LMFDB - Embedded newform 120.4.w.c.53.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.33
Character	$\chi$	$=$	120.53
Dual form			120.4.w.c.77.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0740349 + 2.82746i) q^{2} +(-1.65046 - 4.92707i) q^{3} +(-7.98904 + 0.418661i) q^{4} +(9.98780 - 5.02432i) q^{5} +(13.8089 - 5.03137i) q^{6} +(-17.9179 + 17.9179i) q^{7} +(-1.77521 - 22.5577i) q^{8} +(-21.5520 + 16.2638i) q^{9} +(14.9455 + 27.8681i) q^{10} -22.2199 q^{11} +(15.2483 + 38.6715i) q^{12} +(-31.5577 + 31.5577i) q^{13} +(-51.9887 - 49.3356i) q^{14} +(-41.2396 - 40.9182i) q^{15} +(63.6494 - 6.68940i) q^{16} +(-17.9116 - 17.9116i) q^{17} +(-47.5809 - 59.7333i) q^{18} -149.688 q^{19} +(-77.6894 + 44.3210i) q^{20} +(117.855 + 58.7100i) q^{21} +(-1.64505 - 62.8258i) q^{22} +(-44.6598 + 44.6598i) q^{23} +(-108.213 + 45.9771i) q^{24} +(74.5124 - 100.364i) q^{25} +(-91.5643 - 86.8916i) q^{26} +(115.704 + 79.3454i) q^{27} +(135.645 - 150.648i) q^{28} -145.403i q^{29} +(112.641 - 119.633i) q^{30} +102.917 q^{31} +(23.6263 + 179.471i) q^{32} +(36.6730 + 109.479i) q^{33} +(49.3181 - 51.9703i) q^{34} +(-88.9352 + 268.986i) q^{35} +(165.371 - 138.955i) q^{36} +(-2.90700 - 2.90700i) q^{37} +(-11.0821 - 423.236i) q^{38} +(207.571 + 103.402i) q^{39} +(-131.067 - 216.382i) q^{40} +163.475i q^{41} +(-157.275 + 337.578i) q^{42} +(-251.330 + 251.330i) q^{43} +(177.516 - 9.30261i) q^{44} +(-133.542 + 270.724i) q^{45} +(-129.580 - 122.967i) q^{46} +(-269.250 - 269.250i) q^{47} +(-138.010 - 302.565i) q^{48} -299.102i q^{49} +(289.291 + 203.250i) q^{50} +(-58.6892 + 117.814i) q^{51} +(238.903 - 265.327i) q^{52} +(411.760 + 411.760i) q^{53} +(-215.780 + 333.021i) q^{54} +(-221.928 + 111.640i) q^{55} +(435.994 + 372.378i) q^{56} +(247.053 + 737.521i) q^{57} +(411.121 - 10.7649i) q^{58} -91.0255i q^{59} +(346.596 + 309.631i) q^{60} -602.630i q^{61} +(7.61948 + 290.994i) q^{62} +(94.7529 - 677.580i) q^{63} +(-505.697 + 80.0894i) q^{64} +(-156.636 + 473.747i) q^{65} +(-306.832 + 111.797i) q^{66} +(571.973 + 571.973i) q^{67} +(150.595 + 135.597i) q^{68} +(293.751 + 146.333i) q^{69} +(-767.130 - 231.546i) q^{70} -802.988i q^{71} +(405.133 + 457.291i) q^{72} +(348.690 + 348.690i) q^{73} +(8.00420 - 8.43464i) q^{74} +(-617.479 - 201.481i) q^{75} +(1195.86 - 62.6684i) q^{76} +(398.134 - 398.134i) q^{77} +(-276.998 + 594.554i) q^{78} -923.691i q^{79} +(602.108 - 386.608i) q^{80} +(199.976 - 701.035i) q^{81} +(-462.218 + 12.1028i) q^{82} +(-501.421 - 501.421i) q^{83} +(-966.131 - 419.695i) q^{84} +(-268.891 - 88.9037i) q^{85} +(-729.232 - 692.018i) q^{86} +(-716.410 + 239.981i) q^{87} +(39.4451 + 501.229i) q^{88} +178.422 q^{89} +(-775.347 - 357.542i) q^{90} -1130.89i q^{91} +(338.091 - 375.486i) q^{92} +(-169.861 - 507.081i) q^{93} +(741.358 - 781.226i) q^{94} +(-1495.05 + 752.079i) q^{95} +(845.271 - 412.617i) q^{96} +(-82.1236 + 82.1236i) q^{97} +(845.699 - 22.1440i) q^{98} +(478.883 - 361.380i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) $ 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Character values

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

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0740349	+	2.82746i	0.0261753	+	0.999657i
$2$	0.0740349	+	2.82746i	0.0261753	+	0.999657i
$3$	−1.65046	−	4.92707i	−0.317630	−	0.948215i
$3$	−1.65046	−	4.92707i	−0.317630	−	0.948215i
$4$	−7.98904	+	0.418661i	−0.998630	+	0.0523327i
$5$	9.98780	−	5.02432i	0.893336	−	0.449389i
$5$	9.98780	−	5.02432i	0.893336	−	0.449389i
$6$	13.8089	−	5.03137i	0.939576	−	0.342341i
$7$	−17.9179	+	17.9179i	−0.967476	+	0.967476i	−0.999487	−	0.0320118i	$-0.989809\pi$
$7$	−17.9179	+	17.9179i	−0.967476	+	0.967476i	0.0320118	+	0.999487i	$0.489809\pi$
$8$	−1.77521	−	22.5577i	−0.0784542	−	0.996918i
$9$	−21.5520	+	16.2638i	−0.798222	+	0.602364i
$10$	14.9455	+	27.8681i	0.472618	+	0.881267i
$11$	−22.2199			−0.609050			−0.304525	−	0.952504i	$-0.598498\pi$
$11$	−22.2199			−0.609050			−0.304525	+	0.952504i	$0.598498\pi$
$12$	15.2483	+	38.6715i	0.366818	+	0.930293i
$13$	−31.5577	+	31.5577i	−0.673271	+	0.673271i	−0.958469	−	0.285198i	$-0.907941\pi$
$13$	−31.5577	+	31.5577i	−0.673271	+	0.673271i	0.285198	+	0.958469i	$0.407941\pi$
$14$	−51.9887	−	49.3356i	−0.992468	−	0.941820i
$15$	−41.2396	−	40.9182i	−0.709868	−	0.704335i
$16$	63.6494	−	6.68940i	0.994523	−	0.104522i
$17$	−17.9116	−	17.9116i	−0.255541	−	0.255541i	0.567697	−	0.823238i	$-0.307835\pi$
$17$	−17.9116	−	17.9116i	−0.255541	−	0.255541i	−0.823238	+	0.567697i	$0.807835\pi$
$18$	−47.5809	−	59.7333i	−0.623051	−	0.782181i
$19$	−149.688			−1.80741			−0.903703	−	0.428160i	$-0.859162\pi$
$19$	−149.688			−1.80741			−0.903703	+	0.428160i	$0.859162\pi$
$20$	−77.6894	+	44.3210i	−0.868594	+	0.495524i
$21$	117.855	+	58.7100i	1.22467	+	0.610075i
$22$	−1.64505	−	62.8258i	−0.0159421	−	0.608842i
$23$	−44.6598	+	44.6598i	−0.404879	+	0.404879i	−0.879948	−	0.475070i	$-0.842423\pi$
$23$	−44.6598	+	44.6598i	−0.404879	+	0.404879i	0.475070	+	0.879948i	$0.342423\pi$
$24$	−108.213	+	45.9771i	−0.920372	+	0.391043i
$25$	74.5124	−	100.364i	0.596099	−	0.802911i
$26$	−91.5643	−	86.8916i	−0.690663	−	0.655417i
$27$	115.704	+	79.3454i	0.824710	+	0.565556i
$28$	135.645	−	150.648i	0.915519	−	1.01678i
$29$		−	145.403i		−	0.931056i	−0.885033	−	0.465528i	$-0.845864\pi$
$29$		−	145.403i		−	0.931056i	0.885033	−	0.465528i	$-0.154136\pi$
$30$	112.641	−	119.633i	0.685512	−	0.728061i
$31$	102.917			0.596274			0.298137	−	0.954523i	$-0.403635\pi$
$31$	102.917			0.596274			0.298137	+	0.954523i	$0.403635\pi$
$32$	23.6263	+	179.471i	0.130518	+	0.991446i
$33$	36.6730	+	109.479i	0.193453	+	0.577510i
$34$	49.3181	−	51.9703i	0.248764	−	0.262142i
$35$	−88.9352	+	268.986i	−0.429508	+	1.29905i
$36$	165.371	−	138.955i	0.765605	−	0.643311i
$37$	−2.90700	−	2.90700i	−0.0129164	−	0.0129164i	0.700619	−	0.713536i	$-0.252907\pi$
$37$	−2.90700	−	2.90700i	−0.0129164	−	0.0129164i	−0.713536	+	0.700619i	$0.752907\pi$
$38$	−11.0821	−	423.236i	−0.0473094	−	1.80679i
$39$	207.571	+	103.402i	0.852256	+	0.424554i
$40$	−131.067	−	216.382i	−0.518090	−	0.855326i
$41$			163.475i			0.622694i	0.950296	+	0.311347i	$0.100780\pi$
$41$			163.475i			0.622694i	−0.950296	+	0.311347i	$0.899220\pi$
$42$	−157.275	+	337.578i	−0.577810	+	1.24022i
$43$	−251.330	+	251.330i	−0.891336	+	0.891336i	−0.994649	−	0.103313i	$-0.967056\pi$
$43$	−251.330	+	251.330i	−0.891336	+	0.891336i	0.103313	+	0.994649i	$0.467056\pi$
$44$	177.516	−	9.30261i	0.608216	−	0.0318732i
$45$	−133.542	+	270.724i	−0.442385	+	0.896825i
$46$	−129.580	−	122.967i	−0.415338	−	0.394142i
$47$	−269.250	−	269.250i	−0.835619	−	0.835619i	0.152660	−	0.988279i	$-0.451216\pi$
$47$	−269.250	−	269.250i	−0.835619	−	0.835619i	−0.988279	+	0.152660i	$0.951216\pi$
$48$	−138.010	−	302.565i	−0.415000	−	0.909821i
$49$		−	299.102i		−	0.872019i
$50$	289.291	+	203.250i	0.818239	+	0.574879i
$51$	−58.6892	+	117.814i	−0.161140	+	0.323475i
$52$	238.903	−	265.327i	0.637114	−	0.707582i
$53$	411.760	+	411.760i	1.06716	+	1.06716i	0.997576	+	0.0695869i	$0.0221681\pi$
$53$	411.760	+	411.760i	1.06716	+	1.06716i	0.0695869	+	0.997576i	$0.477832\pi$
$54$	−215.780	+	333.021i	−0.543776	+	0.839231i
$55$	−221.928	+	111.640i	−0.544087	+	0.273700i
$56$	435.994	+	372.378i	1.04040	+	0.888591i
$57$	247.053	+	737.521i	0.574087	+	1.71381i
$58$	411.121	−	10.7649i	0.930737	−	0.0243707i
$59$		−	91.0255i		−	0.200856i	−0.994944	−	0.100428i	$-0.967979\pi$
$59$		−	91.0255i		−	0.200856i	0.994944	−	0.100428i	$-0.0320212\pi$
$60$	346.596	+	309.631i	0.745755	+	0.666220i
$61$		−	602.630i		−	1.26490i	−0.774601	−	0.632450i	$-0.782049\pi$
$61$		−	602.630i		−	1.26490i	0.774601	−	0.632450i	$-0.217951\pi$
$62$	7.61948	+	290.994i	0.0156077	+	0.596070i
$63$	94.7529	−	677.580i	0.189488	−	1.35503i
$64$	−505.697	+	80.0894i	−0.987690	+	0.156425i
$65$	−156.636	+	473.747i	−0.298897	+	0.904018i
$66$	−306.832	+	111.797i	−0.572249	+	0.208503i
$67$	571.973	+	571.973i	1.04295	+	1.04295i	0.999035	+	0.0439134i	$0.0139826\pi$
$67$	571.973	+	571.973i	1.04295	+	1.04295i	0.0439134	+	0.999035i	$0.486017\pi$
$68$	150.595	+	135.597i	0.268564	+	0.241817i
$69$	293.751	+	146.333i	0.512514	+	0.255310i
$70$	−767.130	−	231.546i	−1.30985	−	0.395358i
$71$		−	802.988i		−	1.34221i	−0.741361	−	0.671107i	$-0.765819\pi$
$71$		−	802.988i		−	1.34221i	0.741361	−	0.671107i	$-0.234181\pi$
$72$	405.133	+	457.291i	0.663131	+	0.748503i
$73$	348.690	+	348.690i	0.559057	+	0.559057i	0.929039	−	0.369982i	$-0.120636\pi$
$73$	348.690	+	348.690i	0.559057	+	0.559057i	−0.369982	+	0.929039i	$0.620636\pi$
$74$	8.00420	−	8.43464i	0.0125739	−	0.0132501i
$75$	−617.479	−	201.481i	−0.950671	−	0.310201i
$76$	1195.86	−	62.6684i	1.80493	−	0.0945863i
$77$	398.134	−	398.134i	0.589241	−	0.589241i
$78$	−276.998	+	594.554i	−0.402100	+	0.863077i
$79$		−	923.691i		−	1.31549i	−0.753243	−	0.657743i	$-0.771511\pi$
