LMFDB - Embedded newform 12.7.d.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,7,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	12.d (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:	$2.76064900344$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.50898483.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8x^{4} - 10x^{3} + 64x^{2} - 40x + 25 $ x^6 + 8x^4 - 10x^3 + 64x^2 - 40x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.3
Root			$1.21966 - 2.11251i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.7.d.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.33979 - 5.95706i) q^{2} -15.5885i q^{3} +(-6.97319 + 63.6190i) q^{4} -212.349 q^{5} +(-92.8614 + 83.2392i) q^{6} -87.6116i q^{7} +(416.218 - 298.173i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(-5.33979 - 5.95706i) q^{2} -15.5885i q^{3} +(-6.97319 + 63.6190i) q^{4} -212.349 q^{5} +(-92.8614 + 83.2392i) q^{6} -87.6116i q^{7} +(416.218 - 298.173i) q^{8} -243.000 q^{9} +(1133.90 + 1264.98i) q^{10} -2016.84i q^{11} +(991.722 + 108.701i) q^{12} -27.7102 q^{13} +(-521.908 + 467.828i) q^{14} +3310.19i q^{15} +(-3998.75 - 887.254i) q^{16} -1074.07 q^{17} +(1297.57 + 1447.57i) q^{18} -2475.99i q^{19} +(1480.75 - 13509.4i) q^{20} -1365.73 q^{21} +(-12014.4 + 10769.5i) q^{22} +13955.5i q^{23} +(-4648.05 - 6488.19i) q^{24} +29467.0 q^{25} +(147.967 + 165.071i) q^{26} +3788.00i q^{27} +(5573.76 + 610.932i) q^{28} -6459.25 q^{29} +(19719.0 - 17675.7i) q^{30} -38771.2i q^{31} +(16067.1 + 28558.6i) q^{32} -31439.4 q^{33} +(5735.30 + 6398.29i) q^{34} +18604.2i q^{35} +(1694.48 - 15459.4i) q^{36} -39691.5 q^{37} +(-14749.6 + 13221.3i) q^{38} +431.959i q^{39} +(-88383.3 + 63316.6i) q^{40} -50888.9 q^{41} +(7292.72 + 8135.74i) q^{42} -83506.5i q^{43} +(128309. + 14063.8i) q^{44} +51600.8 q^{45} +(83133.5 - 74519.3i) q^{46} +28755.6i q^{47} +(-13830.9 + 62334.3i) q^{48} +109973. q^{49} +(-157348. - 175537. i) q^{50} +16743.1i q^{51} +(193.228 - 1762.89i) q^{52} +149356. q^{53} +(22565.3 - 20227.1i) q^{54} +428274. i q^{55} +(-26123.4 - 36465.5i) q^{56} -38596.9 q^{57} +(34491.1 + 38478.2i) q^{58} -366109. i q^{59} +(-210591. - 23082.6i) q^{60} -200673. q^{61} +(-230962. + 207030. i) q^{62} +21289.6i q^{63} +(84330.2 - 248209. i) q^{64} +5884.23 q^{65} +(167880. + 187287. i) q^{66} -100020. i q^{67} +(7489.68 - 68331.1i) q^{68} +217544. q^{69} +(110827. - 99342.7i) q^{70} +293132. i q^{71} +(-101141. + 72455.9i) q^{72} -439866. q^{73} +(211945. + 236445. i) q^{74} -459345. i q^{75} +(157520. + 17265.5i) q^{76} -176699. q^{77} +(2573.21 - 2306.57i) q^{78} -199713. i q^{79} +(849130. + 188407. i) q^{80} +59049.0 q^{81} +(271736. + 303148. i) q^{82} -47053.2i q^{83} +(9523.49 - 86886.4i) q^{84} +228077. q^{85} +(-497453. + 445908. i) q^{86} +100690. i q^{87} +(-601366. - 839444. i) q^{88} +552376. q^{89} +(-275537. - 307389. i) q^{90} +2427.74i q^{91} +(-887832. - 97314.1i) q^{92} -604383. q^{93} +(171299. - 153549. i) q^{94} +525773. i q^{95} +(445184. - 250461. i) q^{96} +332298. q^{97} +(-587234. - 655117. i) q^{98} +490092. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9}+O(q^{10}) $ 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9	\( 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9} + 84 q^{10} - 972 q^{12} - 3348 q^{13} + 4776 q^{14} - 9744 q^{16} + 12220 q^{17} + 2430 q^{18} + 17608 q^{20} - 9720 q^{21} - 13512 q^{22} - 7776 q^{24} + 56418 q^{25} - 59252 q^{26} - 17808 q^{28} - 84860 q^{29} + 57348 q^{30} + 61280 q^{32} + 4536 q^{33} + 109404 q^{34} - 37908 q^{36} + 20796 q^{37} - 128088 q^{38} - 195552 q^{40} - 65252 q^{41} + 210600 q^{42} + 445008 q^{44} + 10692 q^{45} + 81120 q^{46} - 276048 q^{48} - 111546 q^{49} - 743118 q^{50} - 179592 q^{52} + 470308 q^{53} + 39366 q^{54} + 793728 q^{56} - 204120 q^{57} + 529860 q^{58} - 723816 q^{60} + 12924 q^{61} - 513384 q^{62} - 642432 q^{64} + 321512 q^{65} + 771768 q^{66} + 690328 q^{68} + 541728 q^{69} + 938928 q^{70} - 276048 q^{72} - 1283412 q^{73} - 1522916 q^{74} + 67824 q^{76} - 1487328 q^{77} + 396252 q^{78} + 1272352 q^{80} + 354294 q^{81} + 240444 q^{82} - 143856 q^{84} + 814920 q^{85} - 1154568 q^{86} + 489600 q^{88} + 730924 q^{89} - 20412 q^{90} - 1338816 q^{92} - 83592 q^{93} - 390288 q^{94} + 624672 q^{96} + 3249420 q^{97} + 1604918 q^{98}+O(q^{100}) \) 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9 + 84 * q^10 - 972 * q^12 - 3348 * q^13 + 4776 * q^14 - 9744 * q^16 + 12220 * q^17 + 2430 * q^18 + 17608 * q^20 - 9720 * q^21 - 13512 * q^22 - 7776 * q^24 + 56418 * q^25 - 59252 * q^26 - 17808 * q^28 - 84860 * q^29 + 57348 * q^30 + 61280 * q^32 + 4536 * q^33 + 109404 * q^34 - 37908 * q^36 + 20796 * q^37 - 128088 * q^38 - 195552 * q^40 - 65252 * q^41 + 210600 * q^42 + 445008 * q^44 + 10692 * q^45 + 81120 * q^46 - 276048 * q^48 - 111546 * q^49 - 743118 * q^50 - 179592 * q^52 + 470308 * q^53 + 39366 * q^54 + 793728 * q^56 - 204120 * q^57 + 529860 * q^58 - 723816 * q^60 + 12924 * q^61 - 513384 * q^62 - 642432 * q^64 + 321512 * q^65 + 771768 * q^66 + 690328 * q^68 + 541728 * q^69 + 938928 * q^70 - 276048 * q^72 - 1283412 * q^73 - 1522916 * q^74 + 67824 * q^76 - 1487328 * q^77 + 396252 * q^78 + 1272352 * q^80 + 354294 * q^81 + 240444 * q^82 - 143856 * q^84 + 814920 * q^85 - 1154568 * q^86 + 489600 * q^88 + 730924 * q^89 - 20412 * q^90 - 1338816 * q^92 - 83592 * q^93 - 390288 * q^94 + 624672 * q^96 + 3249420 * q^97 + 1604918 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$1$	$-1$

