i
$565$		−	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	$0.266009\pi$
$569$			20135.5i			1.48352i	−0.670664	+	0.741761i	$0.733991\pi$
$570$	2111.50	−	3443.58i	0.155160	−	0.253045i
$571$	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
$576$	5352.91	+	12745.6i	0.387218	+	0.921988i
$577$	−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
$582$	−2279.04	+	3716.81i	−0.162318	+	0.264719i
$583$			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	$0.133004\pi$
$587$			11542.2i			0.811582i	−0.913966	+	0.405791i	$0.866996\pi$
$588$	−2474.68	−	11220.3i	−0.173561	−	0.786934i
$589$		−	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	$-0.913192\pi$
$593$		−	7779.03i		−	0.538695i	0.963043	−	0.269348i	$-0.0868081\pi$
$594$	6347.07	+	271.833i	0.438423	+	0.0187769i
$595$	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	$-0.712563\pi$
$599$	−18156.7			−1.23850			−0.619250	+	0.785194i	$0.712563\pi$
$600$	2448.02	+	1627.03i	0.166566	+	0.110705i
$601$	−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
$606$	−272.999	+	445.226i	−0.0183001	+	0.0298450i
$607$			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
$612$	−16042.2	+	8163.03i	−1.05958	+	0.539168i
$613$		−	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	$0.180022\pi$
$617$			16425.9i			1.07177i	−0.844292	+	0.535884i	$0.819978\pi$
$618$	9996.90	+	6129.80i	0.650703	+	0.398992i
$619$	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
$624$	2474.52	+	13557.4i	0.158750	+	0.869762i
$625$	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
$630$	−2980.11	−	910.195i	−0.188461	−	0.0575604i
$631$			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
$636$	4604.31	+	20876.1i	0.287064	+	1.30156i
$637$		−	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	$-0.924839\pi$
$641$		−	7593.09i		−	0.467877i	0.972251	−	0.233939i	$-0.0751614\pi$
$642$	−14351.4	−	8799.87i	−0.882251	−	0.540970i
$643$	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	$-0.504450\pi$
$647$	−460.162			−0.0279611			−0.0139805	+	0.999902i	$0.504450\pi$
$648$	16245.5	−	2860.23i	0.984852	−	0.173396i
$649$	−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	$-0.555558\pi$
$653$	−5795.47			−0.347312			−0.173656	+	0.984806i	$0.555558\pi$
$654$	−8748.66	−	5364.42i	−0.523088	−	0.320742i
$655$		−	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	$0.189284\pi$
$659$			18954.8i			1.12044i	−0.828343	+	0.560222i	$0.810716\pi$
$660$	3249.44	−	716.676i	0.191643	−	0.0422675i
$661$		−	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
$666$	−17928.6	−	5475.80i	−1.04312	−	0.318593i
$667$	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
$672$	−6233.20	−	4479.51i	−0.357814	−	0.257144i
$673$	−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	$-0.192224\pi$
$677$	28999.0			1.64627			0.823133	+	0.567849i	$0.192224\pi$
$678$	−24938.2	−	15291.4i	−1.41260	−	0.866167i
$679$		−	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	$-0.923094\pi$
$683$		−	8541.52i		−	0.478524i	0.970955	−	0.239262i	$-0.0769055\pi$
$684$	−5384.69	−	10582.1i	−0.301007	−	0.591546i
$685$			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
$690$	2552.53	−	4162.84i	0.140831	−	0.229676i
$691$	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
$696$	15071.2	+	10016.8i	0.820796	+	0.545526i
$697$	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	$-0.946751\pi$
$701$	−36601.7			−1.97208			−0.986040	+	0.166507i	$0.946751\pi$
$702$	16429.5	+	703.646i	0.883321	+	0.0378311i
$703$			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
$708$	−19847.1	+	4377.36i	−1.05353	+	0.232360i
$709$			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
$714$	5224.34	−	8520.21i	0.273832	−	0.446584i
$715$	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	$-0.721608\pi$
$719$	−24728.1			−1.28262			−0.641309	+	0.767283i	$0.721608\pi$
$720$	7838.42	−	3634.38i	0.405723	−	0.188119i
$721$	−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
$726$	−8256.32	+	13465.0i	−0.422067	+	0.688336i
$727$			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
$732$	36005.3	−	7941.11i	1.81803	−	0.400973i
$733$		−	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
$738$	−1048.92	−	320.363i	−0.0523186	−	0.0159793i