$79$		−	923.691i		−	1.31549i	0.753243	−	0.657743i	$-0.228489\pi$
$80$	602.108	−	386.608i	0.841472	−	0.540301i
$81$	199.976	−	701.035i	0.274316	−	0.961640i
$82$	−462.218	+	12.1028i	−0.622480	+	0.0162992i
$83$	−501.421	−	501.421i	−0.663109	−	0.663109i	0.293003	−	0.956112i	$-0.405346\pi$
$83$	−501.421	−	501.421i	−0.663109	−	0.663109i	−0.956112	+	0.293003i	$0.905346\pi$
$84$	−966.131	−	419.695i	−1.25492	−	0.545148i
$85$	−268.891	−	88.9037i	−0.343121	−	0.113447i
$86$	−729.232	−	692.018i	−0.914362	−	0.867700i
$87$	−716.410	+	239.981i	−0.882841	+	0.295732i
$88$	39.4451	+	501.229i	0.0477825	+	0.607173i
$89$	178.422			0.212502			0.106251	−	0.994339i	$-0.466115\pi$
$89$	178.422			0.212502			0.106251	+	0.994339i	$0.466115\pi$
$90$	−775.347	−	357.542i	−0.908098	−	0.418759i
$91$		−	1130.89i		−	1.30275i
$92$	338.091	−	375.486i	0.383135	−	0.425512i
$93$	−169.861	−	507.081i	−0.189395	−	0.565396i
$94$	741.358	−	781.226i	0.813460	−	0.857205i
$95$	−1495.05	+	752.079i	−1.61462	+	0.812228i
$96$	845.271	−	412.617i	0.898647	−	0.438673i
$97$	−82.1236	+	82.1236i	−0.0859628	+	0.0859628i	−0.748781	−	0.662818i	$-0.769360\pi$
$97$	−82.1236	+	82.1236i	−0.0859628	+	0.0859628i	0.662818	+	0.748781i	$0.269360\pi$
$98$	845.699	−	22.1440i	0.871720	−	0.0228253i
$99$	478.883	−	361.380i	0.486157	−	0.366870i
$100$	−553.264	+	833.006i	−0.553264	+	0.833006i
$101$	−356.837			−0.351551			−0.175775	−	0.984430i	$-0.556243\pi$
$101$	−356.837			−0.351551			−0.175775	+	0.984430i	$0.556243\pi$
$102$	−337.458	−	157.219i	−0.327582	−	0.152618i
$103$	1013.72	+	1013.72i	0.969759	+	0.969759i	0.999556	−	0.0297966i	$-0.00948596\pi$
$103$	1013.72	+	1013.72i	0.969759	+	0.969759i	−0.0297966	+	0.999556i	$0.509486\pi$
$104$	767.889	+	655.846i	0.724016	+	0.618375i
$105$	1472.09	−	5.75960i	1.36821	−	0.00535314i
$106$	−1133.75	+	1194.72i	−1.03886	+	1.09473i
$107$	118.350	−	118.350i	0.106928	−	0.106928i	−0.651619	−	0.758547i	$-0.725910\pi$
$107$	118.350	−	118.350i	0.106928	−	0.106928i	0.758547	+	0.651619i	$0.225910\pi$
$108$	−957.579	−	585.453i	−0.853177	−	0.521622i
$109$	−111.674			−0.0981327			−0.0490663	−	0.998796i	$-0.515625\pi$
$109$	−111.674			−0.0981327			−0.0490663	+	0.998796i	$0.515625\pi$
$110$	−332.088	−	619.227i	−0.287848	−	0.536736i
$111$	−9.52511	+	19.1209i	−0.00814490	+	0.0163502i
$112$	−1020.60	+	1260.32i	−0.861054	+	1.06330i
$113$	−1577.96	+	1577.96i	−1.31364	+	1.31364i	−0.394936	+	0.918709i	$0.629233\pi$
$113$	−1577.96	+	1577.96i	−1.31364	+	1.31364i	−0.918709	+	0.394936i	$0.870767\pi$
$114$	−2067.02	+	753.134i	−1.69819	+	0.618750i
$115$	−221.668	+	670.438i	−0.179745	+	0.543641i
$116$	60.8746	+	1161.63i	0.0487247	+	0.929781i
$117$	166.882	−	1193.38i	0.131866	−	0.942973i
$118$	257.371	−	6.73907i	0.200787	−	0.00525747i
$119$	641.875			0.494459
$120$	−849.809	+	1002.91i	−0.646472	+	0.762938i
$121$	−837.276			−0.629058
$122$	1703.91	−	44.6157i	1.26447	−	0.0331091i
$123$	805.450	−	269.808i	0.590447	−	0.197786i
$124$	−822.210	+	43.0875i	−0.595457	+	0.0312046i
$125$	239.955	−	1376.79i	0.171698	−	0.985150i
$126$	1922.84	+	217.745i	1.35953	+	0.153955i
$127$	−838.981	+	838.981i	−0.586201	+	0.586201i	−0.936600	−	0.350399i	$-0.886046\pi$
$127$	−838.981	+	838.981i	−0.586201	+	0.586201i	0.350399	+	0.936600i	$0.386046\pi$
$128$	−263.889	−	1423.91i	−0.182224	−	0.983257i
$129$	1653.13	+	823.511i	1.12829	+	0.562063i
$130$	−1351.10	−	407.808i	−0.911532	−	0.275131i
$131$	−1691.20			−1.12795			−0.563973	−	0.825793i	$-0.690728\pi$
$131$	−1691.20			−1.12795			−0.563973	+	0.825793i	$0.690728\pi$
$132$	−338.816	−	859.278i	−0.223410	−	0.566595i
$133$	2682.09	−	2682.09i	1.74862	−	1.74862i
$134$	−1574.88	+	1659.57i	−1.01529	+	1.06989i
$135$	1554.28	+	211.154i	0.990898	+	0.134617i
$136$	−372.246	+	435.840i	−0.234705	+	0.274801i
$137$	−1612.74	−	1612.74i	−1.00573	−	1.00573i	−0.999983	−	0.00575124i	$-0.998169\pi$
$137$	−1612.74	−	1612.74i	−1.00573	−	1.00573i	−0.00575124	−	0.999983i	$-0.501831\pi$
$138$	−392.002	+	841.402i	−0.241807	+	0.519021i
$139$	−85.9424			−0.0524428			−0.0262214	−	0.999656i	$-0.508347\pi$
$139$	−85.9424			−0.0524428			−0.0262214	+	0.999656i	$0.508347\pi$
$140$	597.893	−	2186.17i	0.360937	−	1.31975i
$141$	−882.226	+	1771.00i	−0.526928	+	1.05776i
$142$	2270.42	−	59.4492i	1.34175	−	0.0351329i
$143$	701.208	−	701.208i	0.410056	−	0.410056i
$144$	−1262.98	+	1179.35i	−0.730889	+	0.682496i
$145$	−730.551	−	1452.26i	−0.418406	−	0.831746i
$146$	−960.092	+	1011.72i	−0.544231	+	0.573498i
$147$	−1473.70	+	493.655i	−0.826861	+	0.276980i
$148$	24.4412	+	22.0071i	0.0135747	+	0.0122228i
$149$			2184.24i			1.20094i	0.799647	+	0.600471i	$0.205020\pi$
$149$			2184.24i			1.20094i	−0.799647	+	0.600471i	$0.794980\pi$
$150$	523.965	−	1760.81i	0.285211	−	0.958465i
$151$	334.973			0.180528			0.0902640	−	0.995918i	$-0.471229\pi$
$151$	334.973			0.180528			0.0902640	+	0.995918i	$0.471229\pi$
$152$	265.728	+	3376.61i	0.141798	+	1.80183i
$153$	677.340	+	94.7193i	0.357907	+	0.0500497i
$154$	1155.18	+	1096.23i	0.604463	+	0.573616i
$155$	1027.92	−	517.090i	0.532673	−	0.267959i
$156$	−1701.59	−	739.182i	−0.873307	−	0.379371i
$157$	466.545	+	466.545i	0.237162	+	0.237162i	0.815674	−	0.578512i	$-0.196366\pi$
$157$	466.545	+	466.545i	0.237162	+	0.237162i	−0.578512	+	0.815674i	$0.696366\pi$
$158$	2611.70	−	68.3854i	1.31503	−	0.0344332i
$159$	1349.18	−	2708.36i	0.672936	−	1.35086i
$160$	1137.69	+	1673.81i	0.562141	+	0.827041i
$161$		−	1600.42i		−	0.783420i
$162$	1996.95	+	513.524i	0.968490	+	0.249051i
$163$	−1944.38	+	1944.38i	−0.934331	+	0.934331i	−0.997973	−	0.0636417i	$-0.979729\pi$
$163$	−1944.38	+	1944.38i	−0.934331	+	0.934331i	0.0636417	+	0.997973i	$0.479729\pi$
$164$	−68.4405	−	1306.00i	−0.0325872	−	0.621840i
$165$	916.340	+	909.197i	0.432345	+	0.428975i
$166$	1380.62	−	1454.87i	0.645525	−	0.680239i
$167$	−633.228	−	633.228i	−0.293417	−	0.293417i	0.545011	−	0.838429i	$-0.316525\pi$
$167$	−633.228	−	633.228i	−0.293417	−	0.293417i	−0.838429	+	0.545011i	$0.816525\pi$
$168$	1115.14	−	2762.77i	0.512114	−	1.26876i
$169$			205.228i			0.0934129i
$170$	231.464	−	766.859i	0.104426	−	0.345973i
$171$	3226.07	−	2434.49i	1.44271	−	1.08872i
$172$	1902.66	−	2113.11i	0.843469	−	0.936761i
$173$	−818.451	−	818.451i	−0.359686	−	0.359686i	0.504011	−	0.863697i	$-0.331857\pi$
$173$	−818.451	−	818.451i	−0.359686	−	0.359686i	−0.863697	+	0.504011i	$0.831857\pi$
$174$	−731.576	−	2007.85i	−0.318739	−	0.874798i
$175$	463.204	+	3133.42i	0.200085	+	1.35351i
$176$	−1414.28	+	148.638i	−0.605714	+	0.0636591i
$177$	−448.489	+	150.234i	−0.190455	+	0.0637980i
$178$	13.2095	+	504.481i	0.00556231	+	0.212429i
$179$			1046.94i			0.437162i	0.975819	+	0.218581i	$0.0701428\pi$
$179$			1046.94i			0.437162i	−0.975819	+	0.218581i	$0.929857\pi$
$180$	953.533	−	2218.73i	0.394845	−	0.918748i
$181$			2786.63i			1.14436i	0.820130	+	0.572178i	$0.193901\pi$
$181$			2786.63i			1.14436i	−0.820130	+	0.572178i	$0.806099\pi$
$182$	3197.56	−	83.7257i	1.30230	−	0.0340998i
$183$	−2969.20	+	994.615i	−1.19940	+	0.401771i
$184$	1086.70	+	928.140i	0.435395	+	0.371866i
$185$	−43.6403	−	14.4288i	−0.0173432	−	0.00573422i
$186$	1421.17	−	517.815i	0.560245	−	0.204129i
$187$	397.993	+	397.993i	0.155637	+	0.155637i
$188$	2263.77	+	2038.32i	0.878204	+	0.790744i
$189$	−3494.87	+	651.462i	−1.34505	+	0.250724i
$190$	−2237.16	−	4171.51i	−0.854213	−	1.59281i
$191$			2755.23i			1.04378i	0.853014	+	0.521888i	$0.174772\pi$
$191$			2755.23i			1.04378i	−0.853014	+	0.521888i	$0.825228\pi$
$192$	1229.24	+	2359.42i	0.462045	+	0.886857i
$193$	−2294.84	−	2294.84i	−0.855886	−	0.855886i	0.134965	−	0.990850i	$-0.456908\pi$
$193$	−2294.84	−	2294.84i	−0.855886	−	0.855886i	−0.990850	+	0.134965i	$0.956908\pi$
$194$	−238.281	−	226.121i	−0.0881834	−	0.0836832i
$195$	2592.71	−	10.1440i	0.952141	−	0.00372528i
$196$	125.223	+	2389.54i	0.0456350	+	0.870824i
$197$	−2519.40	+	2519.40i	−0.911166	+	0.911166i	−0.996364	−	0.0851980i	$-0.972848\pi$
$197$	−2519.40	+	2519.40i	−0.911166	+	0.911166i	0.0851980	+	0.996364i	$0.472848\pi$
$198$	1057.24	+	1327.27i	0.379469	+	0.476388i
$199$		−	1923.48i		−	0.685186i	−0.939484	−	0.342593i	$-0.888695\pi$
$199$		−	1923.48i		−	0.685186i	0.939484	−	0.342593i	$-0.111305\pi$
$200$	−2396.25	−	1502.66i	−0.847202	−	0.531270i
$201$	1874.13	−	3762.16i	0.657667	−	1.32021i
$202$	−26.4184	−	1008.94i	−0.00920194	−	0.351430i
$203$	2605.31	+	2605.31i	0.900775	+	0.900775i
$204$	419.546	−	965.789i	0.143991	−	0.331465i
$205$	821.349	+	1632.75i	0.279832	+	0.556275i
$206$	−2791.21	+	2941.31i	−0.944043	+	0.994811i
$207$	236.168	−	1688.85i	0.0792987	−	0.567067i
$208$	−1797.53	+	2219.73i	−0.599211	+	0.739955i
$209$	3326.05			1.10080
$210$	125.271	+	4161.86i	0.0411645	+	1.36760i
$211$			2678.68i			0.873972i	0.899468	+	0.436986i	$0.143954\pi$
$211$			2678.68i			0.873972i	−0.899468	+	0.436986i	$0.856046\pi$