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 $

$2$	−5.33979	−	5.95706i	−0.667474	−	0.744633i
$2$	−5.33979	−	5.95706i	−0.667474	−	0.744633i
$3$		−	15.5885i		−	0.577350i
$3$		−	15.5885i		−	0.577350i
$4$	−6.97319	+	63.6190i	−0.108956	+	0.994047i
$5$	−212.349			−1.69879			−0.849395	−	0.527757i	$-0.823033\pi$
$5$	−212.349			−1.69879			−0.849395	+	0.527757i	$0.823033\pi$
$6$	−92.8614	+	83.2392i	−0.429914	+	0.385366i
$7$		−	87.6116i		−	0.255428i	−0.991811	−	0.127714i	$-0.959236\pi$
$7$		−	87.6116i		−	0.255428i	0.991811	−	0.127714i	$-0.0407639\pi$
$8$	416.218	−	298.173i	0.812925	−	0.582368i
$9$	−243.000			−0.333333
$10$	1133.90	+	1264.98i	1.13390	+	1.26498i
$11$		−	2016.84i		−	1.51528i	−0.652672	−	0.757641i	$-0.726352\pi$
$11$		−	2016.84i		−	1.51528i	0.652672	−	0.757641i	$-0.273648\pi$
$12$	991.722	+	108.701i	0.573913	+	0.0629058i
$13$	−27.7102			−0.0126127			−0.00630637	−	0.999980i	$-0.502007\pi$
$13$	−27.7102			−0.0126127			−0.00630637	+	0.999980i	$0.502007\pi$
$14$	−521.908	+	467.828i	−0.190200	+	0.170491i
$15$			3310.19i			0.980797i
$16$	−3998.75	−	887.254i	−0.976257	−	0.216615i
$17$	−1074.07			−0.218617			−0.109309	−	0.994008i	$-0.534864\pi$
$17$	−1074.07			−0.218617			−0.109309	+	0.994008i	$0.534864\pi$
$18$	1297.57	+	1447.57i	0.222491	+	0.248211i
$19$		−	2475.99i		−	0.360984i	−0.983576	−	0.180492i	$-0.942231\pi$
$19$		−	2475.99i		−	0.360984i	0.983576	−	0.180492i	$-0.0577690\pi$
$20$	1480.75	−	13509.4i	0.185094	−	1.68868i
$21$	−1365.73			−0.147471
$22$	−12014.4	+	10769.5i	−1.12833	+	1.01141i
$23$			13955.5i			1.14699i	0.819208	+	0.573496i	$0.194413\pi$
$23$			13955.5i			1.14699i	−0.819208	+	0.573496i	$0.805587\pi$
$24$	−4648.05	−	6488.19i	−0.336230	−	0.469343i
$25$	29467.0			1.88589
$26$	147.967	+	165.071i	0.00841868	+	0.00939186i
$27$			3788.00i			0.192450i
$28$	5573.76	+	610.932i	0.253907	+	0.0278304i
$29$	−6459.25			−0.264843			−0.132421	−	0.991194i	$-0.542275\pi$
$29$	−6459.25			−0.264843			−0.132421	+	0.991194i	$0.542275\pi$
$30$	19719.0	−	17675.7i	0.730334	−	0.654657i
$31$		−	38771.2i		−	1.30144i	−0.759318	−	0.650720i	$-0.774467\pi$
$31$		−	38771.2i		−	1.30144i	0.759318	−	0.650720i	$-0.225533\pi$
$32$	16067.1	+	28558.6i	0.490328	+	0.871538i
$33$	−31439.4			−0.874848
$34$	5735.30	+	6398.29i	0.145922	+	0.162790i
$35$			18604.2i			0.433918i
$36$	1694.48	−	15459.4i	0.0363187	−	0.331349i
$37$	−39691.5			−0.783596			−0.391798	−	0.920051i	$-0.628147\pi$
$37$	−39691.5			−0.783596			−0.391798	+	0.920051i	$0.628147\pi$
$38$	−14749.6	+	13221.3i	−0.268801	+	0.240948i
$39$			431.959i			0.00728197i
$40$	−88383.3	+	63316.6i	−1.38099	+	0.989322i
$41$	−50888.9			−0.738365			−0.369182	−	0.929357i	$-0.620362\pi$
$41$	−50888.9			−0.738365			−0.369182	+	0.929357i	$0.620362\pi$
$42$	7292.72	+	8135.74i	0.0984332	+	0.109812i
$43$		−	83506.5i		−	1.05030i	−0.851008	−	0.525152i	$-0.824008\pi$
$43$		−	83506.5i		−	1.05030i	0.851008	−	0.525152i	$-0.175992\pi$
$44$	128309.	+	14063.8i	1.50626	+	0.165099i
$45$	51600.8			0.566263
$46$	83133.5	−	74519.3i	0.854088	−	0.765588i
$47$			28755.6i			0.276968i	0.990365	+	0.138484i	$0.0442229\pi$
$47$			28755.6i			0.276968i	−0.990365	+	0.138484i	$0.955777\pi$
$48$	−13830.9	+	62334.3i	−0.125063	+	0.563642i
$49$	109973.			0.934757
$50$	−157348.	−	175537.i	−1.25878	−	1.40429i
$51$			16743.1i			0.126219i
$52$	193.228	−	1762.89i	0.00137423	−	0.0125377i
$53$	149356.			1.00321			0.501607	−	0.865096i	$-0.332742\pi$
$53$	149356.			1.00321			0.501607	+	0.865096i	$0.332742\pi$
$54$	22565.3	−	20227.1i	0.143305	−	0.128455i
$55$			428274.i			2.57415i
$56$	−26123.4	−	36465.5i	−0.148753	−	0.207643i
$57$	−38596.9			−0.208414
$58$	34491.1	+	38478.2i	0.176776	+	0.197211i
$59$		−	366109.i		−	1.78260i	−0.453414	−	0.891300i	$-0.649794\pi$
$59$		−	366109.i		−	1.78260i	0.453414	−	0.891300i	$-0.350206\pi$
$60$	−210591.	−	23082.6i	−0.974958	−	0.106864i
$61$	−200673.			−0.884094			−0.442047	−	0.896992i	$-0.645748\pi$
$61$	−200673.			−0.884094			−0.442047	+	0.896992i	$0.645748\pi$
$62$	−230962.	+	207030.i	−0.969095	+	0.868678i
$63$			21289.6i			0.0851425i
$64$	84330.2	−	248209.i	0.321694	−	0.946844i
$65$	5884.23			0.0214264
$66$	167880.	+	187287.i	0.583939	+	0.651441i
$67$		−	100020.i		−	0.332553i	−0.986079	−	0.166277i	$-0.946826\pi$
$67$		−	100020.i		−	0.332553i	0.986079	−	0.166277i	$-0.0531745\pi$
$68$	7489.68	−	68331.1i	0.0238197	−	0.217316i
$69$	217544.			0.662217
$70$	110827.	−	99342.7i	0.323109	−	0.289629i
$71$			293132.i			0.819008i	0.912308	+	0.409504i	$0.134298\pi$
$71$			293132.i			0.819008i	−0.912308	+	0.409504i	$0.865702\pi$
$72$	−101141.	+	72455.9i	−0.270975	+	0.194123i
$73$	−439866.			−1.13071			−0.565355	−	0.824848i	$-0.691261\pi$
$73$	−439866.			−1.13071			−0.565355	+	0.824848i	$0.691261\pi$
$74$	211945.	+	236445.i	0.523030	+	0.583492i
$75$		−	459345.i		−	1.08882i
$76$	157520.	+	17265.5i	0.358835	+	0.0393314i
$77$	−176699.			−0.387045
$78$	2573.21	−	2306.57i	0.00542239	−	0.00486053i
$79$		−	199713.i		−	0.405065i	−0.979276	−	0.202533i	$-0.935083\pi$
$79$		−	199713.i		−	0.405065i	0.979276	−	0.202533i	$-0.0649172\pi$
$80$	849130.	+	188407.i	1.65846	+	0.367983i
$81$	59049.0			0.111111