$739$	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	$-0.235836\pi$
$743$	29887.3			1.47572			0.737860	+	0.674954i	$0.235836\pi$
$744$	745.511	−	1121.69i	0.0367363	−	0.0552732i
$745$	−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
$750$	960.312	−	1566.14i	0.0467542	−	0.0762499i
$751$			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
$756$	−6859.73	+	6069.13i	−0.330008	+	0.291974i
$757$			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	$0.0275912\pi$
$761$			3634.83i			0.173144i	−0.996246	+	0.0865719i	$0.972409\pi$
$762$	18785.6	+	11518.8i	0.893086	+	0.547614i
$763$	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
$768$	21160.7	−	2282.42i	0.994233	−	0.107239i
$769$	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	$-0.352263\pi$
$773$	19241.3			0.895291			0.447646	+	0.894211i	$0.352263\pi$
$774$	10828.7	−	35454.7i	0.502880	−	1.64650i
$775$		−	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
$780$	8411.23	−	1855.13i	0.386116	−	0.0851593i
$781$		−	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
$786$	−17587.7	−	10784.2i	−0.798131	−	0.489391i
$787$	−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
$792$	3196.89	−	9243.70i	0.143430	−	0.414723i
$793$	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	$-0.526823\pi$
$797$	−3787.61			−0.168336			−0.0841682	+	0.996452i	$0.526823\pi$
$798$	5620.31	+	3446.21i	0.249319	+	0.152875i
$799$			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
$804$	6987.95	+	31683.7i	0.306525	+	1.38980i
$805$			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	$-0.939661\pi$
$809$		−	8671.52i		−	0.376853i	0.982087	−	0.188427i	$-0.0603388\pi$
$810$	−2157.42	−	10081.4i	−0.0935850	−	0.437312i
$811$	−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
$816$	4975.87	+	27261.8i	0.213469	+	1.16955i
$817$	−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	$-0.568666\pi$
$821$	−10070.8			−0.428102			−0.214051	+	0.976822i	$0.568666\pi$
$822$	9017.91	+	5529.52i	0.382647	+	0.234628i
$823$		−	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	$-0.674263\pi$
$827$		−	40613.3i		−	1.70770i	0.520523	−	0.853848i	$-0.325737\pi$
$828$	−6509.40	−	12792.4i	−0.273209	−	0.536917i
$829$		−	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
$834$	−3152.45	+	5141.24i	−0.130888	+	0.213461i
$835$	−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	$-0.370431\pi$
$839$	19242.7			0.791812			0.395906	+	0.918291i	$0.370431\pi$
$840$	−2655.49	+	3995.44i	−0.109075	+	0.164114i
$841$	−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
$846$	1575.55	−	5158.59i	0.0640291	−	0.209640i
$847$		−	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
$852$	−4661.81	−	21136.8i	−0.187454	−	0.849925i
$853$		−	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	$0.164681\pi$
$857$			24816.7i			0.989174i	−0.869128	+	0.494587i	$0.835319\pi$
$858$	5097.00	−	8312.53i	0.202807	−	0.330752i
$859$	−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	$-0.517089\pi$
$863$	−2720.77			−0.107319			−0.0536594	+	0.998559i	$0.517089\pi$
$864$	2936.61	−	25226.0i	0.115631	−	0.993292i
$865$	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
$870$	5912.17	−	9641.97i	0.230392	−	0.375740i
$871$			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
$876$	−4389.40	−	19901.7i	−0.169297	−	0.767599i
$877$			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	$-0.655953\pi$
$881$		−	46146.6i		−	1.76472i	0.470575	−	0.882360i	$-0.344047\pi$
$882$	−6165.82	+	20187.8i	−0.235390	+	0.770701i
$883$	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	$-0.840990\pi$
$887$	−46378.0			−1.75560			−0.877801	+	0.479025i	$0.840990\pi$
$888$	−15975.6	+	24036.8i	−0.603723	+	0.908359i
$889$	−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
$894$	−26275.0	+	42851.0i	−0.982961	+	1.60308i
$895$			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
$900$	−2448.96	−	4812.75i	−0.0907023	−	0.178250i
$901$			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
$906$	−34881.8	−	21388.5i	−1.27911	−	0.784310i
$907$	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	$-0.642832\pi$
$911$	−23856.7			−0.867627			−0.433813	+	0.901003i	$0.642832\pi$
$912$	−17983.1	+	3282.30i	−0.652938	+	0.119175i