$212$	−3461.96	−	3117.18i	−1.12155	−	1.00985i
$213$	−3956.38	+	1325.30i	−1.27271	+	0.426328i
$214$	343.392	+	325.868i	0.109691	+	0.104093i
$215$	−1247.47	+	3773.00i	−0.395706	+	1.19682i
$216$	1584.45	−	2750.86i	0.499111	−	0.866538i
$217$	−1844.06	+	1844.06i	−0.576881	+	0.576881i
$218$	−8.26780	−	315.755i	−0.00256865	−	0.0980991i
$219$	1142.52	−	2293.52i	0.352532	−	0.707679i
$220$	1726.25	−	984.808i	0.529018	−	0.301799i
$221$	1130.49			0.344096
$222$	−54.7686	−	25.5162i	−0.0165578	−	0.00771413i
$223$	4279.51	+	4279.51i	1.28510	+	1.28510i	0.937728	+	0.347370i	$0.112925\pi$
$223$	4279.51	+	4279.51i	1.28510	+	1.28510i	0.347370	+	0.937728i	$0.387075\pi$
$224$	−3639.07	−	2792.41i	−1.08547	−	0.832927i
$225$	26.4091	+	3374.90i	0.00782493	+	0.999969i
$226$	−4578.44	−	4344.79i	−1.34758	−	1.27881i
$227$	3976.88	−	3976.88i	1.16280	−	1.16280i	0.178935	−	0.983861i	$-0.442735\pi$
$227$	3976.88	−	3976.88i	1.16280	−	1.16280i	0.983861	−	0.178935i	$-0.0572651\pi$
$228$	−2282.49	−	5788.65i	−0.662989	−	1.68142i
$229$	−380.398			−0.109770			−0.0548852	−	0.998493i	$-0.517479\pi$
$229$	−380.398			−0.109770			−0.0548852	+	0.998493i	$0.517479\pi$
$230$	−1912.05	−	577.121i	−0.548159	−	0.165453i
$231$	−2618.74	−	1304.53i	−0.745888	−	0.371566i
$232$	−3279.95	+	258.121i	−0.928187	+	0.0730452i
$233$	1647.38	−	1647.38i	0.463191	−	0.463191i	−0.436509	−	0.899700i	$-0.643785\pi$
$233$	1647.38	−	1647.38i	0.463191	−	0.463191i	0.899700	+	0.436509i	$0.143785\pi$
$234$	3386.58	+	383.501i	0.946102	+	0.107138i
$235$	−4042.01	−	1336.42i	−1.12201	−	0.370971i
$236$	38.1089	+	727.206i	0.0105113	+	0.200581i
$237$	−4551.09	+	1524.51i	−1.24736	+	0.417838i
$238$	47.5212	+	1814.87i	0.0129426	+	0.494289i
$239$	2423.10			0.655806			0.327903	−	0.944711i	$-0.393658\pi$
$239$	2423.10			0.655806			0.327903	+	0.944711i	$0.393658\pi$
$240$	−2898.60	−	2328.55i	−0.779598	−	0.626280i
$241$	−5354.99			−1.43131			−0.715654	−	0.698455i	$-0.753871\pi$
$241$	−5354.99			−1.43131			−0.715654	+	0.698455i	$0.753871\pi$
$242$	−61.9877	−	2367.36i	−0.0164658	−	0.628842i
$243$	−3784.10	+	171.731i	−0.998972	+	0.0453356i
$244$	252.298	+	4814.44i	0.0661956	+	1.26317i
$245$	−1502.79	−	2987.38i	−0.391875	−	0.779006i
$246$	822.501	+	2257.40i	0.213174	+	0.585068i
$247$	4723.79	−	4723.79i	1.21687	−	1.21687i
$248$	−182.700	−	2321.58i	−0.0467802	−	0.594436i
$249$	−1642.96	+	3298.11i	−0.418146	+	0.839393i
$250$	3910.58	+	576.532i	0.989306	+	0.145852i
$251$	2326.68			0.585096			0.292548	−	0.956251i	$-0.405497\pi$
$251$	2326.68			0.585096			0.292548	+	0.956251i	$0.405497\pi$
$252$	−473.308	+	5452.88i	−0.118316	+	1.36309i
$253$	992.336	−	992.336i	0.246591	−	0.246591i
$254$	−2434.30	−	2310.07i	−0.601344	−	0.570656i
$255$	5.75757	+	1471.57i	0.00141393	+	0.361386i
$256$	4006.50	−	851.553i	0.978150	−	0.207899i
$257$	−86.8875	−	86.8875i	−0.0210891	−	0.0210891i	0.696484	−	0.717573i	$-0.254747\pi$
$257$	−86.8875	−	86.8875i	−0.0210891	−	0.0210891i	−0.717573	+	0.696484i	$0.754747\pi$
$258$	−2206.05	+	4735.12i	−0.532336	+	1.14262i
$259$	104.175			0.0249927
$260$	1053.03	−	3850.36i	0.251178	−	0.918421i
$261$	2364.81	+	3133.72i	0.560835	+	0.743190i
$262$	−125.208	−	4781.80i	−0.0295243	−	1.12756i
$263$	34.6193	−	34.6193i	0.00811680	−	0.00811680i	−0.703037	−	0.711154i	$-0.748173\pi$
$263$	34.6193	−	34.6193i	0.00811680	−	0.00811680i	0.711154	+	0.703037i	$0.248173\pi$
$264$	2404.49	−	1021.61i	0.560553	−	0.238165i
$265$	6181.40	+	2043.76i	1.43291	+	0.473764i
$266$	7782.06	+	7384.93i	1.79379	+	1.70225i
$267$	−294.478	−	879.097i	−0.0674971	−	0.201498i
$268$	−4808.97	−	4330.05i	−1.09610	−	0.986939i
$269$			230.792i			0.0523109i	0.999658	+	0.0261554i	$0.00832648\pi$
$269$			230.792i			0.0523109i	−0.999658	+	0.0261554i	$0.991674\pi$
$270$	−481.959	+	4410.30i	−0.108634	+	0.994082i
$271$	−2370.13			−0.531275			−0.265637	−	0.964073i	$-0.585582\pi$
$271$	−2370.13			−0.531275			−0.265637	+	0.964073i	$0.585582\pi$
$272$	−1259.88	−	1020.24i	−0.280851	−	0.227431i
$273$	−5571.99	+	1866.49i	−1.23528	+	0.413792i
$274$	4440.55	−	4679.35i	0.979065	−	1.03172i
$275$	−1655.66	+	2230.07i	−0.363054	+	0.489013i
$276$	−2408.05	−	1046.08i	−0.525172	−	0.228139i
$277$	−3598.09	−	3598.09i	−0.780463	−	0.780463i	0.199446	−	0.979909i	$-0.436086\pi$
$277$	−3598.09	−	3598.09i	−0.780463	−	0.780463i	−0.979909	+	0.199446i	$0.936086\pi$
$278$	−6.36274	−	242.999i	−0.00137270	−	0.0524248i
$279$	−2218.07	+	1673.83i	−0.475959	+	0.359174i
$280$	6225.57	+	1528.66i	1.32875	+	0.326268i
$281$			949.576i			0.201591i	0.994907	+	0.100795i	$0.0321387\pi$
$281$			949.576i			0.201591i	−0.994907	+	0.100795i	$0.967861\pi$
$282$	−5072.73	−	2363.34i	−1.07119	−	0.499060i
$283$	−556.282	+	556.282i	−0.116846	+	0.116846i	−0.763112	−	0.646266i	$-0.776330\pi$
$283$	−556.282	+	556.282i	−0.116846	+	0.116846i	0.646266	+	0.763112i	$0.276330\pi$
$284$	336.180	+	6415.10i	0.0702416	+	1.34037i
$285$	6173.06	+	6124.94i	1.28302	+	1.27302i
$286$	2034.55	+	1930.72i	0.420649	+	0.399182i
$287$	−2929.12	−	2929.12i	−0.602441	−	0.602441i
$288$	−3428.08	−	3483.70i	−0.701393	−	0.712774i
$289$		−	4271.35i		−	0.869398i
$290$	4052.10	−	2173.12i	0.820510	−	0.440034i
$291$	540.170	+	269.087i	0.108816	+	0.0542067i
$292$	−2931.68	−	2639.72i	−0.587547	−	0.529034i
$293$	−1344.57	−	1344.57i	−0.268090	−	0.268090i	0.560240	−	0.828330i	$-0.310709\pi$
$293$	−1344.57	−	1344.57i	−0.268090	−	0.268090i	−0.828330	+	0.560240i	$0.810709\pi$
$294$	−1504.89	−	4130.27i	−0.298528	−	0.819327i
$295$	−457.341	−	909.145i	−0.0902625	−	0.179432i
$296$	−60.4146	+	70.7357i	−0.0118633	+	0.0138900i
$297$	−2570.92	−	1763.05i	−0.502290	−	0.344452i
$298$	−6175.86	+	161.710i	−1.20053	+	0.0314350i
$299$		−	2818.72i		−	0.545186i
$300$	5017.41	+	1351.13i	0.965602	+	0.260025i
$301$		−	9006.61i		−	1.72469i
$302$	24.7997	+	947.123i	0.00472538	+	0.180466i
$303$	588.944	+	1758.16i	0.111663	+	0.333345i
$304$	−9527.54	+	1001.32i	−1.79751	+	0.188913i
$305$	−3027.81	−	6018.95i	−0.568432	−	1.12998i
$306$	−217.668	+	1922.16i	−0.0406642	+	0.359094i
$307$	3044.04	+	3044.04i	0.565904	+	0.565904i	0.930978	−	0.365074i	$-0.118956\pi$
$307$	3044.04	+	3044.04i	0.565904	+	0.565904i	−0.365074	+	0.930978i	$0.618956\pi$
$308$	−3014.02	+	3347.39i	−0.557597	+	0.619270i
$309$	3321.58	−	6667.80i	0.611515	−	1.22757i
$310$	1538.15	+	2868.11i	0.281810	+	0.525477i
$311$		−	1374.55i		−	0.250623i	−0.992117	−	0.125312i	$-0.960007\pi$
$311$		−	1374.55i		−	0.250623i	0.992117	−	0.125312i	$-0.0399930\pi$
$312$	1964.03	−	4865.89i	0.356382	−	0.882938i
$313$	−5002.57	−	5002.57i	−0.903392	−	0.903392i	0.0923356	−	0.995728i	$-0.470567\pi$
$313$	−5002.57	−	5002.57i	−0.903392	−	0.903392i	−0.995728	+	0.0923356i	$0.970567\pi$
$314$	−1284.60	+	1353.68i	−0.230872	+	0.243288i
$315$	−2458.01	−	7243.60i	−0.439660	−	1.29565i
$316$	386.714	+	7379.40i	0.0688429	+	1.31368i
$317$	1885.81	−	1885.81i	0.334125	−	0.334125i	−0.520026	−	0.854151i	$-0.674078\pi$
$317$	1885.81	−	1885.81i	0.334125	−	0.334125i	0.854151	+	0.520026i	$0.174078\pi$
$318$	7757.67	+	3614.23i	1.36801	+	0.637346i
$319$			3230.84i			0.567060i
$320$	−4648.41	+	3340.70i	−0.812044	+	0.583597i
$321$	−778.450	−	387.787i	−0.135355	−	0.0674273i
$322$	4525.12	−	118.487i	0.783152	−	0.0205063i
$323$	2681.14	+	2681.14i	0.461866	+	0.461866i
$324$	−1304.12	+	5684.32i	−0.223615	+	0.974678i
$325$	815.811	+	5518.69i	0.139240	+	0.941913i
$326$	−5641.62	−	5353.71i	−0.958467	−	0.909555i
$327$	184.314	+	550.227i	0.0311699	+	0.0930508i
$328$	3687.61	−	290.203i	0.620774	−	0.0488529i
$329$	9648.78			1.61688
$330$	−2502.88	+	2658.22i	−0.417512	+	0.443426i
$331$		−	4768.05i		−	0.791770i	−0.918300	−	0.395885i	$-0.870438\pi$
$331$		−	4768.05i		−	0.791770i	0.918300	−	0.395885i	$-0.129562\pi$
$332$	4215.79	+	3795.94i	0.696903	+	0.627498i
$333$	109.931	+	15.3727i	0.0180906	+	0.00252979i
$334$	1743.55	−	1837.31i	0.285636	−	0.300997i
$335$	8586.52	+	2838.98i	1.40039	+	0.463014i
$336$	7894.17	+	2948.48i	1.28173	+	0.478728i
$337$	−2480.60	+	2480.60i	−0.400970	+	0.400970i	−0.878575	−	0.477605i	$-0.841505\pi$
$337$	−2480.60	+	2480.60i	−0.400970	+	0.400970i	0.477605	+	0.878575i	$0.341505\pi$
$338$	−580.274	+	15.1940i	−0.0933809	+	0.00244511i
$339$	10379.1	+	5170.36i	1.66287	+	0.828363i
$340$	2185.40	+	597.681i	0.348588	+	0.0953347i
$341$	−2286.81			−0.363161
$342$	7122.27	+	8941.33i	1.12611	+	1.41372i
$343$	−786.554	−	786.554i	−0.123819	−	0.123819i
$344$	6115.58	+	5223.25i	0.958518	+	0.818660i
$345$	3669.15	−	14.3556i	0.572580	−	0.00224023i
$346$	2253.54	−	2374.73i	0.350148	−	0.368978i
$347$	−6507.43	+	6507.43i	−1.00674	+	1.00674i	−0.00675821	+	0.999977i	$0.502151\pi$
$347$	−6507.43	+	6507.43i	−1.00674	+	1.00674i	−0.999977	+	0.00675821i	$0.997849\pi$
$348$	5622.95	−	2217.15i	0.866155	−	0.341528i
$349$	−1305.92			−0.200298			−0.100149	−	0.994972i	$-0.531932\pi$