$82$	271736.	+	303148.i	0.492840	+	0.549811i
$83$		−	47053.2i		−	0.0822914i	−0.999153	−	0.0411457i	$-0.986899\pi$
$83$		−	47053.2i		−	0.0822914i	0.999153	−	0.0411457i	$-0.0131008\pi$
$84$	9523.49	−	86886.4i	0.0160679	−	0.146593i
$85$	228077.			0.371385
$86$	−497453.	+	445908.i	−0.782091	+	0.701051i
$87$			100690.i			0.152907i
$88$	−601366.	−	839444.i	−0.882452	−	1.23181i
$89$	552376.			0.783547			0.391773	−	0.920062i	$-0.371862\pi$
$89$	552376.			0.783547			0.391773	+	0.920062i	$0.371862\pi$
$90$	−275537.	−	307389.i	−0.377966	−	0.421658i
$91$			2427.74i			0.00322164i
$92$	−887832.	−	97314.1i	−1.14016	−	0.124972i
$93$	−604383.			−0.751387
$94$	171299.	−	153549.i	0.206239	−	0.184869i
$95$			525773.i			0.613236i
$96$	445184.	−	250461.i	0.503183	−	0.283091i
$97$	332298.			0.364093			0.182047	−	0.983290i	$-0.441728\pi$
$97$	332298.			0.364093			0.182047	+	0.983290i	$0.441728\pi$
$98$	−587234.	−	655117.i	−0.623926	−	0.696051i
$99$			490092.i			0.505094i
$100$	−205479.	+	1.87466e6i	−0.205479	+	1.87466i
$101$	−878783.			−0.852938			−0.426469	−	0.904502i	$-0.640243\pi$
$101$	−878783.			−0.852938			−0.426469	+	0.904502i	$0.640243\pi$
$102$	99739.4	−	89404.5i	0.0939867	−	0.0842478i
$103$			756192.i			0.692023i	0.938230	+	0.346011i	$0.112464\pi$
$103$			756192.i			0.692023i	−0.938230	+	0.346011i	$0.887536\pi$
$104$	−11533.5	+	8262.42i	−0.0102532	+	0.00734526i
$105$	290011.			0.250523
$106$	−797528.	−	889720.i	−0.669620	−	0.747026i
$107$		−	252281.i		−	0.205937i	−0.994685	−	0.102968i	$-0.967166\pi$
$107$		−	252281.i		−	0.205937i	0.994685	−	0.102968i	$-0.0328341\pi$
$108$	−240988.	−	26414.4i	−0.191304	−	0.0209686i
$109$	2.33669e6			1.80435			0.902176	−	0.431368i	$-0.141969\pi$
$109$	2.33669e6			1.80435			0.902176	+	0.431368i	$0.141969\pi$
$110$	2.55125e6	−	2.28689e6i	1.91679	−	1.71818i
$111$			618729.i			0.452410i
$112$	−77733.8	+	350337.i	−0.0553294	+	0.249363i
$113$	894293.			0.619790			0.309895	−	0.950771i	$-0.399706\pi$
$113$	894293.			0.619790			0.309895	+	0.950771i	$0.399706\pi$
$114$	206099.	+	229924.i	0.139111	+	0.155192i
$115$		−	2.96343e6i		−	1.94850i
$116$	45041.6	−	410931.i	0.0288562	−	0.263266i
$117$	6733.58			0.00420425
$118$	−2.18093e6	+	1.95495e6i	−1.32738	+	1.18984i
$119$			94100.8i			0.0558409i
$120$	987008.	+	1.37776e6i	0.571185	+	0.797315i
$121$	−2.29608e6			−1.29608
$122$	1.07155e6	+	1.19542e6i	0.590110	+	0.658325i
$123$			793279.i			0.426295i
$124$	2.46658e6	+	270359.i	1.29369	+	0.141800i
$125$	−2.93933e6			−1.50494
$126$	126824.	−	113682.i	0.0633999	−	0.0568304i
$127$			26939.0i			0.0131514i	0.999978	+	0.00657568i	$0.00209312\pi$
$127$			26939.0i			0.0131514i	−0.999978	+	0.00657568i	$0.997907\pi$
$128$	−1.92890e6	+	823026.i	−0.919774	+	0.392450i
$129$	−1.30174e6			−0.606393
$130$	−31420.6	−	35052.7i	−0.0143016	−	0.0159548i
$131$		−	1.59684e6i		−	0.710308i	−0.934808	−	0.355154i	$-0.884428\pi$
$131$		−	1.59684e6i		−	0.710308i	0.934808	−	0.355154i	$-0.115572\pi$
$132$	219233.	−	2.00014e6i	0.0953200	−	0.869640i
$133$	−216925.			−0.0922053
$134$	−595824.	+	534085.i	−0.247630	+	0.221971i
$135$		−	804376.i		−	0.326932i
$136$	−447046.	+	320257.i	−0.177720	+	0.127316i
$137$	806762.			0.313750			0.156875	−	0.987618i	$-0.449858\pi$
$137$	806762.			0.313750			0.156875	+	0.987618i	$0.449858\pi$
$138$	−1.16164e6	−	1.29592e6i	−0.442013	−	0.493108i
$139$			2.85023e6i			1.06129i	0.847593	+	0.530647i	$0.178051\pi$
$139$			2.85023e6i			1.06129i	−0.847593	+	0.530647i	$0.821949\pi$
$140$	−1.18358e6	−	129731.i	−0.431334	−	0.0472780i
$141$	448256.			0.159908
$142$	1.74621e6	−	1.56526e6i	0.609860	−	0.546667i
$143$			55887.0i			0.0191119i
$144$	971696.	+	215603.i	0.325419	+	0.0722049i
$145$	1.37161e6			0.449913
$146$	2.34879e6	+	2.62031e6i	0.754720	+	0.841964i
$147$		−	1.71431e6i		−	0.539682i
$148$	276776.	−	2.52513e6i	0.0853776	−	0.778931i
$149$	3.93098e6			1.18834			0.594171	−	0.804339i	$-0.297480\pi$
$149$	3.93098e6			1.18834			0.594171	+	0.804339i	$0.297480\pi$
$150$	−2.73635e6	+	2.45281e6i	−0.810770	+	0.726758i
$151$		−	3.00450e6i		−	0.872653i	−0.899788	−	0.436327i	$-0.856279\pi$
$151$		−	3.00450e6i		−	0.872653i	0.899788	−	0.436327i	$-0.143721\pi$
$152$	−738272.	−	1.03055e6i	−0.210226	−	0.293453i
$153$	260998.			0.0728725
$154$	943535.	+	1.05260e6i	0.258342	+	0.288206i
$155$			8.23302e6i			2.21087i
$156$	−27480.8	−	3012.13i	−0.00723862	−	0.000793415i
$157$	478918.			0.123755			0.0618774	−	0.998084i	$-0.480291\pi$
$157$	478918.			0.123755			0.0618774	+	0.998084i	$0.480291\pi$
$158$	−1.18970e6	+	1.06643e6i	−0.301625	+	0.270371i
$159$		−	2.32822e6i		−	0.579206i
$160$	−3.41182e6	−	6.06437e6i	−0.832965	−	1.48056i
$161$	1.22266e6			0.292973
$162$	−315310.	−	351759.i	−0.0741638	−	0.0827370i
$163$			7.89039e6i			1.82195i	0.412466	+	0.910973i	$0.364668\pi$
$163$			7.89039e6i			1.82195i	−0.412466	+	0.910973i	$0.635332\pi$
$164$	354858.	−	3.23750e6i	0.0804493	−	0.733969i
$165$	6.67612e6			1.48618
$166$	−280299.	+	251254.i	−0.0612769	+	0.0549274i
$167$		−	5.56469e6i		−	1.19479i	−0.801947	−	0.597395i	$-0.796202\pi$
$167$		−	5.56469e6i		−	1.19479i	0.801947	−	0.597395i	$-0.203798\pi$
$168$	−568441.	+	407223.i	−0.119883	+	0.0858825i
$169$	−4.82604e6			−0.999841
$170$	−1.21788e6	−	1.35867e6i	−0.247890	−	0.276546i
$171$			601665.i			0.120328i
$172$	5.31260e6	+	582307.i	1.04405	+	0.114437i
$173$	−4.87420e6			−0.941380			−0.470690	−	0.882299i	$-0.655995\pi$