$913$	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
$918$	33037.1	+	1414.92i	1.18779	+	0.0508707i
$919$		−	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
$924$	1169.70	+	5303.45i	0.0416452	+	0.188821i
$925$			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	$-0.933259\pi$
$929$		−	11787.2i		−	0.416280i	0.978099	−	0.208140i	$-0.0667410\pi$
$930$	−717.614	−	440.020i	−0.0253027	−	0.0155149i
$931$	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
$936$	8275.22	−	23927.5i	0.288979	−	0.835571i
$937$	−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	$-0.537717\pi$
$941$	−6824.77			−0.236431			−0.118215	+	0.992988i	$0.537717\pi$
$942$	43706.5	+	26799.5i	1.51171	+	0.926939i
$943$			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	$-0.628447\pi$
$947$		−	53603.4i		−	1.83936i	0.392664	−	0.919682i	$-0.371553\pi$
$948$	−47019.0	+	10370.2i	−1.61087	+	0.355284i
$949$		−	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	$-0.688467\pi$
$953$		−	48823.8i		−	1.65956i	0.558093	−	0.829778i	$-0.311533\pi$
$954$	11471.9	−	37560.7i	0.389326	−	1.27471i
$955$	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
$960$	−1908.77	−	13164.5i	−0.0641720	−	0.442586i
$961$	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
$966$	6794.23	+	4166.02i	0.226295	+	0.138757i
$967$		−	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	$-0.871444\pi$
$971$		−	23781.1i		−	0.785964i	0.919546	−	0.392982i	$-0.128556\pi$
$972$	−28577.0	−	10083.9i	−0.943012	−	0.332758i
$973$		−	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	$0.108568\pi$
$977$			20430.1i			0.669005i	−0.942395	+	0.334502i	$0.891432\pi$
$978$	−6868.95	+	11202.4i	−0.224586	+	0.366270i
$979$	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	$-0.321830\pi$
$983$	32728.4			1.06193			0.530963	+	0.847395i	$0.321830\pi$
$984$	−934.658	+	1406.28i	−0.0302803	+	0.0455596i
$985$	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
$990$	−5846.46	−	1785.64i	−0.187690	−	0.0573247i
$991$		−	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
$996$	44907.6	−	9904.54i	1.42867	−	0.315098i
$997$		−	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.b.11.6	yes	24
3.2	odd	2		120.4.b.a.11.19	✓	24
4.3	odd	2		480.4.b.a.431.2		24
8.3	odd	2		120.4.b.a.11.20	yes	24
8.5	even	2		480.4.b.b.431.2		24
12.11	even	2		480.4.b.b.431.1		24
24.5	odd	2		480.4.b.a.431.1		24
24.11	even	2	inner	120.4.b.b.11.5	yes	24

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

\(f(q)\)	\(=\)	\(q+(-2.03621 + 1.96312i) q^{2} +(5.02993 - 1.30378i) q^{3} +(0.292289 - 7.99466i) q^{4} -5.00000 q^{5} +(-7.68250 + 12.5291i) q^{6} -8.16056i q^{7} +(15.0993 + 16.8526i) q^{8} +(23.6003 - 13.1158i) q^{9} +O(q^{10})\)	\(q+(-2.03621 + 1.96312i) q^{2} +(5.02993 - 1.30378i) q^{3} +(0.292289 - 7.99466i) q^{4} -5.00000 q^{5} +(-7.68250 + 12.5291i) 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} +(-8.95308 - 40.5936i) 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} +(-22.3072 + 73.0369i) 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} +(97.9207 + 65.0811i) 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} +(38.4125 - 62.6457i) 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} +(-97.9585 - 192.510i) 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} +(102.245 + 62.6935i) 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} +(-327.149 + 59.7118i) 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} +(-16.9794 + 396.454i) 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} +(44.7654 + 202.968i) 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} +(200.586 + 122.994i) 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} +(577.385 + 199.686i) 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} +(519.222 + 318.371i) 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} +(-331.267 + 73.0622i) 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} +(111.536 - 365.185i) 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} +(548.922 - 763.820i) q^{96} +296.653 q^{97} +(-562.819 + 542.618i) q^{98} +(-209.979 - 377.832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Introduction

L-functions

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