$349$	−1305.92			−0.200298			−0.100149	+	0.994972i	$0.531932\pi$
$350$	−8825.31	+	1541.67i	−1.34781	+	0.235445i
$351$	−6155.29	+	1147.38i	−0.936026	+	0.174480i
$352$	−524.974	−	3987.83i	−0.0794920	−	0.603840i
$353$	−437.926	+	437.926i	−0.0660295	+	0.0660295i	−0.739350	−	0.673321i	$-0.764867\pi$
$353$	−437.926	+	437.926i	−0.0660295	+	0.0660295i	0.673321	+	0.739350i	$0.264867\pi$
$354$	−457.983	−	1256.96i	−0.0687614	−	0.188720i
$355$	−4034.47	−	8020.09i	−0.603176	−	1.19905i
$356$	−1425.42	+	74.6983i	−0.212211	+	0.0111208i
$357$	−1059.39	−	3162.56i	−0.157055	−	0.468853i
$358$	−2960.18	+	77.5102i	−0.437013	+	0.0114429i
$359$	6708.53			0.986247			0.493124	−	0.869959i	$-0.335855\pi$
$359$	6708.53			0.986247			0.493124	+	0.869959i	$0.335855\pi$
$360$	6343.97	+	2531.81i	0.928768	+	0.370662i
$361$	15547.4			2.26672
$362$	−7879.07	+	206.308i	−1.14396	+	0.0299538i
$363$	1381.89	+	4125.32i	0.199808	+	0.596482i
$364$	473.462	+	9034.76i	0.0681762	+	1.30096i
$365$	5234.58	+	1730.72i	0.750659	+	0.248192i
$366$	−3032.06	−	8321.65i	−0.433028	−	1.18847i
$367$	931.679	−	931.679i	0.132516	−	0.132516i	−0.637738	−	0.770254i	$-0.720130\pi$
$367$	931.679	−	931.679i	0.132516	−	0.132516i	0.770254	+	0.637738i	$0.220130\pi$
$368$	−2543.82	+	3141.32i	−0.360342	+	0.444980i
$369$	−2658.72	−	3523.20i	−0.375088	−	0.497048i
$370$	37.5661	−	124.459i	0.00527829	−	0.0174874i
$371$	−14755.8			−2.06491
$372$	1569.32	+	3979.97i	0.218724	+	0.554710i
$373$	8409.81	−	8409.81i	1.16741	−	1.16741i	0.184594	−	0.982815i	$-0.440903\pi$
$373$	8409.81	−	8409.81i	1.16741	−	1.16741i	0.982815	−	0.184594i	$-0.0590971\pi$
$374$	−1095.84	+	1154.77i	−0.151510	+	0.159658i
$375$	−7179.57	+	1090.05i	−0.988670	+	0.150107i
$376$	−5595.67	+	6551.62i	−0.767486	+	0.898601i
$377$	4588.57	+	4588.57i	0.626853	+	0.626853i
$378$	−2100.72	−	9833.36i	−0.285845	−	1.33802i
$379$	2542.19			0.344548			0.172274	−	0.985049i	$-0.444889\pi$
$379$	2542.19			0.344548			0.172274	+	0.985049i	$0.444889\pi$
$380$	11629.2	−	6634.31i	1.56990	−	0.895612i
$381$	5518.42	+	2749.01i	0.742040	+	0.369649i
$382$	−7790.29	+	203.983i	−1.04342	+	0.0273212i
$383$	4068.66	−	4068.66i	0.542817	−	0.542817i	−0.381537	−	0.924354i	$-0.624605\pi$
$383$	4068.66	−	4068.66i	0.542817	−	0.542817i	0.924354	+	0.381537i	$0.124605\pi$
$384$	−6580.16	+	3650.30i	−0.874459	+	0.485100i
$385$	1976.13	−	5976.84i	0.261592	−	0.791189i
$386$	6318.66	−	6658.45i	0.833190	−	0.877996i
$387$	1329.08	−	9504.25i	0.174575	−	1.24839i
$388$	621.706	−	690.470i	0.0813463	−	0.0903436i
$389$			6199.37i			0.808022i	0.914754	+	0.404011i	$0.132384\pi$
$389$			6199.37i			0.808022i	−0.914754	+	0.404011i	$0.867616\pi$
$390$	220.633	+	7330.02i	0.0286466	+	0.951718i
$391$	1599.85			0.206926
$392$	−6747.05	+	530.971i	−0.869331	+	0.0684135i
$393$	2791.25	+	8332.67i	0.358270	+	1.06954i
$394$	−7310.02	−	6936.97i	−0.934704	−	0.887004i
$395$	−4640.92	−	9225.64i	−0.591165	−	1.17517i
$396$	−3674.52	+	3087.57i	−0.466292	+	0.391809i
$397$	5621.44	+	5621.44i	0.710660	+	0.710660i	0.966673	−	0.256013i	$-0.0824090\pi$
$397$	5621.44	+	5621.44i	0.710660	+	0.710660i	−0.256013	+	0.966673i	$0.582409\pi$
$398$	5438.57	−	142.405i	0.684952	−	0.0179350i
$399$	−17641.5	−	8788.16i	−2.21348	−	1.10265i
$400$	4071.30	−	6886.55i	0.508912	−	0.860818i
$401$			15736.5i			1.95970i	0.199723	+	0.979852i	$0.435996\pi$
$401$			15736.5i			1.95970i	−0.199723	+	0.979852i	$0.564004\pi$
$402$	10776.1	+	5020.50i	1.33697	+	0.622885i
$403$	−3247.83	+	3247.83i	−0.401454	+	0.401454i
$404$	2850.78	−	149.394i	0.351069	−	0.0183976i
$405$	−1524.90	−	8006.55i	−0.187094	−	0.982342i
$406$	−7173.53	+	7559.30i	−0.876888	+	0.924044i
$407$	64.5933	+	64.5933i	0.00786676	+	0.00786676i
$408$	2761.79	+	1114.75i	0.335120	+	0.135265i
$409$			14162.8i			1.71224i	0.516775	+	0.856121i	$0.327133\pi$
$409$			14162.8i			1.71224i	−0.516775	+	0.856121i	$0.672867\pi$
$410$	−4555.73	+	2443.21i	−0.548760	+	0.294296i
$411$	−5284.32	+	10607.8i	−0.634200	+	1.27310i
$412$	−8523.09	−	7674.27i	−1.01918	−	0.917680i
$413$	1630.99	+	1630.99i	0.194323	+	0.194323i
$414$	4792.62	+	542.723i	0.568948	+	0.0644284i
$415$	−7527.39	−	2488.79i	−0.890373	−	0.294385i
$416$	−6409.27	−	4918.09i	−0.755386	−	0.579638i
$417$	141.844	+	423.444i	0.0166574	+	0.0497270i
$418$	246.244	+	9404.25i	0.0288138	+	1.10042i
$419$		−	8058.57i		−	0.939586i	−0.882777	−	0.469793i	$-0.844328\pi$
$419$		−	8058.57i		−	0.939586i	0.882777	−	0.469793i	$-0.155672\pi$
$420$	−11758.2	+	662.323i	−1.36605	+	0.0769477i
$421$		−	1221.32i		−	0.141386i	−0.997498	−	0.0706930i	$-0.977479\pi$
$421$		−	1221.32i		−	0.141386i	0.997498	−	0.0706930i	$-0.0225211\pi$
$422$	−7573.86	+	198.316i	−0.873673	+	0.0228765i
$423$	10181.9	+	1423.84i	1.17036	+	0.163663i
$424$	8557.39	−	10019.3i	0.980150	−	1.14760i
$425$	−3132.31	+	463.040i	−0.357504	+	0.0528488i
$426$	−4040.13	−	11088.4i	−0.459495	−	1.26111i
$427$	10797.9	+	10797.9i	1.22376	+	1.22376i
$428$	−895.954	+	995.051i	−0.101186	+	0.112378i
$429$	−4612.21	−	2297.59i	−0.519067	−	0.258575i
$430$	−10760.3	−	3247.84i	−1.20677	−	0.364244i
$431$		−	8915.43i		−	0.996383i	−0.867067	−	0.498192i	$-0.833998\pi$
$431$		−	8915.43i		−	0.996383i	0.867067	−	0.498192i	$-0.166002\pi$
$432$	7895.24	+	4276.30i	0.879305	+	0.476258i
$433$	−9585.68	−	9585.68i	−1.06388	−	1.06388i	−0.997816	−	0.0660601i	$-0.978957\pi$
$433$	−9585.68	−	9585.68i	−1.06388	−	1.06388i	−0.0660601	−	0.997816i	$-0.521043\pi$
$434$	−5350.53	−	5077.48i	−0.591783	−	0.561583i
$435$	−5949.62	+	5996.36i	−0.655775	+	0.660927i
$436$	892.170	−	46.7537i	0.0979982	−	0.00513554i
$437$	6685.02	−	6685.02i	0.731780	−	0.731780i
$438$	6569.42	+	3060.63i	0.716664	+	0.333888i
$439$			1495.80i			0.162621i	0.996689	+	0.0813107i	$0.0259106\pi$
$439$			1495.80i			0.162621i	−0.996689	+	0.0813107i	$0.974089\pi$
$440$	2912.31	+	4807.99i	0.315543	+	0.520937i
$441$	4864.55	+	6446.25i	0.525272	+	0.696064i
$442$	83.6960	+	3196.42i	0.00900682	+	0.343978i
$443$	6444.43	+	6444.43i	0.691161	+	0.691161i	0.962487	−	0.271326i	$-0.0874623\pi$
$443$	6444.43	+	6444.43i	0.691161	+	0.691161i	−0.271326	+	0.962487i	$0.587462\pi$
$444$	68.0913	−	156.745i	0.00727809	−	0.0167540i
$445$	1782.04	−	896.449i	0.189836	−	0.0954961i
$446$	−11783.3	+	12417.0i	−1.25102	+	1.31830i
$447$	10761.9	−	3605.00i	1.13875	−	0.381456i
$448$	7626.00	−	10496.1i	0.804229	−	1.10690i
$449$	−17292.2			−1.81753			−0.908764	−	0.417310i	$-0.862973\pi$
$449$	−17292.2			−1.81753			−0.908764	+	0.417310i	$0.862973\pi$
$450$	−9540.42	+	324.531i	−0.999422	+	0.0339967i
$451$		−	3632.39i		−	0.379252i
$452$	11945.7	−	13267.0i	1.24310	−	1.38059i
$453$	−552.859	−	1650.44i	−0.0573412	−	0.171179i
$454$	11538.9	+	10950.0i	1.19283	+	1.13196i
$455$	−5681.97	−	11295.1i	−0.585440	−	1.16379i
$456$	16198.2	−	6882.20i	1.66349	−	0.706773i
$457$	840.771	−	840.771i	0.0860604	−	0.0860604i	−0.662766	−	0.748826i	$-0.730618\pi$
$457$	840.771	−	840.771i	0.0860604	−	0.0860604i	0.748826	+	0.662766i	$0.230618\pi$
$458$	−28.1627	−	1075.56i	−0.00287327	−	0.109733i
$459$	−651.232	−	3493.63i	−0.0662242	−	0.355270i
$460$	1490.23	−	5448.96i	0.151048	−	0.552302i
$461$	3111.55			0.314359			0.157179	−	0.987570i	$-0.449760\pi$
$461$	3111.55			0.314359			0.157179	+	0.987570i	$0.449760\pi$
$462$	3494.63	−	7500.95i	0.351915	−	0.755358i
$463$	5271.43	+	5271.43i	0.529123	+	0.529123i	0.920311	−	0.391188i	$-0.127936\pi$
$463$	5271.43	+	5271.43i	0.529123	+	0.529123i	−0.391188	+	0.920311i	$0.627936\pi$
$464$	−972.658	−	9254.81i	−0.0973158	−	0.925957i
$465$	−4244.27	−	4211.19i	−0.423276	−	0.419977i
$466$	4779.86	+	4535.94i	0.475156	+	0.450908i
$467$	3307.34	−	3307.34i	0.327720	−	0.327720i	−0.523999	−	0.851719i	$-0.675560\pi$
$467$	3307.34	−	3307.34i	0.327720	−	0.327720i	0.851719	+	0.523999i	$0.175560\pi$
$468$	−833.607	+	9603.81i	−0.0823365	+	0.948582i
$469$	−20497.1			−2.01806
$470$	3479.41	−	11527.6i	0.341475	−	1.13133i
$471$	1528.69	−	3068.71i	0.149550	−	0.300210i
$472$	−2053.32	+	161.590i	−0.200237	+	0.0157580i
$473$	5584.53	−	5584.53i	0.542869	−	0.542869i
$474$	−4647.43	−	12755.1i	−0.450345	−	1.23600i
$475$	−11153.6	+	15023.2i	−1.07739	+	1.45119i
$476$	−5127.96	+	268.728i	−0.493781	+	0.0258763i
$477$	−15571.0	−	2177.46i	−1.49465	−	0.209012i
$478$	179.394	+	6851.22i	0.0171659	+	0.655581i
$479$	−14910.9			−1.42234			−0.711168	−	0.703022i	$-0.751833\pi$
$479$	−14910.9			−1.42234			−0.711168	+	0.703022i	$0.751833\pi$
$480$	6369.28	−	8368.05i	0.605659	−	0.795724i
$481$	183.476			0.0173925
$482$	−396.456	−	15141.0i	−0.0374649	−	1.43082i
$483$	−7885.37	+	2641.42i	−0.742851	+	0.248838i
$484$	6689.03	−	350.535i	0.628196	−	0.0329203i
$485$	−407.619	+	1232.85i	−0.0381629	+	0.115424i
$486$	−765.718	−	10686.7i	−0.0714685	−	0.997443i
$487$	−7011.60	+	7011.60i	−0.652415	+	0.652415i	−0.953574	−	0.301159i	$-0.902626\pi$
$487$	−7011.60	+	7011.60i	−0.652415	+	0.652415i	0.301159	+	0.953574i	$0.402626\pi$