$173$	−4.87420e6			−0.941380			−0.470690	+	0.882299i	$0.655995\pi$
$174$	599815.	−	537663.i	0.113860	−	0.102062i
$175$		−	2.58165e6i		−	0.481708i
$176$	−1.78945e6	+	8.06484e6i	−0.328233	+	1.47930i
$177$	−5.70707e6			−1.02918
$178$	−2.94958e6	−	3.29054e6i	−0.522997	−	0.583455i
$179$		−	5.92803e6i		−	1.03360i	−0.856107	−	0.516798i	$-0.827124\pi$
$179$		−	5.92803e6i		−	1.03360i	0.856107	−	0.516798i	$-0.172876\pi$
$180$	−359822.	+	3.28279e6i	−0.0616978	+	0.562892i
$181$	−9.61512e6			−1.62151			−0.810753	−	0.585388i	$-0.800942\pi$
$181$	−9.61512e6			−1.62151			−0.810753	+	0.585388i	$0.800942\pi$
$182$	14462.2	−	12963.6i	0.00239894	−	0.00215036i
$183$			3.12818e6i			0.510432i
$184$	4.16114e6	+	5.80851e6i	0.667972	+	0.932419i
$185$	8.42844e6			1.33117
$186$	3.22728e6	+	3.60035e6i	0.501531	+	0.559507i
$187$			2.16622e6i			0.331267i
$188$	−1.82940e6	−	200519.i	−0.275319	−	0.0301773i
$189$	331872.			0.0491570
$190$	3.13206e6	−	2.80752e6i	0.456636	−	0.409319i
$191$		−	8.38482e6i		−	1.20335i	−0.798739	−	0.601677i	$-0.794499\pi$
$191$		−	8.38482e6i		−	1.20335i	0.798739	−	0.601677i	$-0.205501\pi$
$192$	−3.86920e6	−	1.31458e6i	−0.546660	−	0.185730i
$193$	8.36229e6			1.16320			0.581599	−	0.813476i	$-0.302427\pi$
$193$	8.36229e6			1.16320			0.581599	+	0.813476i	$0.302427\pi$
$194$	−1.77440e6	−	1.97952e6i	−0.243023	−	0.271116i
$195$		−	91726.0i		−	0.0123705i
$196$	−766864.	+	6.99638e6i	−0.101847	+	0.929192i
$197$	−9.23855e6			−1.20838			−0.604192	−	0.796838i	$-0.706504\pi$
$197$	−9.23855e6			−1.20838			−0.604192	+	0.796838i	$0.706504\pi$
$198$	2.91951e6	−	2.61699e6i	0.376110	−	0.337137i
$199$			3.22069e6i			0.408686i	0.978899	+	0.204343i	$0.0655057\pi$
$199$			3.22069e6i			0.408686i	−0.978899	+	0.204343i	$0.934494\pi$
$200$	1.22647e7	−	8.78625e6i	1.53309	−	1.09828i
$201$	−1.55915e6			−0.192000
$202$	4.69252e6	+	5.23496e6i	0.569314	+	0.635126i
$203$			565906.i			0.0676482i
$204$	−1.06518e6	−	116752.i	−0.125467	−	0.0137523i
$205$	1.08062e7			1.25433
$206$	4.50468e6	−	4.03791e6i	0.515303	−	0.461907i
$207$		−	3.39118e6i		−	0.382331i
$208$	110806.	+	24586.0i	0.0123133	+	0.00273211i
$209$	−4.99367e6			−0.546993
$210$	−1.54860e6	−	1.72761e6i	−0.167217	−	0.186547i
$211$		−	1.01684e7i		−	1.08245i	−0.840879	−	0.541223i	$-0.817961\pi$
$211$		−	1.01684e7i		−	1.08245i	0.840879	−	0.541223i	$-0.182039\pi$
$212$	−1.04148e6	+	9.50185e6i	−0.109306	+	0.997242i
$213$	4.56947e6			0.472854
$214$	−1.50286e6	+	1.34713e6i	−0.153347	+	0.137458i
$215$			1.77325e7i			1.78425i
$216$	1.12948e6	+	1.57663e6i	0.112077	+	0.156448i
$217$	−3.39681e6			−0.332424
$218$	−1.24774e7	−	1.39198e7i	−1.20436	−	1.34358i
$219$			6.85682e6i			0.652816i
$220$	−2.72463e7	−	2.98643e6i	−2.55882	−	0.280469i
$221$	29762.6			0.00275737
$222$	3.68581e6	−	3.30389e6i	0.336879	−	0.301972i
$223$		−	6.40303e6i		−	0.577392i	−0.957421	−	0.288696i	$-0.906778\pi$
$223$		−	6.40303e6i		−	0.577392i	0.957421	−	0.288696i	$-0.0932217\pi$
$224$	2.50206e6	−	1.40766e6i	0.222615	−	0.125243i
$225$	−7.16048e6			−0.628630
$226$	−4.77534e6	−	5.32736e6i	−0.413694	−	0.461516i
$227$			2.00219e7i			1.71170i	0.517227	+	0.855848i	$0.326964\pi$
$227$			2.00219e7i			1.71170i	−0.517227	+	0.855848i	$0.673036\pi$
$228$	269143.	−	2.45549e6i	0.0227080	−	0.207173i
$229$	6.71834e6			0.559443			0.279721	−	0.960081i	$-0.409758\pi$
$229$	6.71834e6			0.559443			0.279721	+	0.960081i	$0.409758\pi$
$230$	−1.76533e7	+	1.58241e7i	−1.45092	+	1.30057i
$231$			2.75446e6i			0.223460i
$232$	−2.68845e6	+	1.92597e6i	−0.215297	+	0.154236i
$233$	2.42175e7			1.91453			0.957265	−	0.289211i	$-0.0933928\pi$
$233$	2.42175e7			1.91453			0.957265	+	0.289211i	$0.0933928\pi$
$234$	−35955.9	−	40112.3i	−0.00280623	−	0.00313062i
$235$		−	6.10623e6i		−	0.470511i
$236$	2.32915e7	+	2.55295e6i	1.77199	+	0.194225i
$237$	−3.11322e6			−0.233865
$238$	560564.	−	502479.i	0.0415810	−	0.0372724i
$239$		−	1.89310e7i		−	1.38669i	−0.720604	−	0.693347i	$-0.756135\pi$
$239$		−	1.89310e7i		−	1.38669i	0.720604	−	0.693347i	$-0.243865\pi$
$240$	2.93698e6	−	1.32366e7i	0.212455	−	0.957510i
$241$	−7.51718e6			−0.537037			−0.268518	−	0.963275i	$-0.586534\pi$
$241$	−7.51718e6			−0.537037			−0.268518	+	0.963275i	$0.586534\pi$
$242$	1.22606e7	+	1.36779e7i	0.865099	+	0.965103i
$243$		−	920483.i		−	0.0641500i
$244$	1.39933e6	−	1.27666e7i	0.0963274	−	0.878831i
$245$	−2.33527e7			−1.58796
$246$	4.72561e6	−	4.23595e6i	0.317433	−	0.284541i
$247$			68610.1i			0.00455300i
$248$	−1.15605e7	−	1.61373e7i	−0.757917	−	1.05797i
$249$	−733486.			−0.0475110
$250$	1.56954e7	+	1.75098e7i	1.00451	+	1.12063i
$251$			212047.i			0.0134095i	0.999978	+	0.00670474i	$0.00213420\pi$
$251$			212047.i			0.0134095i	−0.999978	+	0.00670474i	$0.997866\pi$
$252$	−1.35442e6	−	148457.i	−0.0846356	−	0.00927679i
$253$	2.81459e7			1.73802
$254$	160477.	−	143849.i	0.00979294	−	0.00877820i
$255$		−	3.55537e6i		−	0.214419i
$256$	1.52028e7	+	7.09581e6i	0.906156	+	0.422944i
$257$	7.20696e6			0.424573			0.212287	−	0.977207i	$-0.431909\pi$
$257$	7.20696e6			0.424573			0.212287	+	0.977207i	$0.431909\pi$
$258$	6.95101e6	+	7.75453e6i	0.404752	+	0.451540i
$259$			3.47744e6i			0.200152i
$260$	−41031.8	+	374348.i	−0.00233454	+	0.0212988i
$261$	1.56960e6			0.0882810
$262$	−9.51246e6	+	8.52678e6i	−0.528919	+	0.474113i
$263$			2.39714e7i			1.31773i	0.752262	+	0.658864i	$0.228963\pi$