$488$	−13593.9	+	1069.80i	−1.26100	+	0.0992367i
$489$	12789.2	+	6370.99i	1.18272	+	0.589174i
$490$	8335.42	−	4470.23i	0.768481	−	0.412132i
$491$	−1695.78			−0.155865			−0.0779324	−	0.996959i	$-0.524832\pi$
$491$	−1695.78			−0.155865			−0.0779324	+	0.996959i	$0.524832\pi$
$492$	−6321.81	+	2492.71i	−0.579287	+	0.228415i
$493$	−2604.39	+	2604.39i	−0.237923	+	0.237923i
$494$	13706.1	+	13006.6i	1.24831	+	1.18460i
$495$	2967.30	−	6015.46i	0.269435	−	0.546212i
$496$	6550.63	−	688.455i	0.593008	−	0.0623237i
$497$	14387.9	+	14387.9i	1.29856	+	1.29856i
$498$	−9446.89	−	4401.23i	−0.850051	−	0.396031i
$499$	2603.75			0.233587			0.116794	−	0.993156i	$-0.462738\pi$
$499$	2603.75			0.233587			0.116794	+	0.993156i	$0.462738\pi$
$500$	−1340.60	+	11099.7i	−0.119907	+	0.992785i
$501$	−2074.84	+	4165.08i	−0.185024	+	0.371421i
$502$	172.256	+	6578.60i	0.0153150	+	0.584895i
$503$	303.507	−	303.507i	0.0269040	−	0.0269040i	−0.693527	−	0.720431i	$-0.743944\pi$
$503$	303.507	−	303.507i	0.0269040	−	0.0269040i	0.720431	+	0.693527i	$0.243944\pi$
$504$	−15452.8	−	934.554i	−1.36572	−	0.0825960i
$505$	−3564.02	+	1792.86i	−0.314053	+	0.157983i
$506$	2879.26	+	2732.32i	0.252962	+	0.240052i
$507$	1011.17	−	338.720i	0.0885755	−	0.0296708i
$508$	6351.40	−	7053.90i	0.554720	−	0.616075i
$509$			7479.13i			0.651290i	0.945492	+	0.325645i	$0.105581\pi$
$509$			7479.13i			0.651290i	−0.945492	+	0.325645i	$0.894419\pi$
$510$	−4160.39	+	125.227i	−0.361225	+	0.0108728i
$511$	−12495.6			−1.08175
$512$	2704.35	+	11265.2i	0.233431	+	0.972373i
$513$	−17319.4	−	11877.0i	−1.49058	−	1.02219i
$514$	239.238	−	252.104i	0.0205298	−	0.0216339i
$515$	15218.2	+	5031.60i	1.30212	+	0.430522i
$516$	−13551.7	−	5886.96i	−1.15616	−	0.502246i
$517$	5982.70	+	5982.70i	0.508934	+	0.508934i
$518$	7.71257	+	294.550i	0.000654191	+	0.0249841i
$519$	−2681.75	+	5383.38i	−0.226812	+	0.455307i
$520$	10964.7	+	2692.34i	0.924681	+	0.227052i
$521$		−	17445.9i		−	1.46702i	−0.679677	−	0.733512i	$-0.737880\pi$
$521$		−	17445.9i		−	1.46702i	0.679677	−	0.733512i	$-0.262120\pi$
$522$	−8685.39	+	6918.39i	−0.728255	+	0.580096i
$523$	1548.17	−	1548.17i	0.129439	−	0.129439i	−0.639419	−	0.768858i	$-0.720825\pi$
$523$	1548.17	−	1548.17i	0.129439	−	0.129439i	0.768858	+	0.639419i	$0.220825\pi$
$524$	13511.1	−	708.041i	1.12640	−	0.0590284i
$525$	14674.1	−	7453.80i	1.21986	−	0.619639i
$526$	100.448	+	95.3216i	0.00832648	+	0.00790156i
$527$	−1843.41	−	1843.41i	−0.152372	−	0.152372i
$528$	3066.56	+	6722.95i	0.252756	+	0.554127i
$529$			8178.01i			0.672147i
$530$	−5321.02	+	17628.9i	−0.436095	+	1.44482i
$531$	1480.42	+	1961.78i	0.120988	+	0.160328i
$532$	−20304.4	+	22550.2i	−1.65471	+	1.83773i
$533$	−5158.88	−	5158.88i	−0.419241	−	0.419241i
$534$	2463.81	−	897.707i	0.199662	−	0.0727483i
$535$	587.428	−	1776.68i	0.0474705	−	0.143575i
$536$	11887.0	−	13917.7i	0.957910	−	1.12156i
$537$	5158.35	−	1727.93i	0.414524	−	0.138856i
$538$	−652.554	+	17.0867i	−0.0522929	+	0.00136925i
$539$			6646.03i			0.531103i
$540$	−12505.6	−	1036.20i	−0.996585	−	0.0825760i
$541$			4888.17i			0.388464i	0.980956	+	0.194232i	$0.0622215\pi$
$541$			4888.17i			0.388464i	−0.980956	+	0.194232i	$0.937779\pi$
$542$	−175.473	−	6701.46i	−0.0139063	−	0.531093i
$543$	13729.9	−	4599.21i	1.08509	−	0.363482i
$544$	2791.42	−	3637.79i	0.220002	−	0.286707i
$545$	−1115.38	+	561.088i	−0.0876655	+	0.0440997i
$546$	−5689.95	−	15616.4i	−0.445984	−	1.22403i
$547$	983.991	+	983.991i	0.0769148	+	0.0769148i	0.744518	−	0.667603i	$-0.232680\pi$
$547$	983.991	+	983.991i	0.0769148	+	0.0769148i	−0.667603	+	0.744518i	$0.732680\pi$
$548$	13559.4	+	12209.0i	1.05699	+	0.951724i
$549$	9801.07	+	12987.9i	0.761930	+	1.00967i
$550$	−6428.02	−	4516.20i	−0.498349	−	0.350130i
$551$			21765.0i			1.68280i
$552$	2779.46	−	6886.11i	0.214314	−	0.530964i
$553$	16550.6	+	16550.6i	1.27270	+	1.27270i
$554$	9907.06	−	10439.8i	0.759767	−	0.800625i
$555$	0.934438	+	238.833i	7.14679e−5	+	0.0182665i
$556$	686.597	−	35.9808i	0.0523709	−	0.00274447i
$557$	1200.46	−	1200.46i	0.0913201	−	0.0913201i	−0.659971	−	0.751291i	$-0.729431\pi$
$557$	1200.46	−	1200.46i	0.0913201	−	0.0913201i	0.751291	+	0.659971i	$0.229431\pi$
$558$	−4896.90	−	6147.59i	−0.371509	−	0.466394i
$559$		−	15862.8i		−	1.20022i
$560$	−3861.32	+	17715.7i	−0.291376	+	1.33683i
$561$	1304.07	−	2617.81i	0.0981423	−	0.197012i
$562$	−2684.89	+	70.3018i	−0.201521	+	0.00527669i
$563$	−5174.07	−	5174.07i	−0.387320	−	0.387320i	0.486410	−	0.873730i	$-0.338306\pi$
$563$	−5174.07	−	5174.07i	−0.387320	−	0.387320i	−0.873730	+	0.486410i	$0.838306\pi$
$564$	6306.69	−	14517.9i	0.470850	−	1.08389i
$565$	−7832.17	+	23688.5i	−0.583189	+	1.76386i
$566$	−1614.05	−	1531.68i	−0.119865	−	0.113748i
$567$	8977.92	+	16144.2i	0.664969	+	1.19576i
$568$	−18113.6	+	1425.48i	−1.33808	+	0.105302i
$569$	−22391.8			−1.64976			−0.824879	−	0.565310i	$-0.808757\pi$
$569$	−22391.8			−1.64976			−0.824879	+	0.565310i	$0.808757\pi$
$570$	−16861.0	+	17907.5i	−1.23900	+	1.31590i
$571$		−	18179.2i		−	1.33236i	−0.745791	−	0.666180i	$-0.767928\pi$
$571$		−	18179.2i		−	1.33236i	0.745791	−	0.666180i	$-0.232072\pi$
$572$	−5308.41	+	5895.55i	−0.388035	+	0.430953i
$573$	13575.2	−	4547.38i	0.989724	−	0.331535i
$574$	8065.11	−	8498.83i	0.586466	−	0.618004i
$575$	1154.52	+	7809.93i	0.0837336	+	0.566429i
$576$	9596.22	−	9950.65i	0.694171	−	0.719810i
$577$	−7270.00	+	7270.00i	−0.524531	+	0.524531i	−0.918936	−	0.394406i	$-0.870950\pi$
$577$	−7270.00	+	7270.00i	−0.524531	+	0.524531i	0.394406	+	0.918936i	$0.370950\pi$
$578$	12077.1	−	316.229i	0.869100	−	0.0227567i
$579$	−7519.29	+	15094.3i	−0.539708	+	1.08342i
$580$	6444.40	+	11296.3i	0.461361	+	0.808710i
$581$	17968.8			1.28308
$582$	−720.841	+	1547.23i	−0.0513399	+	0.110197i
$583$	−9149.27	−	9149.27i	−0.649956	−	0.649956i
$584$	7246.64	−	8484.64i	0.513473	−	0.601194i
$585$	−4329.13	−	12757.7i	−0.305961	−	0.901651i
$586$	3702.16	−	3901.25i	0.260981	−	0.275016i
$587$	−11488.4	+	11488.4i	−0.807800	+	0.807800i	−0.984300	−	0.176501i	$-0.943522\pi$
$587$	−11488.4	+	11488.4i	−0.807800	+	0.807800i	0.176501	+	0.984300i	$0.443522\pi$
$588$	11566.8	−	4560.81i	0.811233	−	0.319872i
$589$	−15405.5			−1.07771
$590$	2536.71	−	1360.42i	0.177008	−	0.0949283i
$591$	16571.4	+	8255.09i	1.15340	+	0.574567i
$592$	−204.475	−	165.583i	−0.0141957	−	0.0114956i
$593$	654.026	−	654.026i	0.0452911	−	0.0452911i	−0.684099	−	0.729390i	$-0.739804\pi$
$593$	654.026	−	654.026i	0.0452911	−	0.0452911i	0.729390	+	0.684099i	$0.239804\pi$
$594$	4794.60	−	7399.70i	0.331187	−	0.511134i
$595$	6410.92	−	3224.99i	0.441718	−	0.222204i
$596$	−914.459	−	17450.0i	−0.0628485	−	1.19930i
$597$	−9477.13	+	3174.62i	−0.649704	+	0.217636i
$598$	7969.80	−	208.683i	0.544999	−	0.0142704i
$599$	1176.61			0.0802586			0.0401293	−	0.999194i	$-0.487223\pi$
$599$	1176.61			0.0802586			0.0401293	+	0.999194i	$0.487223\pi$
$600$	−3448.80	+	14286.6i	−0.234661	+	0.972077i
$601$	20394.6			1.38422			0.692109	−	0.721793i	$-0.256682\pi$
$601$	20394.6			1.38422			0.692109	+	0.721793i	$0.256682\pi$
$602$	25465.8	−	666.804i	1.72410	−	0.0451443i
$603$	−21629.6	−	3024.69i	−1.46074	−	0.204270i
$604$	−2676.11	+	140.240i	−0.180281	+	0.00944751i
$605$	−8362.55	+	4206.74i	−0.561960	+	0.282692i
$606$	−4927.52	+	1795.38i	−0.330308	+	0.120350i
$607$	4743.50	−	4743.50i	0.317188	−	0.317188i	−0.530498	−	0.847686i	$-0.677995\pi$
$607$	4743.50	−	4743.50i	0.317188	−	0.317188i	0.847686	+	0.530498i	$0.177995\pi$
$608$	−3536.56	−	26864.6i	−0.235899	−	1.79194i
$609$	8536.60	−	17136.5i	0.568014	−	1.14024i
$610$	16794.2	−	9006.61i	1.11472	−	0.597815i
$611$	16993.8			1.12520
$612$	−5450.95	−	473.140i	−0.360035	−	0.0312509i
$613$	9629.71	−	9629.71i	0.634486	−	0.634486i	−0.314704	−	0.949190i	$-0.601905\pi$
$613$	9629.71	−	9629.71i	0.634486	−	0.634486i	0.949190	+	0.314704i	$0.101905\pi$
$614$	−8381.53	+	8832.26i	−0.550897	+	0.580523i
$615$	6689.08	−	6741.63i	0.438585	−	0.442030i
$616$	−9687.75	−	8274.20i	−0.633654	−	0.541197i
$617$	2583.12	+	2583.12i	0.168545	+	0.168545i	0.786340	−	0.617794i	$-0.211974\pi$
$617$	2583.12	+	2583.12i	0.168545	+	0.168545i	−0.617794	+	0.786340i	$0.711974\pi$
$618$	19098.8	+	8897.98i	1.24315	+	0.579173i
$619$	3150.70			0.204584			0.102292	−	0.994754i	$-0.467382\pi$
$619$	3150.70			0.204584			0.102292	+	0.994754i	$0.467382\pi$
$620$	−7995.59	+	4561.40i	−0.517920	+	0.295468i
$621$	−8710.84	+	1623.75i	−0.562889	+	0.104926i
$622$	3886.49	−	101.765i	0.250537	−	0.00656013i
$623$	−3196.95	+	3196.95i	−0.205591	+	0.205591i
$624$	13903.5	+	5192.96i	0.891964	+	0.333149i
$625$	−4520.80	−	14956.7i	−0.289331	−	0.957229i
$626$	13774.2	−	14514.9i	0.879436	−	0.926729i
$627$	−5489.49	−	16387.7i	−0.349648	−	1.04380i
$628$	−3922.57	−	3531.92i	−0.249248	−	0.224425i
$629$			104.138i			0.00660135i
$630$	20299.0	−	7486.19i	1.28370	−	0.473424i