$263$			2.39714e7i			1.31773i	−0.752262	+	0.658864i	$0.771037\pi$
$264$	−1.30856e7	+	9.37437e6i	−0.711186	+	0.509484i
$265$	−3.17155e7			−1.70425
$266$	1.15834e6	+	1.29224e6i	0.0615446	+	0.0686591i
$267$		−	8.61069e6i		−	0.452381i
$268$	6.36315e6	+	697456.i	0.330573	+	0.0362337i
$269$	−2.74262e7			−1.40899			−0.704496	−	0.709708i	$-0.748827\pi$
$269$	−2.74262e7			−1.40899			−0.704496	+	0.709708i	$0.748827\pi$
$270$	−4.79172e6	+	4.29520e6i	−0.243445	+	0.218219i
$271$		−	1.88129e7i		−	0.945252i	−0.881263	−	0.472626i	$-0.843306\pi$
$271$		−	1.88129e7i		−	0.945252i	0.881263	−	0.472626i	$-0.156694\pi$
$272$	4.29493e6	+	952971.i	0.213427	+	0.0473558i
$273$	37844.6			0.00186002
$274$	−4.30794e6	−	4.80593e6i	−0.209420	−	0.233629i
$275$		−	5.94303e7i		−	2.85765i
$276$	−1.51698e6	+	1.38399e7i	−0.0721525	+	0.658274i
$277$	3.29233e6			0.154904			0.0774521	−	0.996996i	$-0.475322\pi$
$277$	3.29233e6			0.154904			0.0774521	+	0.996996i	$0.475322\pi$
$278$	1.69790e7	−	1.52196e7i	0.790274	−	0.708386i
$279$			9.42140e6i			0.433813i
$280$	5.54727e6	+	7.74341e6i	0.252700	+	0.352743i
$281$	2.27021e6			0.102317			0.0511585	−	0.998691i	$-0.483709\pi$
$281$	2.27021e6			0.102317			0.0511585	+	0.998691i	$0.483709\pi$
$282$	−2.39360e6	−	2.67029e6i	−0.106734	−	0.119072i
$283$			2.64900e7i			1.16875i	0.811483	+	0.584377i	$0.198661\pi$
$283$			2.64900e7i			1.16875i	−0.811483	+	0.584377i	$0.801339\pi$
$284$	−1.86488e7	−	2.04406e6i	−0.814132	−	0.0892359i
$285$	8.19600e6			0.354052
$286$	332923.	−	298425.i	0.0142313	−	0.0127567i
$287$			4.45846e6i			0.188599i
$288$	−3.90430e6	−	6.93973e6i	−0.163443	−	0.290513i
$289$	−2.29839e7			−0.952206
$290$	−7.32414e6	−	8.17079e6i	−0.300305	−	0.335020i
$291$		−	5.18002e6i		−	0.210209i
$292$	3.06727e6	−	2.79838e7i	0.123198	−	1.12398i
$293$	3.19465e7			1.27005			0.635024	−	0.772493i	$-0.280990\pi$
$293$	3.19465e7			1.27005			0.635024	+	0.772493i	$0.280990\pi$
$294$	−1.02123e7	+	9.15408e6i	−0.401865	+	0.360224i
$295$			7.77427e7i			3.02826i
$296$	−1.65203e7	+	1.18349e7i	−0.637005	+	0.456342i
$297$	7.63978e6			0.291616
$298$	−2.09906e7	−	2.34171e7i	−0.793188	−	0.884879i
$299$		−	386708.i		−	0.0144667i
$300$	2.92231e7	+	3.20310e6i	1.08234	+	0.118633i
$301$	−7.31614e6			−0.268276
$302$	−1.78980e7	+	1.60434e7i	−0.649806	+	0.582474i
$303$			1.36989e7i			0.492444i
$304$	−2.19683e6	+	9.90086e6i	−0.0781945	+	0.352413i
$305$	4.26126e7			1.50189
$306$	−1.39368e6	−	1.55478e6i	−0.0486405	−	0.0542632i
$307$		−	5.64830e7i		−	1.95210i	−0.217540	−	0.976052i	$-0.569803\pi$
$307$		−	5.64830e7i		−	1.95210i	0.217540	−	0.976052i	$-0.430197\pi$
$308$	1.23215e6	−	1.12414e7i	0.0421709	−	0.384740i
$309$	1.17879e7			0.399540
$310$	4.90446e7	−	4.39626e7i	1.64629	−	1.47570i
$311$			8.81143e6i			0.292931i	0.989216	+	0.146465i	$0.0467897\pi$
$311$			8.81143e6i			0.292931i	−0.989216	+	0.146465i	$0.953210\pi$
$312$	128798.	+	179789.i	0.00424079	+	0.00591970i
$313$	1.66184e7			0.541945			0.270972	−	0.962587i	$-0.412655\pi$
$313$	1.66184e7			0.541945			0.270972	+	0.962587i	$0.412655\pi$
$314$	−2.55732e6	−	2.85294e6i	−0.0826032	−	0.0921519i
$315$		−	4.52083e6i		−	0.144639i
$316$	1.27055e7	+	1.39264e6i	0.402654	+	0.0441343i
$317$	−1.21660e7			−0.381917			−0.190958	−	0.981598i	$-0.561160\pi$
$317$	−1.21660e7			−0.381917			−0.190958	+	0.981598i	$0.561160\pi$
$318$	−1.38694e7	+	1.24322e7i	−0.431296	+	0.386605i
$319$			1.30273e7i			0.401312i
$320$	−1.79074e7	+	5.27070e7i	−0.546491	+	1.60849i
$321$	−3.93268e6			−0.118898
$322$	−6.52876e6	−	7.28347e6i	−0.195552	−	0.218158i
$323$			2.65938e6i			0.0789174i
$324$	−411760.	+	3.75664e6i	−0.0121062	+	0.110450i
$325$	−816537.			−0.0237862
$326$	4.70035e7	−	4.21330e7i	1.35668	−	1.21610i
$327$		−	3.64254e7i		−	1.04174i
$328$	−2.11808e7	+	1.51737e7i	−0.600235	+	0.430000i
$329$	2.51933e6			0.0707452
$330$	−3.56491e7	−	3.97701e7i	−0.991990	−	1.10666i
$331$			1.24259e7i			0.342643i	0.985215	+	0.171322i	$0.0548037\pi$
$331$			1.24259e7i			0.342643i	−0.985215	+	0.171322i	$0.945196\pi$
$332$	2.99347e6	+	328111.i	0.0818015	+	0.00896615i
$333$	9.64504e6			0.261199
$334$	−3.31492e7	+	2.97143e7i	−0.889681	+	0.797492i
$335$			2.12391e7i			0.564938i
$336$	5.46121e6	+	1.21175e6i	0.143970	+	0.0319444i
$337$	1.42367e7			0.371980			0.185990	−	0.982552i	$-0.440451\pi$
$337$	1.42367e7			0.371980			0.185990	+	0.982552i	$0.440451\pi$
$338$	2.57701e7	+	2.87490e7i	0.667368	+	0.744514i
$339$		−	1.39407e7i		−	0.357836i
$340$	−1.59042e6	+	1.45100e7i	−0.0404647	+	0.369174i
$341$	−7.81953e7			−1.97205
$342$	3.58416e6	−	3.21277e6i	0.0896002	−	0.0803159i
$343$		−	1.99424e7i		−	0.494190i
$344$	−2.48993e7	−	3.47569e7i	−0.611664	−	0.853818i
$345$	−4.61952e7			−1.12497
$346$	2.60272e7	+	2.90359e7i	0.628347	+	0.700982i
$347$			4.08022e7i			0.976551i	0.872689	+	0.488276i	$0.162374\pi$
$347$			4.08022e7i			0.976551i	−0.872689	+	0.488276i	$0.837626\pi$
$348$	−6.40578e6	−	702129.i	−0.151997	−	0.0166602i
$349$	−5.77566e7			−1.35871			−0.679353	−	0.733812i	$-0.737739\pi$
$349$	−5.77566e7			−1.35871			−0.679353	+	0.733812i	$0.737739\pi$
$350$	−1.53791e7	+	1.37855e7i	−0.358695	+	0.321528i
$351$		−	104966.i		−	0.00242732i
$352$	5.75980e7	−	3.24047e7i	1.32063	−	0.742985i
$353$	−3.96364e7			−0.901094			−0.450547	−	0.892753i	$-0.648771\pi$
$353$	−3.96364e7			−0.901094			−0.450547	+	0.892753i	$0.648771\pi$
$354$	3.04746e7	+	3.39974e7i	0.686954	+	0.766365i
$355$		−	6.22462e7i		−	1.39132i
$356$	−3.85182e6	+	3.51416e7i	−0.0853722	+	0.778882i
$357$	1.46689e6			0.0322398
$358$	−3.53136e7	+	3.16544e7i	−0.769650	+	0.689899i
$359$		−	3.68043e7i		−	0.795454i	−0.917504	−	0.397727i	$-0.869799\pi$
$359$		−	3.68043e7i		−	0.795454i	0.917504	−	0.397727i	$-0.130201\pi$
$360$	2.14771e7	−	1.53859e7i	0.460330	−	0.329774i
$361$	4.09154e7			0.869691
$362$	5.13427e7	+	5.72778e7i	1.08231	+	1.20743i
$363$			3.57924e7i			0.748292i
$364$	−154450.	−	16929.1i	−0.00320246	−	0.000351017i
$365$	9.34049e7			1.92084
$366$	1.86347e7	−	1.67038e7i	0.380084	−	0.340700i
$367$		−	5.99183e7i		−	1.21216i	−0.795402	−	0.606082i	$-0.792740\pi$
$367$		−	5.99183e7i		−	1.21216i	0.795402	−	0.606082i	$-0.207260\pi$
$368$	1.23820e7	−	5.58044e7i	0.248456	−	1.11976i
$369$	1.23660e7			0.246122
$370$	−4.50062e7	−	5.02088e7i	−0.888519	−	0.991230i
$371$		−	1.30853e7i		−	0.256249i
$372$	4.21448e6	−	3.84502e7i	0.0818682	−	0.746914i
$373$	3.96240e7			0.763541			0.381770	−	0.924257i	$-0.375315\pi$
$373$	3.96240e7			0.763541			0.381770	+	0.924257i	$0.375315\pi$
$374$	1.29043e7	−	1.15672e7i	0.246672	−	0.221112i
$375$			4.58197e7i			0.868877i
$376$	8.57414e6	+	1.19686e7i	0.161297	+	0.225154i
$377$	178987.			0.00334039
$378$	−1.77213e6	−	1.97698e6i	−0.0328111	−	0.0366040i
$379$			8.32669e7i			1.52952i	0.644316	+	0.764759i	$0.277142\pi$
$379$			8.32669e7i			1.52952i	−0.644316	+	0.764759i	$0.722858\pi$
$380$	−3.34492e7	−	3.66632e6i	−0.609585	−	0.0668158i
$381$	419938.			0.00759294
$382$	−4.99489e7	+	4.47732e7i	−0.896057	+	0.803208i
$383$		−	3.54095e7i		−	0.630266i	−0.949048	−	0.315133i	$-0.897951\pi$
$383$		−	3.54095e7i		−	0.630266i	0.949048	−	0.315133i	$-0.102049\pi$
$384$	1.28297e7	+	3.00687e7i	0.226581	+	0.531031i
$385$	3.75217e7			0.657508
$386$	−4.46529e7	−	4.98147e7i	−0.776404	−	0.866155i
$387$			2.02921e7i			0.350101i
$388$	−2.31718e6	+	2.11405e7i	−0.0396702	+	0.361926i
$389$	1.96650e7			0.334076			0.167038	−	0.985950i	$-0.446580\pi$
$389$	1.96650e7			0.334076			0.167038	+	0.985950i	$0.446580\pi$
$390$	−546418.	+	489798.i	−0.00921151	+	0.00825702i
$391$		−	1.49891e7i		−	0.250753i
$392$	4.57728e7	−	3.27910e7i	0.759887	−	0.544373i
$393$	−2.48922e7			−0.410097
$394$	4.93320e7	+	5.50346e7i	0.806566	+	0.899803i
$395$			4.24088e7i			0.688121i
$396$	−3.11792e7	−	3.41751e6i	−0.502087	−	0.0550331i
$397$	−3.94391e7			−0.630312			−0.315156	−	0.949040i	$-0.602057\pi$
$397$	−3.94391e7			−0.630312			−0.315156	+	0.949040i	$0.602057\pi$
$398$	1.91858e7	−	1.71978e7i	0.304321	−	0.272787i
$399$			3.38153e6i			0.0532347i
$400$	−1.17831e8	−	2.61447e7i	−1.84111	−	0.408511i
$401$	−6.15521e7			−0.954575			−0.477287	−	0.878747i	$-0.658380\pi$
$401$	−6.15521e7			−0.954575			−0.477287	+	0.878747i	$0.658380\pi$
$402$	8.32556e6	+	9.28797e6i	0.128155	+	0.142969i
$403$			1.07436e6i			0.0164147i
$404$	6.12792e6	−	5.59073e7i	0.0929328	−	0.847860i
$405$	−1.25390e7			−0.188754
$406$	3.37114e6	−	3.02182e6i	0.0503730	−	0.0451534i
$407$			8.00514e7i			1.18737i
$408$	4.99232e6	+	6.96876e6i	0.0735059	+	0.102606i
$409$	5.05211e7			0.738420			0.369210	−	0.929346i	$-0.379628\pi$
$409$	5.05211e7			0.738420			0.369210	+	0.929346i	$0.379628\pi$
$410$	−5.77028e7	−	6.43731e7i	−0.837231	−	0.934013i
$411$		−	1.25762e7i		−	0.181144i
$412$	−4.81082e7	−	5.27307e6i	−0.687903	−	0.0754001i
$413$	−3.20754e7			−0.455325
$414$	−2.02015e7	+	1.81082e7i	−0.284696	+	0.255196i
$415$			9.99168e6i			0.139796i
$416$	−445222.	−	791363.i	−0.00618438	−	0.0109925i
$417$	4.44307e7			0.612738
$418$	2.66652e7	+	2.97476e7i	0.365103	+	0.407309i
$419$		−	4.21905e7i		−	0.573551i	−0.957998	−	0.286776i	$-0.907417\pi$
$419$		−	4.21905e7i		−	0.573551i	0.957998	−	0.286776i	$-0.0925834\pi$
$420$	−2.02230e6	+	1.84502e7i	−0.0272960	+	0.249031i
$421$	1.05717e8			1.41677			0.708384	−	0.705828i	$-0.249425\pi$
$421$	1.05717e8			1.41677			0.708384	+	0.705828i	$0.249425\pi$
$422$	−6.05740e7	+	5.42973e7i	−0.806025	+	0.722505i
$423$		−	6.98762e6i		−	0.0923227i
$424$	6.21644e7	−	4.45337e7i	0.815538	−	0.584240i
$425$	−3.16496e7			−0.412288
$426$	−2.44001e7	−	2.72206e7i	−0.315618	−	0.352103i
$427$			1.75812e7i			0.225822i
$428$	1.60499e7	+	1.75921e6i	0.204711	+	0.0224381i
$429$	871193.			0.0110342
$430$	1.05634e8	−	9.46879e7i	1.32861	−	1.19094i
$431$		−	8.13966e7i		−	1.01666i	−0.861163	−	0.508328i	$-0.830264\pi$
$431$		−	8.13966e7i		−	1.01666i	0.861163	−	0.508328i	$-0.169736\pi$
$432$	3.36091e6	−	1.51472e7i	0.0416875	−	0.187881i
$433$	−9.51282e7			−1.17178			−0.585889	−	0.810391i	$-0.699255\pi$
$433$	−9.51282e7			−1.17178			−0.585889	+	0.810391i	$0.699255\pi$
$434$	1.81383e7	+	2.02350e7i	0.221884	+	0.247534i
$435$		−	2.13814e7i		−	0.259757i
$436$	−1.62942e7	+	1.48658e8i	−0.196595	+	1.79361i
$437$	3.45536e7			0.414046
$438$	4.08465e7	−	3.66140e7i	0.486108	−	0.435738i
$439$		−	4.54537e7i		−	0.537249i	−0.963245	−	0.268625i	$-0.913431\pi$
$439$		−	4.54537e7i		−	0.537249i	0.963245	−	0.268625i	$-0.0865691\pi$
$440$	1.27699e8	+	1.78255e8i	1.49910	+	2.09259i
$441$	−2.67235e7			−0.311586
$442$	−158926.	−	177298.i	−0.00184047	−	0.00205322i
$443$		−	2.61358e7i		−	0.300625i	−0.988639	−	0.150312i	$-0.951972\pi$
$443$		−	2.61358e7i		−	0.300625i	0.988639	−	0.150312i	$-0.0480280\pi$
$444$	−3.93629e7	−	4.31452e6i	−0.449716	−	0.0492928i