$631$	12739.1			0.803698			0.401849	−	0.915706i	$-0.368368\pi$
$631$	12739.1			0.803698			0.401849	+	0.915706i	$0.368368\pi$
$632$	−20836.3	+	1639.75i	−1.31143	+	0.103205i
$633$	13198.1	−	4421.05i	0.828713	−	0.277600i
$634$	5471.66	+	5192.43i	0.342756	+	0.325265i
$635$	−4164.27	+	12594.9i	−0.260242	+	0.787107i
$636$	−9644.75	+	22202.1i	−0.601320	+	1.38423i
$637$	9438.97	+	9438.97i	0.587105	+	0.587105i
$638$	−9135.06	+	239.195i	−0.566866	+	0.0148430i
$639$	13059.7	+	17306.0i	0.808501	+	1.07138i
$640$	−9789.84	−	12895.9i	−0.604652	−	0.796490i
$641$			5622.26i			0.346437i	0.984883	+	0.173218i	$0.0554167\pi$
$641$			5622.26i			0.346437i	−0.984883	+	0.173218i	$0.944583\pi$
$642$	1038.82	−	2229.74i	0.0638612	−	0.137073i
$643$	21965.1	−	21965.1i	1.34715	−	1.34715i	0.458412	−	0.888740i	$-0.348418\pi$
$643$	21965.1	−	21965.1i	1.34715	−	1.34715i	0.888740	−	0.458412i	$-0.151582\pi$
$644$	670.033	+	12785.8i	0.0409985	+	0.782347i
$645$	20648.7	−	80.7886i	1.26053	−	0.00493185i
$646$	−7382.31	+	7779.31i	−0.449618	+	0.473797i
$647$	−5158.09	−	5158.09i	−0.313424	−	0.313424i	0.532811	−	0.846235i	$-0.321136\pi$
$647$	−5158.09	−	5158.09i	−0.313424	−	0.313424i	−0.846235	+	0.532811i	$0.821136\pi$
$648$	−16168.7	−	3266.51i	−0.980197	−	0.198026i
$649$			2022.58i			0.122332i
$650$	−15543.5	+	2715.25i	−0.937945	+	0.163847i
$651$	12129.4	+	6042.28i	0.730242	+	0.363772i
$652$	14719.7	−	16347.8i	0.884155	−	0.981947i
$653$	−22326.0	−	22326.0i	−1.33795	−	1.33795i	−0.898040	−	0.439914i	$-0.855009\pi$
$653$	−22326.0	−	22326.0i	−1.33795	−	1.33795i	−0.439914	−	0.898040i	$-0.644991\pi$
$654$	−1542.10	+	561.875i	−0.0922031	+	0.0335949i
$655$	−16891.4	+	8497.14i	−1.00764	+	0.506887i
$656$	1093.55	+	10405.1i	0.0650851	+	0.619283i
$657$	−13186.0	−	1843.93i	−0.783006	−	0.109496i
$658$	714.346	+	27281.5i	0.0423224	+	1.61633i
$659$		−	17475.9i		−	1.03302i	−0.856280	−	0.516512i	$-0.827230\pi$
$659$		−	17475.9i		−	1.03302i	0.856280	−	0.516512i	$-0.172770\pi$
$660$	−7701.32	−	6879.98i	−0.454202	−	0.405762i
$661$			1319.72i			0.0776569i	0.999246	+	0.0388284i	$0.0123626\pi$
$661$			1319.72i			0.0776569i	−0.999246	+	0.0388284i	$0.987637\pi$
$662$	13481.5	−	353.002i	0.791498	−	0.0207248i
$663$	−1865.83	−	5570.02i	−0.109295	−	0.326277i
$664$	−10420.8	+	12201.0i	−0.609042	+	0.713089i
$665$	13312.5	−	40263.8i	0.776296	−	2.34792i
$666$	−35.3270	+	311.962i	−0.00205539	+	0.0181506i
$667$	6493.66	+	6493.66i	0.376965	+	0.376965i
$668$	5323.99	+	4793.78i	0.308371	+	0.277660i
$669$	14022.3	−	28148.6i	0.810362	−	1.62674i
$670$	−7391.38	+	24488.2i	−0.426200	+	1.41203i
$671$			13390.4i			0.770388i
$672$	−7752.25	+	22538.7i	−0.445014	+	1.29382i
$673$	−3357.26	−	3357.26i	−0.192292	−	0.192292i	0.604394	−	0.796686i	$-0.293415\pi$
$673$	−3357.26	−	3357.26i	−0.192292	−	0.192292i	−0.796686	+	0.604394i	$0.793415\pi$
$674$	−7197.44	−	6830.14i	−0.411328	−	0.390337i
$675$	16584.8	−	5700.24i	0.945700	−	0.325040i
$676$	−85.9211	−	1639.58i	−0.00488855	−	0.0932849i
$677$	−4964.42	+	4964.42i	−0.281829	+	0.281829i	−0.833838	−	0.552009i	$-0.813861\pi$
$677$	−4964.42	+	4964.42i	−0.281829	+	0.281829i	0.552009	+	0.833838i	$0.313861\pi$
$678$	−13850.6	+	29729.1i	−0.784554	+	1.68398i
$679$		−	2942.96i		−	0.166334i
$680$	−1528.12	+	6223.37i	−0.0861777	+	0.350964i
$681$	−26158.0	−	13030.7i	−1.47192	−	0.733241i
$682$	−169.304	−	6465.87i	−0.00950585	−	0.363036i
$683$	−1093.51	−	1093.51i	−0.0612622	−	0.0612622i	0.675812	−	0.737074i	$-0.263793\pi$
$683$	−1093.51	−	1093.51i	−0.0612622	−	0.0612622i	−0.737074	+	0.675812i	$0.763793\pi$
$684$	−24753.9	+	20799.9i	−1.38376	+	1.16272i
$685$	−24210.6	−	8004.80i	−1.35043	−	0.446493i
$686$	2165.72	−	2282.18i	0.120536	−	0.127018i
$687$	627.830	+	1874.25i	0.0348664	+	0.104086i
$688$	−14315.8	+	17678.3i	−0.793290	+	0.979618i
$689$	−25988.4			−1.43698
$690$	312.235	+	10373.3i	0.0172269	+	0.572326i
$691$		−	26962.7i		−	1.48438i	−0.670187	−	0.742192i	$-0.733786\pi$
$691$		−	26962.7i		−	1.48438i	0.670187	−	0.742192i	$-0.266214\pi$
$692$	6881.29	+	6195.98i	0.378017	+	0.340370i
$693$	−2105.40	+	15055.8i	−0.115408	+	0.825283i
$694$	−18881.3	−	17917.7i	−1.03274	−	0.980039i
$695$	−858.376	+	431.802i	−0.0468490	+	0.0235672i
$696$	6685.20	+	15734.5i	0.364083	+	0.856919i
$697$	2928.08	−	2928.08i	0.159124	−	0.159124i
$698$	−96.6835	−	3692.43i	−0.00524287	−	0.200230i
$699$	−10835.7	−	5397.83i	−0.586328	−	0.292081i
$700$	−5012.39	−	24839.0i	−0.270644	−	1.34118i
$701$	−27376.2			−1.47501			−0.737506	−	0.675340i	$-0.763997\pi$
$701$	−27376.2			−1.47501			−0.737506	+	0.675340i	$0.763997\pi$
$702$	−3699.87	−	17318.9i	−0.198921	−	0.931138i
$703$	435.142	+	435.142i	0.0233452	+	0.0233452i
$704$	11236.5	−	1779.58i	0.601553	−	0.0952705i
$705$	86.5487	+	22120.9i	0.00462356	+	1.18173i
$706$	−1270.64	−	1205.79i	−0.0677352	−	0.0642786i
$707$	6393.77	−	6393.77i	0.340117	−	0.340117i
$708$	3520.10	−	1387.99i	0.186855	−	0.0736776i
$709$	32452.9			1.71903			0.859517	−	0.511108i	$-0.170765\pi$
$709$	32452.9			1.71903			0.859517	+	0.511108i	$0.170765\pi$
$710$	22377.8	−	12001.1i	1.18285	−	0.634355i
$711$	15022.7	+	19907.4i	0.792401	+	1.05005i
$712$	−316.737	−	4024.78i	−0.0166717	−	0.211847i
$713$	−4596.27	+	4596.27i	−0.241419	+	0.241419i
$714$	8863.58	−	3229.51i	0.464581	−	0.169274i
$715$	3480.43	−	10526.6i	0.182043	−	0.550592i
$716$	−438.314	−	8364.05i	−0.0228779	−	0.436563i
$717$	−3999.23	−	11938.8i	−0.208304	−	0.621844i
$718$	496.666	+	18968.1i	0.0258153	+	0.985909i
$719$	−8713.04			−0.451936			−0.225968	−	0.974135i	$-0.572554\pi$
$719$	−8713.04			−0.451936			−0.225968	+	0.974135i	$0.572554\pi$
$720$	−6688.92	+	18124.7i	−0.346224	+	0.938152i
$721$	−36327.6			−1.87644
$722$	1151.05	+	43959.6i	0.0593319	+	2.26594i
$723$	8838.18	+	26384.4i	0.454627	+	1.35719i
$724$	−1166.65	−	22262.5i	−0.0598872	−	1.14279i
$725$	−14593.2	−	10834.3i	−0.747555	−	0.555002i
$726$	−11561.8	+	4212.65i	−0.591047	+	0.215353i
$727$	4746.24	−	4746.24i	0.242130	−	0.242130i	−0.575601	−	0.817731i	$-0.695232\pi$
$727$	4746.24	−	4746.24i	0.242130	−	0.242130i	0.817731	+	0.575601i	$0.195232\pi$
$728$	−25510.3	+	2007.58i	−1.29873	+	0.102206i
$729$	7091.62	+	18361.1i	0.360292	+	0.932840i
$730$	−4505.99	+	14928.7i	−0.228458	+	0.756899i
$731$	9003.42			0.455545
$732$	23304.6	−	9189.11i	1.17673	−	0.463988i
$733$	−1502.23	+	1502.23i	−0.0756975	+	0.0756975i	−0.743942	−	0.668244i	$-0.767046\pi$
$733$	−1502.23	+	1502.23i	−0.0756975	+	0.0756975i	0.668244	+	0.743942i	$0.267046\pi$
$734$	2703.26	+	2565.31i	0.135939	+	0.129002i
$735$	−12238.7	+	12334.9i	−0.614193	+	0.619018i
$736$	−9070.27	−	6959.99i	−0.454259	−	0.348571i
$737$	−12709.2	−	12709.2i	−0.635208	−	0.635208i
$738$	9764.87	−	7778.26i	0.487059	−	0.387970i
$739$	−22621.6			−1.12605			−0.563024	−	0.826441i	$-0.690362\pi$
$739$	−22621.6			−1.12605			−0.563024	+	0.826441i	$0.690362\pi$
$740$	354.684	+	97.0021i	0.0176195	+	0.00481874i
$741$	−31070.9	−	15478.0i	−1.54037	−	0.767341i
$742$	−1092.44	−	41721.3i	−0.0540496	−	2.06420i
$743$	−25212.3	+	25212.3i	−1.24488	+	1.24488i	−0.286932	+	0.957951i	$0.592635\pi$
$743$	−25212.3	+	25212.3i	−1.24488	+	1.24488i	−0.957951	+	0.286932i	$0.907365\pi$
$744$	−11137.0	+	4731.84i	−0.548794	+	0.233169i
$745$	10974.3	+	21815.8i	0.539690	+	1.07284i
$746$	24401.0	+	23155.8i	1.19757	+	1.13645i
$747$	18961.6	+	2651.60i	0.928741	+	0.129875i
$748$	−3346.21	−	3012.96i	−0.163569	−	0.147279i
$749$			4241.17i			0.206901i
$750$	−3613.62	−	20219.2i	−0.175934	−	0.984402i
$751$	19496.6			0.947323			0.473662	−	0.880707i	$-0.342932\pi$
$751$	19496.6			0.947323			0.473662	+	0.880707i	$0.342932\pi$
$752$	−18938.7	−	15336.5i	−0.918382	−	0.743701i
$753$	−3840.09	−	11463.7i	−0.185844	−	0.554796i
$754$	−12634.3	+	13313.7i	−0.610230	+	0.643046i
$755$	3345.65	−	1683.01i	0.161272	−	0.0811273i
$756$	27647.9	−	6667.72i	1.33008	−	0.320771i
$757$	−11487.8	−	11487.8i	−0.551559	−	0.551559i	0.375332	−	0.926891i	$-0.377529\pi$
$757$	−11487.8	−	11487.8i	−0.551559	−	0.551559i	−0.926891	+	0.375332i	$0.877529\pi$
$758$	188.211	+	7187.94i	0.00901864	+	0.344430i
$759$	−6527.11	−	3251.50i	−0.312147	−	0.155497i
$760$	19619.2	+	32389.8i	0.936398	+	1.54592i
$761$			13242.6i			0.630807i	0.948958	+	0.315404i	$0.102140\pi$
$761$			13242.6i			0.630807i	−0.948958	+	0.315404i	$0.897860\pi$
$762$	−7364.17	+	15806.6i	−0.350099	+	0.751461i
$763$	2000.97	−	2000.97i	0.0949410	−	0.0949410i
$764$	−1153.51	−	22011.6i	−0.0546236	−	1.04235i
$765$	7241.04	−	2457.14i	0.342223	−	0.116128i
$766$	11805.2	+	11202.8i	0.556840	+	0.528423i
$767$	2872.55	+	2872.55i	0.135231	+	0.135231i
$768$	−10808.2	−	18334.9i	−0.507823	−	0.861461i
$769$			1402.68i			0.0657763i	0.999459	+	0.0328881i	$0.0104705\pi$
$769$			1402.68i			0.0657763i	−0.999459	+	0.0328881i	$0.989529\pi$
$770$	17045.6	+	5144.93i	0.797765	+	0.240793i
$771$	−284.697	+	571.505i	−0.0132984	+	0.0266955i