$445$	−1.17296e8			−1.33108
$446$	−3.81432e7	+	3.41908e7i	−0.429945	+	0.385394i
$447$		−	6.12778e7i		−	0.686090i
$448$	−2.17460e7	−	7.38831e6i	−0.241850	−	0.0821696i
$449$	1.09326e8			1.20777			0.603887	−	0.797070i	$-0.293618\pi$
$449$	1.09326e8			1.20777			0.603887	+	0.797070i	$0.293618\pi$
$450$	3.82355e7	+	4.26554e7i	0.419594	+	0.468098i
$451$			1.02635e8i			1.11883i
$452$	−6.23608e6	+	5.68940e7i	−0.0675299	+	0.616100i
$453$	−4.68356e7			−0.503827
$454$	1.19271e8	−	1.06913e8i	1.27459	−	1.14251i
$455$		−	515527.i		−	0.00547289i
$456$	−1.60647e7	+	1.15085e7i	−0.169425	+	0.121374i
$457$	−1.24277e8			−1.30209			−0.651046	−	0.759038i	$-0.725670\pi$
$457$	−1.24277e8			−1.30209			−0.651046	+	0.759038i	$0.725670\pi$
$458$	−3.58746e7	−	4.00216e7i	−0.373414	−	0.416579i
$459$		−	4.06856e6i		−	0.0420729i
$460$	1.88530e8	+	2.06645e7i	1.93690	+	0.212301i
$461$	1.15265e8			1.17651			0.588254	−	0.808676i	$-0.299816\pi$
$461$	1.15265e8			1.17651			0.588254	+	0.808676i	$0.299816\pi$
$462$	1.64085e7	−	1.47082e7i	0.166396	−	0.149154i
$463$		−	6.86420e7i		−	0.691588i	−0.938311	−	0.345794i	$-0.887610\pi$
$463$		−	6.86420e7i		−	0.691588i	0.938311	−	0.345794i	$-0.112390\pi$
$464$	2.58289e7	+	5.73100e6i	0.258555	+	0.0573689i
$465$	1.28340e8			1.27645
$466$	−1.29317e8	−	1.44265e8i	−1.27790	−	1.42562i
$467$			1.37951e8i			1.35448i	0.735762	+	0.677240i	$0.236824\pi$
$467$			1.37951e8i			1.35448i	−0.735762	+	0.677240i	$0.763176\pi$
$468$	−46954.5	+	428383.i	−0.000458078	+	0.00417922i
$469$	−8.76289e6			−0.0849432
$470$	−3.63752e7	+	3.26060e7i	−0.350358	+	0.314054i
$471$		−	7.46559e6i		−	0.0714499i
$472$	−1.09164e8	−	1.52381e8i	−1.03813	−	1.44912i
$473$	−1.68419e8			−1.59151
$474$	1.66239e7	+	1.85456e7i	0.156099	+	0.174143i
$475$		−	7.29600e7i		−	0.680776i
$476$	−5.98660e6	−	656183.i	−0.0555085	−	0.00608421i
$477$	−3.62934e7			−0.334405
$478$	−1.12773e8	+	1.01088e8i	−1.03258	+	0.925582i
$479$		−	1.21454e8i		−	1.10511i	−0.833478	−	0.552553i	$-0.813654\pi$
$479$		−	1.21454e8i		−	1.10511i	0.833478	−	0.552553i	$-0.186346\pi$
$480$	−9.45342e7	+	5.31851e7i	−0.854802	+	0.480912i
$481$	1.09986e6			0.00988330
$482$	4.01402e7	+	4.47803e7i	0.358458	+	0.399895i
$483$		−	1.90594e7i		−	0.169148i
$484$	1.60110e7	−	1.46074e8i	0.141216	−	1.28836i
$485$	−7.05631e7			−0.618518
$486$	−5.48337e6	+	4.91519e6i	−0.0477682	+	0.0428185i
$487$			8.98857e7i			0.778222i	0.921191	+	0.389111i	$0.127218\pi$
$487$			8.98857e7i			0.778222i	−0.921191	+	0.389111i	$0.872782\pi$
$488$	−8.35234e7	+	5.98350e7i	−0.718702	+	0.514868i
$489$	1.22999e8			1.05190
$490$	1.24698e8	+	1.39113e8i	1.05992	+	1.18244i
$491$			1.64824e8i			1.39244i	0.717828	+	0.696220i	$0.245136\pi$
$491$			1.64824e8i			1.39244i	−0.717828	+	0.696220i	$0.754864\pi$
$492$	−5.04676e7	−	5.53168e6i	−0.423757	−	0.0464475i
$493$	6.93767e6			0.0578993
$494$	408715.	−	366364.i	0.00339031	−	0.00303901i
$495$		−	1.04070e8i		−	0.858049i
$496$	−3.43999e7	+	1.55036e8i	−0.281911	+	1.27054i
$497$	2.56818e7			0.209197
$498$	3.91667e6	+	4.36942e6i	0.0317124	+	0.0353782i
$499$			2.40882e8i			1.93866i	0.245755	+	0.969332i	$0.420964\pi$
$499$			2.40882e8i			1.93866i	−0.245755	+	0.969332i	$0.579036\pi$
$500$	2.04965e7	−	1.86997e8i	0.163972	−	1.49598i
$501$	−8.67450e7			−0.689813
$502$	1.26318e6	−	1.13229e6i	0.00998513	−	0.00895048i
$503$		−	4.94592e7i		−	0.388636i	−0.980939	−	0.194318i	$-0.937751\pi$
$503$		−	4.94592e7i		−	0.388636i	0.980939	−	0.194318i	$-0.0622494\pi$
$504$	6.34798e6	+	8.86112e6i	0.0495843	+	0.0692145i
$505$	1.86608e8			1.44896
$506$	−1.50293e8	−	1.67667e8i	−1.16008	−	1.29418i
$507$			7.52305e7i			0.577258i
$508$	−1.71383e6	−	187851.i	−0.0130731	−	0.00143292i
$509$	1.18372e8			0.897623			0.448811	−	0.893627i	$-0.351848\pi$
$509$	1.18372e8			0.897623			0.448811	+	0.893627i	$0.351848\pi$
$510$	−2.11795e7	+	1.89849e7i	−0.159664	+	0.143119i
$511$			3.85373e7i			0.288815i
$512$	−3.89095e7	−	1.28454e8i	−0.289898	−	0.957057i
$513$	9.37904e6			0.0694714
$514$	−3.84837e7	−	4.29323e7i	−0.283392	−	0.316151i
$515$		−	1.60576e8i		−	1.17560i
$516$	9.07726e6	−	8.28152e7i	0.0660702	−	0.602783i
$517$	5.79955e7			0.419685
$518$	2.07153e7	−	1.85688e7i	0.149040	−	0.133596i
$519$			7.59812e7i			0.543506i
$520$	2.44912e6	−	1.75451e6i	0.0174181	−	0.0124781i
$521$	1.97661e8			1.39768			0.698841	−	0.715277i	$-0.253699\pi$
$521$	1.97661e8			1.39768			0.698841	+	0.715277i	$0.253699\pi$
$522$	−8.38133e6	−	9.35020e6i	−0.0589253	−	0.0657369i
$523$		−	1.40616e8i		−	0.982948i	−0.870892	−	0.491474i	$-0.836458\pi$
$523$		−	1.40616e8i		−	0.982948i	0.870892	−	0.491474i	$-0.163542\pi$
$524$	1.01589e8	+	1.11350e7i	0.706079	+	0.0773924i
$525$	−4.02440e7			−0.278114
$526$	1.42799e8	−	1.28002e8i	0.981224	−	0.879550i
$527$			4.16429e7i			0.284518i
$528$	1.25718e8	+	2.78948e7i	0.854077	+	0.189505i
$529$	−4.67190e7			−0.315592
$530$	1.69354e8	+	1.88931e8i	1.13754	+	1.26904i
$531$			8.89644e7i			0.594200i
$532$	1.51266e6	−	1.38006e7i	0.0100463	−	0.0916563i
$533$	1.41014e6			0.00931281
$534$	−5.12944e7	+	4.59793e7i	−0.336858	+	0.301953i
$535$			5.35717e7i			0.349843i
$536$	−2.98231e7	−	4.16300e7i	−0.193668	−	0.270341i
$537$	−9.24088e7			−0.596747
$538$	1.46450e8	+	1.63380e8i	0.940466	+	1.04918i
$539$		−	2.21798e8i		−	1.41642i
$540$	5.11736e7	+	5.60907e6i	0.324986	+	0.0356213i
$541$	−1.58829e7			−0.100309			−0.0501543	−	0.998741i	$-0.515971\pi$