$772$	19294.3	+	17372.8i	0.899504	+	0.809922i
$773$	10870.3	+	10870.3i	0.505792	+	0.505792i	0.913232	−	0.407440i	$-0.133578\pi$
$773$	10870.3	+	10870.3i	0.505792	+	0.505792i	−0.407440	+	0.913232i	$0.633578\pi$
$774$	26971.3	+	3054.26i	1.25253	+	0.141839i
$775$	7668.62	−	10329.2i	0.355439	−	0.478755i
$776$	1998.30	+	1706.73i	0.0924419	+	0.0789537i
$777$	−171.936	−	513.276i	−0.00793843	−	0.0236984i
$778$	−17528.5	+	458.970i	−0.807745	+	0.0211502i
$779$		−	24470.1i		−	1.12546i
$780$	−20709.0	+	1166.51i	−0.950642	+	0.0535483i
$781$			17842.3i			0.817476i
$782$	118.445	+	4523.52i	0.00541635	+	0.206855i
$783$	11537.0	−	16823.6i	0.526565	−	0.767851i
$784$	−2000.82	−	19037.7i	−0.0911450	−	0.867242i
$785$	7003.83	+	2315.69i	0.318443	+	0.105287i
$786$	−23353.6	+	8509.06i	−1.05979	+	0.386143i
$787$	2534.22	+	2534.22i	0.114784	+	0.114784i	0.762166	−	0.647382i	$-0.224136\pi$
$787$	2534.22	+	2534.22i	0.114784	+	0.114784i	−0.647382	+	0.762166i	$0.724136\pi$
$788$	19072.8	−	21182.3i	0.862234	−	0.957601i
$789$	−227.709	−	113.434i	−0.0102746	−	0.00511832i
$790$	25741.5	−	13805.0i	1.15929	−	0.621723i
$791$		−	56547.4i		−	2.54184i
$792$	−9002.02	−	10161.0i	−0.403880	−	0.455876i
$793$	19017.6	+	19017.6i	0.851620	+	0.851620i
$794$	−15478.2	+	16310.6i	−0.691815	+	0.729018i
$795$	−132.358	−	33829.3i	−0.00590472	−	1.50918i
$796$	805.288	+	15366.8i	0.0358576	+	0.684247i
$797$	−5900.82	+	5900.82i	−0.262256	+	0.262256i	−0.825970	−	0.563714i	$-0.809372\pi$
$797$	−5900.82	+	5900.82i	−0.262256	+	0.262256i	0.563714	+	0.825970i	$0.309372\pi$
$798$	23542.1	−	50531.2i	1.04434	−	2.24159i
$799$			9645.36i			0.427069i
$800$	19772.8	+	11001.6i	0.873844	+	0.486206i
$801$	−3845.35	+	2901.82i	−0.169624	+	0.128004i
$802$	−44494.2	+	1165.05i	−1.95903	+	0.0512959i
$803$	−7747.87	−	7747.87i	−0.340494	−	0.340494i
$804$	−13397.4	+	30840.7i	−0.587676	+	1.35282i
$805$	−8041.02	−	15984.7i	−0.352060	−	0.699858i
$806$	−9423.56	−	8942.65i	−0.411825	−	0.390808i
$807$	1137.13	−	380.912i	0.0496019	−	0.0166155i
$808$	633.463	+	8049.41i	0.0275806	+	0.350467i
$809$	6182.42			0.268680			0.134340	−	0.990935i	$-0.457109\pi$
$809$	6182.42			0.268680			0.134340	+	0.990935i	$0.457109\pi$
$810$	22525.3	−	4904.36i	0.977108	−	0.212743i
$811$			18828.2i			0.815225i	0.913155	+	0.407612i	$0.133639\pi$
$811$			18828.2i			0.815225i	−0.913155	+	0.407612i	$0.866361\pi$
$812$	−21904.7	−	19723.2i	−0.946680	−	0.852400i
$813$	3911.80	+	11677.8i	0.168749	+	0.503762i
$814$	−177.853	+	187.417i	−0.00765815	+	0.00806998i
$815$	−9650.92	+	29189.3i	−0.414794	+	1.25455i
$816$	−2947.43	+	7891.37i	−0.126447	+	0.338546i
$817$	37621.0	−	37621.0i	1.61101	−	1.61101i
$818$	−40044.8	+	1048.54i	−1.71166	+	0.0448185i
$819$	18392.7	+	24373.0i	0.784727	+	1.03988i
$820$	−7245.36	−	12700.2i	−0.308560	−	0.540868i
$821$	17933.9			0.762361			0.381180	−	0.924501i	$-0.375518\pi$
$821$	17933.9			0.762361			0.381180	+	0.924501i	$0.375518\pi$
$822$	−30384.4	−	14155.8i	−1.28927	−	0.600659i
$823$	−15323.0	−	15323.0i	−0.649000	−	0.649000i	0.303751	−	0.952751i	$-0.401761\pi$
$823$	−15323.0	−	15323.0i	−0.649000	−	0.649000i	−0.952751	+	0.303751i	$0.901761\pi$
$824$	21067.7	−	24666.8i	0.890689	−	1.04285i
$825$	13720.3	+	4476.90i	0.579006	+	0.188928i
$826$	−4490.80	+	4732.30i	−0.189170	+	0.199343i
$827$	−5860.11	+	5860.11i	−0.246404	+	0.246404i	−0.819493	−	0.573089i	$-0.805745\pi$
$827$	−5860.11	+	5860.11i	−0.246404	+	0.246404i	0.573089	+	0.819493i	$0.305745\pi$
$828$	−1179.70	+	13591.1i	−0.0495140	+	0.570440i
$829$	8730.17			0.365755			0.182878	−	0.983136i	$-0.441459\pi$
$829$	8730.17			0.365755			0.182878	+	0.983136i	$0.441459\pi$
$830$	6479.66	−	21467.6i	0.270979	−	0.897774i
$831$	−11789.5	+	23666.5i	−0.492148	+	0.987945i
$832$	13431.2	−	18486.1i	0.559667	−	0.770299i
$833$	−5357.39	+	5357.39i	−0.222836	+	0.222836i
$834$	−1186.77	+	432.408i	−0.0492739	+	0.0179533i
$835$	−9506.10	−	3143.02i	−0.393979	−	0.130262i
$836$	−26571.9	+	1392.49i	−1.09929	+	0.0576078i
$837$	11907.9	+	8166.01i	0.491753	+	0.337227i
$838$	22785.3	−	596.615i	0.939264	−	0.0245940i
$839$	26349.6			1.08425			0.542127	−	0.840296i	$-0.317619\pi$
$839$	26349.6			1.08425			0.542127	+	0.840296i	$0.317619\pi$
$840$	−2743.21	−	33196.8i	−0.112678	−	1.36357i
$841$	3247.00			0.133134
$842$	3453.23	−	90.4203i	0.141337	−	0.00370082i
$843$	4678.62	−	1567.23i	0.191151	−	0.0640313i
$844$	−1121.46	−	21400.1i	−0.0457373	−	0.872775i
$845$	1031.13	+	2049.78i	0.0419787	+	0.0834491i
$846$	−3272.02	+	28894.3i	−0.132972	+	1.17424i
$847$	15002.2	−	15002.2i	0.608598	−	0.608598i
$848$	28962.7	+	23453.9i	1.17286	+	0.949776i
$849$	3658.96	+	1822.72i	0.147909	+	0.0736815i
$850$	−1541.13	−	8822.18i	−0.0621884	−	0.355998i
$851$	259.652			0.0104592
$852$	31052.8	−	12244.2i	1.24865	−	0.492348i
$853$	−30358.1	+	30358.1i	−1.21857	+	1.21857i	−0.250441	+	0.968132i	$0.580576\pi$
$853$	−30358.1	+	30358.1i	−1.21857	+	1.21857i	−0.968132	+	0.250441i	$0.919424\pi$
$854$	−29731.1	+	31329.9i	−1.19131	+	1.25537i
$855$	19989.6	−	40524.0i	0.799569	−	1.62093i
$856$	−2879.80	−	2459.60i	−0.114988	−	0.0982097i
$857$	12312.1	+	12312.1i	0.490752	+	0.490752i	0.908543	−	0.417791i	$-0.137196\pi$
$857$	12312.1	+	12312.1i	0.490752	+	0.490752i	−0.417791	+	0.908543i	$0.637196\pi$
$858$	6154.86	−	13210.9i	0.244899	−	0.525657i
$859$	13088.1			0.519860			0.259930	−	0.965627i	$-0.416300\pi$
$859$	13088.1			0.519860			0.259930	+	0.965627i	$0.416300\pi$
$860$	8386.49	−	30664.9i	0.332531	−	1.21589i
$861$	−9597.59	+	19266.4i	−0.379890	+	0.762597i
$862$	25208.0	−	660.053i	0.996042	−	0.0260806i
$863$	24242.8	−	24242.8i	0.956240	−	0.956240i	−0.0428419	−	0.999082i	$-0.513641\pi$
$863$	24242.8	−	24242.8i	0.956240	−	0.956240i	0.999082	+	0.0428419i	$0.0136412\pi$
$864$	−11506.5	+	22640.1i	−0.453079	+	0.891470i
$865$	−12286.7	−	4062.37i	−0.482960	−	0.159682i
$866$	26393.4	−	27812.8i	1.03566	−	1.09136i
$867$	−21045.2	+	7049.68i	−0.824376	+	0.276147i
$868$	13960.2	−	15504.3i	0.545901	−	0.606280i
$869$			20524.3i			0.801197i
$870$	−17394.9	−	16378.4i	−0.677866	−	0.638251i
$871$	−36100.2			−1.40437
$872$	198.246	+	2519.11i	0.00769892	+	0.0978302i
$873$	434.283	−	3105.57i	0.0168365	−	0.120398i
$874$	19396.5	+	18406.7i	0.750684	+	0.712375i
$875$	20369.7	+	28968.7i	0.786995	+	1.11922i
$876$	−8167.45	+	18801.3i	−0.315014	+	0.725158i
$877$	2316.61	+	2316.61i	0.0891975	+	0.0891975i	0.750298	−	0.661100i	$-0.229910\pi$
$877$	2316.61	+	2316.61i	0.0891975	+	0.0891975i	−0.661100	+	0.750298i	$0.729910\pi$
$878$	−4229.32	+	110.742i	−0.162566	+	0.00425666i
$879$	−4405.63	+	8843.93i	−0.169054	+	0.339361i
$880$	−13378.8	+	8590.38i	−0.512499	+	0.329070i
$881$		−	13145.1i		−	0.502692i	−0.967897	−	0.251346i	$-0.919127\pi$
$881$		−	13145.1i		−	0.502692i	0.967897	−	0.251346i	$-0.0808731\pi$
$882$	−17866.4	+	14231.5i	−0.682077	+	0.543312i
$883$	−3867.58	+	3867.58i	−0.147400	+	0.147400i	−0.776956	−	0.629555i	$-0.783237\pi$
$883$	−3867.58	+	3867.58i	−0.147400	+	0.147400i	0.629555	+	0.776956i	$0.283237\pi$
$884$	−9031.56	+	473.294i	−0.343625	+	0.0180075i
$885$	−3724.60	+	3753.86i	−0.141470	+	0.142581i
$886$	−17744.3	+	18698.5i	−0.672833	+	0.709016i
$887$	20707.3	+	20707.3i	0.783858	+	0.783858i	0.980479	−	0.196621i	$-0.0629970\pi$
$887$	20707.3	+	20707.3i	0.783858	+	0.783858i	−0.196621	+	0.980479i	$0.562997\pi$
$888$	448.231	+	180.921i	0.0169388	+	0.00683705i
$889$		−	30065.6i		−	1.13427i
$890$	2666.61	+	4972.28i	0.100432	+	0.187271i
$891$	−4443.46	+	15576.9i	−0.167072	+	0.585687i
$892$	−35980.8	−	32397.5i	−1.35059	−	1.21608i
$893$	40303.3	+	40303.3i	1.51030	+	1.51030i
$894$	10989.7	+	30162.0i	0.411132	+	1.12838i
$895$	5260.17	+	10456.6i	0.196456	+	0.390533i
$896$	30241.8	+	20785.1i	1.12757	+	0.774980i
$897$	−13888.0	+	4652.17i	−0.516953	+	0.173168i
$898$	−1280.23	−	48893.0i	−0.0475744	−	1.81691i
$899$		−	14964.5i		−	0.555165i
$900$	−1623.92	−	26951.1i	−0.0601453	−	0.998190i
$901$		−	14750.5i		−	0.545407i
$902$	10270.4	−	268.924i	0.379122	−	0.00992703i
$903$	−44376.2	+	14865.0i	−1.63538	+	0.547815i
$904$	38396.3	+	32793.9i	1.41266	+	1.20653i
$905$	14000.9	+	27832.3i	0.514261	+	1.02229i
$906$	4625.61	−	1685.37i	0.169620	−	0.0618022i
$907$	−35323.3	−	35323.3i	−1.29315	−	1.29315i	−0.932825	−	0.360330i	$-0.882664\pi$
$907$	−35323.3	−	35323.3i	−1.29315	−	1.29315i	−0.360330	−	0.932825i	$-0.617336\pi$
$908$	−30106.5	+	33436.4i	−1.10035	+	1.22205i
$909$	7690.55	−	5803.53i	0.280615	−	0.211761i
$910$	31515.9	−	16901.8i	1.14807	−	0.615702i
$911$		−	8493.20i		−	0.308883i	−0.988002	−	0.154441i	$-0.950642\pi$
$911$		−	8493.20i		−	0.308883i	0.988002	−	0.154441i	$-0.0493578\pi$
$912$	20658.4	+	45290.2i	0.750073	+	1.64442i
$913$	11141.5	+	11141.5i	0.403867	+	0.403867i
$914$	2439.49	+	2315.00i	0.0882835	+	0.0837782i
$915$	−24658.5	+	24852.2i	−0.890913	+	0.897912i
$916$	3039.01	−	159.258i	0.109620	−	0.00574457i
$917$	30302.8	−	30302.8i	1.09126	−	1.09126i
$918$	9829.88	−	2099.98i	0.353414	−	0.0755008i
$919$			12966.9i			0.465439i	0.972544	+	0.232720i	$0.0747624\pi$
$919$			12966.9i			0.465439i	−0.972544	+	0.232720i	$0.925238\pi$
$920$	15517.0	+	3810.14i	0.556067	+	0.136540i
$921$	9974.13	−	20022.2i	0.356850	−	0.716347i
$922$	230.363	+	8797.78i	0.00822843	+	0.314251i
$923$	25340.4	+	25340.4i	0.903673	+	0.903673i
$924$	21467.3	+	9325.58i	0.764311	+	0.332023i
$925$	−508.365	+	75.1502i	−0.0180702	+	0.00267127i
$926$	−14514.5	+	15295.0i	−0.515092	+	0.542792i
$927$	−38334.8	−	5360.74i	−1.35823	−	0.189935i
$928$	26095.6	−	3435.33i	0.923092	−	0.121520i
$929$	19015.3			0.671552			0.335776	−	0.941942i	$-0.391002\pi$
$929$	19015.3			0.671552			0.335776	+	0.941942i	$0.391002\pi$
$930$	11592.7	−	12312.3i	0.408753	−	0.434124i
$931$			44771.9i			1.57609i
$932$	−12471.3	+	13850.7i	−0.438316	+	0.486796i
$933$	−6772.52	+	2268.64i	−0.237644	+	0.0796055i
$934$	9596.21	+	9106.50i	0.336186	+	0.319030i
$935$	5974.72	+	1975.43i	0.208978	+	0.0690947i
$936$	−27216.1	−	1645.97i	−0.950412	−	0.0574789i
$937$	−17181.0	+	17181.0i	−0.599016	+	0.599016i	−0.940051	−	0.341035i	$-0.889223\pi$
$937$	−17181.0	+	17181.0i	−0.599016	+	0.599016i	0.341035	+	0.940051i	$0.389223\pi$
$938$	−1517.50	−	57954.7i	−0.0528232	−	2.01736i
$939$	−16391.5	+	32904.5i	−0.569665	+	1.14355i
$940$	32851.3	+	8984.44i	1.13988	+	0.311745i
$941$	31792.8			1.10140			0.550700	−	0.834704i	$-0.314361\pi$
$941$	31792.8			1.10140			0.550700	+	0.834704i	$0.314361\pi$
$942$	8789.83	+	4095.11i	0.304021	+	0.141641i
$943$	−7300.74	−	7300.74i	−0.252115	−	0.252115i
$944$	−608.906	−	5793.72i	−0.0209939	−	0.199756i
$945$	−31632.9	+	24066.0i	−1.08891	+	0.828431i
$946$	16203.5	+	15376.6i	0.556892	+	0.528473i
$947$	−18557.5	+	18557.5i	−0.636787	+	0.636787i	−0.949762	−	0.312974i	$-0.898675\pi$
$947$	−18557.5	+	18557.5i	−0.636787	+	0.636787i	0.312974	+	0.949762i	$0.398675\pi$
$948$	35720.6	−	14084.7i	1.22379	−	0.482544i
$949$	−22007.7			−0.752793
$950$	−43303.3	−	30424.1i	−1.47889	−	1.03904i
$951$	−12404.0	−	6179.07i	−0.422951	−	0.210694i
$952$	−1139.47	−	14479.2i	−0.0387923	−	0.492935i
$953$	1848.74	−	1848.74i	0.0628400	−	0.0628400i	−0.674988	−	0.737828i	$-0.735851\pi$
$953$	1848.74	−	1848.74i	0.0628400	−	0.0628400i	0.737828	+	0.674988i	$0.235851\pi$
$954$	5003.87	−	44187.7i	0.169818	−	1.49961i
$955$	13843.2	+	27518.7i	0.469062	+	0.932443i
$956$	−19358.3	+	1014.46i	−0.654907	+	0.0343201i
$957$	15918.6	−	5332.36i	0.537695	−	0.180116i
$958$	−1103.93	−	42160.1i	−0.0372300	−	1.42185i
$959$	57793.8			1.94605
$960$	24131.9	+	17389.3i	0.811305	+	0.584624i
$961$	−19199.0			−0.644457
$962$	13.5837	+	518.771i	0.000455254	+	0.0173866i
$963$	−625.855	+	4475.50i	−0.0209428	+	0.149762i
$964$	42781.2	−	2241.93i	1.42935	−	0.0749042i
$965$	−34450.4	−	11390.4i	−1.14922	−	0.379968i
$966$	−8052.30	−	22100.0i	−0.268197	−	0.736083i
$967$	−32422.2	+	32422.2i	−1.07821	+	1.07821i	−0.0815378	+	0.996670i	$0.525983\pi$
$967$	−32422.2	+	32422.2i	−1.07821	+	1.07821i	−0.996670	+	0.0815378i	$0.974017\pi$
$968$	1486.34	+	18887.0i	0.0493522	+	0.627119i
$969$	8785.05	−	17635.3i	0.291245	−	0.584650i
$970$	−3516.01	−	1061.25i	−0.116384	−	0.0351286i
$971$	−46272.4			−1.52930			−0.764650	−	0.644445i	$-0.777088\pi$
$971$	−46272.4			−1.52930			−0.764650	+	0.644445i	$0.777088\pi$
$972$	30159.4	−	2956.22i	0.995230	−	0.0975524i
$973$	1539.91	−	1539.91i	0.0507371	−	0.0507371i
$974$	−20344.1	−	19305.9i	−0.669268	−	0.635114i
$975$	25844.5	−	13127.9i	0.848908	−	0.431210i
$976$	−4031.24	−	38357.1i	−0.132210	−	1.25797i
$977$	−14928.0	−	14928.0i	−0.488831	−	0.488831i	0.419106	−	0.907937i	$-0.362344\pi$
$977$	−14928.0	−	14928.0i	−0.488831	−	0.488831i	−0.907937	+	0.419106i	$0.862344\pi$
$978$	−17066.9	+	36632.7i	−0.558014	+	1.19774i
$979$	−3964.52			−0.129424
$980$	13256.5	+	23237.1i	0.432106	+	0.757430i
$981$	2406.80	−	1816.25i	0.0783316	−	0.0591116i
$982$	−125.547	−	4794.75i	−0.00407981	−	0.155811i
$983$	−19226.6	+	19226.6i	−0.623839	+	0.623839i	−0.946511	−	0.322672i	$-0.895419\pi$
$983$	−19226.6	+	19226.6i	−0.623839	+	0.623839i	0.322672	+	0.946511i	$0.395419\pi$
$984$	−7516.08	−	17690.1i	−0.243500	−	0.573110i
$985$	−12505.0	+	37821.5i	−0.404510	+	1.22345i
$986$	−7556.63	−	7170.99i	−0.244069	−	0.231614i
$987$	−15924.9	−	47540.2i	−0.513571	−	1.53315i
$988$	−35760.9	+	39716.2i	−1.15152	+	1.27889i
$989$		−	22448.7i		−	0.721766i
$990$	17228.1	+	7944.56i	0.553077	+	0.255045i
$991$	−6178.69			−0.198055			−0.0990275	−	0.995085i	$-0.531573\pi$
$991$	−6178.69			−0.198055			−0.0990275	+	0.995085i	$0.531573\pi$
$992$	2431.55	+	18470.7i	0.0778245	+	0.591174i
$993$	−23492.5	+	7869.46i	−0.750768	+	0.251490i
$994$	−39615.9	+	41746.3i	−1.26412	+	1.33210i
$995$	−9664.19	−	19211.4i	−0.307915	−	0.612102i
$996$	11744.9	−	27036.5i	0.373645	−	0.860126i
$997$	25834.7	+	25834.7i	0.820655	+	0.820655i	0.986202	−	0.165547i	$-0.0529389\pi$
$997$	25834.7	+	25834.7i	0.820655	+	0.820655i	−0.165547	+	0.986202i	$0.552939\pi$
$998$	192.769	+	7362.00i	0.00611421	+	0.233507i
$999$	−105.693	−	567.007i	−0.00334733	−	0.0179573i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.w.c.53.33	yes	128
3.2	odd	2	inner	120.4.w.c.53.32	yes	128
5.2	odd	4	inner	120.4.w.c.77.1	yes	128
8.5	even	2	inner	120.4.w.c.53.64	yes	128
15.2	even	4	inner	120.4.w.c.77.64	yes	128
24.5	odd	2	inner	120.4.w.c.53.1	✓	128
40.37	odd	4	inner	120.4.w.c.77.32	yes	128
120.77	even	4	inner	120.4.w.c.77.33	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.w.c.53.1	✓	128	24.5	odd	2	inner
120.4.w.c.53.32	yes	128	3.2	odd	2	inner
120.4.w.c.53.33	yes	128	1.1	even	1	trivial
120.4.w.c.53.64	yes	128	8.5	even	2	inner
120.4.w.c.77.1	yes	128	5.2	odd	4	inner
120.4.w.c.77.32	yes	128	40.37	odd	4	inner
120.4.w.c.77.33	yes	128	120.77	even	4	inner
120.4.w.c.77.64	yes	128	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.0740349 + 2.82746i) q^{2} +(-1.65046 - 4.92707i) q^{3} +(-7.98904 + 0.418661i) q^{4} +(9.98780 - 5.02432i) q^{5} +(13.8089 - 5.03137i) q^{6} +(-17.9179 + 17.9179i) q^{7} +(-1.77521 - 22.5577i) q^{8} +(-21.5520 + 16.2638i) q^{9} +(14.9455 + 27.8681i) q^{10} -22.2199 q^{11} +(15.2483 + 38.6715i) q^{12} +(-31.5577 + 31.5577i) q^{13} +(-51.9887 - 49.3356i) q^{14} +(-41.2396 - 40.9182i) q^{15} +(63.6494 - 6.68940i) q^{16} +(-17.9116 - 17.9116i) q^{17} +(-47.5809 - 59.7333i) q^{18} -149.688 q^{19} +(-77.6894 + 44.3210i) q^{20} +(117.855 + 58.7100i) q^{21} +(-1.64505 - 62.8258i) q^{22} +(-44.6598 + 44.6598i) q^{23} +(-108.213 + 45.9771i) q^{24} +(74.5124 - 100.364i) q^{25} +(-91.5643 - 86.8916i) q^{26} +(115.704 + 79.3454i) q^{27} +(135.645 - 150.648i) q^{28} -145.403i q^{29} +(112.641 - 119.633i) q^{30} +102.917 q^{31} +(23.6263 + 179.471i) q^{32} +(36.6730 + 109.479i) q^{33} +(49.3181 - 51.9703i) q^{34} +(-88.9352 + 268.986i) q^{35} +(165.371 - 138.955i) q^{36} +(-2.90700 - 2.90700i) q^{37} +(-11.0821 - 423.236i) q^{38} +(207.571 + 103.402i) q^{39} +(-131.067 - 216.382i) q^{40} +163.475i q^{41} +(-157.275 + 337.578i) q^{42} +(-251.330 + 251.330i) q^{43} +(177.516 - 9.30261i) q^{44} +(-133.542 + 270.724i) q^{45} +(-129.580 - 122.967i) q^{46} +(-269.250 - 269.250i) q^{47} +(-138.010 - 302.565i) q^{48} -299.102i q^{49} +(289.291 + 203.250i) q^{50} +(-58.6892 + 117.814i) q^{51} +(238.903 - 265.327i) q^{52} +(411.760 + 411.760i) q^{53} +(-215.780 + 333.021i) q^{54} +(-221.928 + 111.640i) q^{55} +(435.994 + 372.378i) q^{56} +(247.053 + 737.521i) q^{57} +(411.121 - 10.7649i) q^{58} -91.0255i q^{59} +(346.596 + 309.631i) q^{60} -602.630i q^{61} +(7.61948 + 290.994i) q^{62} +(94.7529 - 677.580i) q^{63} +(-505.697 + 80.0894i) q^{64} +(-156.636 + 473.747i) q^{65} +(-306.832 + 111.797i) q^{66} +(571.973 + 571.973i) q^{67} +(150.595 + 135.597i) q^{68} +(293.751 + 146.333i) q^{69} +(-767.130 - 231.546i) q^{70} -802.988i q^{71} +(405.133 + 457.291i) q^{72} +(348.690 + 348.690i) q^{73} +(8.00420 - 8.43464i) q^{74} +(-617.479 - 201.481i) q^{75} +(1195.86 - 62.6684i) q^{76} +(398.134 - 398.134i) q^{77} +(-276.998 + 594.554i) q^{78} -923.691i q^{79} +(602.108 - 386.608i) q^{80} +(199.976 - 701.035i) q^{81} +(-462.218 + 12.1028i) q^{82} +(-501.421 - 501.421i) q^{83} +(-966.131 - 419.695i) q^{84} +(-268.891 - 88.9037i) q^{85} +(-729.232 - 692.018i) q^{86} +(-716.410 + 239.981i) q^{87} +(39.4451 + 501.229i) q^{88} +178.422 q^{89} +(-775.347 - 357.542i) q^{90} -1130.89i q^{91} +(338.091 - 375.486i) q^{92} +(-169.861 - 507.081i) q^{93} +(741.358 - 781.226i) q^{94} +(-1495.05 + 752.079i) q^{95} +(845.271 - 412.617i) q^{96} +(-82.1236 + 82.1236i) q^{97} +(845.699 - 22.1440i) q^{98} +(478.883 - 361.380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) \) 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Introduction

L-functions

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