$541$	−1.58829e7			−0.100309			−0.0501543	+	0.998741i	$0.515971\pi$
$542$	−1.12070e8	+	1.00457e8i	−0.703866	+	0.630931i
$543$			1.49885e8i			0.936177i
$544$	−1.72571e7	−	3.06738e7i	−0.107194	−	0.190533i
$545$	−4.96193e8			−3.06522
$546$	−202083.	−	225443.i	−0.00124151	−	0.00138503i
$547$		−	2.16901e8i		−	1.32525i	−0.748949	−	0.662627i	$-0.769441\pi$
$547$		−	2.16901e8i		−	1.32525i	0.748949	−	0.662627i	$-0.230559\pi$
$548$	−5.62571e6	+	5.13254e7i	−0.0341850	+	0.311882i
$549$	4.87634e7			0.294698
$550$	−3.54030e8	+	3.17345e8i	−2.12790	+	1.90741i
$551$			1.59930e7i			0.0956040i
$552$	9.05457e7	−	6.48657e7i	0.538332	−	0.385654i
$553$	−1.74972e7			−0.103465
$554$	−1.75803e7	−	1.96126e7i	−0.103395	−	0.115347i
$555$		−	1.31386e8i		−	0.768549i
$556$	−1.81329e8	−	1.98752e7i	−1.05498	−	0.115634i
$557$	9.06128e7			0.524353			0.262177	−	0.965020i	$-0.415560\pi$
$557$	9.06128e7			0.524353			0.262177	+	0.965020i	$0.415560\pi$
$558$	5.61239e7	−	5.03084e7i	0.323032	−	0.289559i
$559$			2.31398e6i			0.0132472i
$560$	1.65067e7	−	7.43936e7i	0.0939930	−	0.423615i
$561$	3.37681e7			0.191257
$562$	−1.21225e7	−	1.35238e7i	−0.0682940	−	0.0761886i
$563$			1.04908e8i			0.587875i	0.955825	+	0.293937i	$0.0949657\pi$
$563$			1.04908e8i			0.587875i	−0.955825	+	0.293937i	$0.905034\pi$
$564$	−3.12577e6	+	2.85176e7i	−0.0174229	+	0.158956i
$565$	−1.89902e8			−1.05289
$566$	1.57803e8	−	1.41451e8i	0.870292	−	0.780113i
$567$		−	5.17338e6i		−	0.0283808i
$568$	8.74039e7	+	1.22007e8i	0.476964	+	0.665792i
$569$	−3.42405e7			−0.185868			−0.0929338	−	0.995672i	$-0.529624\pi$
$569$	−3.42405e7			−0.185868			−0.0929338	+	0.995672i	$0.529624\pi$
$570$	−4.37649e7	−	4.88241e7i	−0.236321	−	0.263639i
$571$		−	2.14565e8i		−	1.15252i	−0.817265	−	0.576262i	$-0.804511\pi$
$571$		−	2.14565e8i		−	1.15252i	0.817265	−	0.576262i	$-0.195489\pi$
$572$	−3.55548e6	−	389711.i	−0.0189981	−	0.00208235i
$573$	−1.30706e8			−0.694757
$574$	2.65593e7	−	2.38072e7i	0.140437	−	0.125885i
$575$			4.11226e8i			2.16310i
$576$	−2.04922e7	+	6.03149e7i	−0.107231	+	0.315615i
$577$	2.92664e8			1.52350			0.761749	−	0.647873i	$-0.224341\pi$
$577$	2.92664e8			1.52350			0.761749	+	0.647873i	$0.224341\pi$
$578$	1.22730e8	+	1.36917e8i	0.635573	+	0.709044i
$579$		−	1.30355e8i		−	0.671572i
$580$	−9.56453e6	+	8.72607e7i	−0.0490207	+	0.447234i
$581$	−4.12240e6			−0.0210195
$582$	−3.08577e7	+	2.76602e7i	−0.156529	+	0.140309i
$583$		−	3.01226e8i		−	1.52015i
$584$	−1.83080e8	+	1.31156e8i	−0.919183	+	0.658490i
$585$	−1.42987e6			−0.00714213
$586$	−1.70588e8	−	1.90307e8i	−0.847724	−	0.945719i
$587$		−	8.46355e7i		−	0.418445i	−0.977868	−	0.209222i	$-0.932907\pi$
$587$		−	8.46355e7i		−	0.418445i	0.977868	−	0.209222i	$-0.0670933\pi$
$588$	1.09063e8	+	1.19542e7i	0.536469	+	0.0588016i
$589$	−9.59971e7			−0.469799
$590$	4.63118e8	−	4.15130e8i	2.25495	−	2.02129i
$591$			1.44015e8i			0.697661i
$592$	1.58716e8	+	3.52165e7i	0.764992	+	0.169739i
$593$	−2.56927e8			−1.23210			−0.616049	−	0.787708i	$-0.711268\pi$
$593$	−2.56927e8			−1.23210			−0.616049	+	0.787708i	$0.711268\pi$
$594$	−4.07949e7	−	4.55107e7i	−0.194646	−	0.217147i
$595$		−	1.99822e7i		−	0.0948620i
$596$	−2.74114e7	+	2.50085e8i	−0.129477	+	1.18127i
$597$	5.02055e7			0.235955
$598$	−2.30365e6	+	2.06494e6i	−0.0107724	+	0.00965617i
$599$			1.68626e8i			0.784594i	0.919839	+	0.392297i	$0.128319\pi$
$599$			1.68626e8i			0.784594i	−0.919839	+	0.392297i	$0.871681\pi$
$600$	−1.36964e8	−	1.91188e8i	−0.634093	−	0.885128i
$601$	3.08169e8			1.41960			0.709799	−	0.704405i	$-0.248786\pi$
$601$	3.08169e8			1.41960			0.709799	+	0.704405i	$0.248786\pi$
$602$	3.90667e7	+	4.35827e7i	0.179068	+	0.199767i
$603$			2.43048e7i			0.110851i
$604$	1.91143e8	+	2.09510e7i	0.867458	+	0.0950809i
$605$	4.87570e8			2.20177
$606$	8.16050e7	−	7.31491e7i	0.366690	−	0.328694i
$607$			2.47849e8i			1.10821i	0.832447	+	0.554104i	$0.186939\pi$
$607$			2.47849e8i			1.10821i	−0.832447	+	0.554104i	$0.813061\pi$
$608$	7.07107e7	−	3.97819e7i	0.314611	−	0.177001i
$609$	8.82160e6			0.0390567
$610$	−2.27542e8	−	2.53846e8i	−1.00247	−	1.11836i
$611$		−	796824.i		−	0.00349333i
$612$	−1.81999e6	+	1.66045e7i	−0.00793990	+	0.0724386i
$613$	1.81086e7			0.0786148			0.0393074	−	0.999227i	$-0.487485\pi$
$613$	1.81086e7			0.0786148			0.0393074	+	0.999227i	$0.487485\pi$
$614$	−3.36473e8	+	3.01608e8i	−1.45360	+	1.30298i
$615$		−	1.68452e8i		−	0.724186i
$616$	−7.35451e7	+	5.26867e7i	−0.314638	+	0.225403i
$617$	9.17308e7			0.390535			0.195267	−	0.980750i	$-0.437443\pi$
$617$	9.17308e7			0.390535			0.195267	+	0.980750i	$0.437443\pi$
$618$	−6.29448e7	−	7.02211e7i	−0.266682	−	0.297510i
$619$			3.68653e8i			1.55434i	0.629291	+	0.777170i	$0.283346\pi$
$619$			3.68653e8i			1.55434i	−0.629291	+	0.777170i	$0.716654\pi$
$620$	−5.23776e8	−	5.74104e7i	−2.19771	−	0.240888i
$621$	−5.28632e7			−0.220739
$622$	5.24902e7	−	4.70512e7i	0.218126	−	0.195524i
$623$		−	4.83946e7i		−	0.200139i
$624$	383258.	−	1.72730e6i	0.00157738	−	0.00710907i
$625$	1.63742e8			0.670688
$626$	−8.87386e7	−	9.89966e7i	−0.361734	−	0.403550i
$627$			7.78437e7i			0.315806i
$628$	−3.33959e6	+	3.04683e7i	−0.0134838	+	0.123018i
$629$	4.26314e7			0.171308
$630$	−2.69308e7	+	2.41403e7i	−0.107703	+	0.0965430i
$631$			1.13782e8i			0.452882i	0.974025	+	0.226441i	$0.0727090\pi$
$631$			1.13782e8i			0.452882i	−0.974025	+	0.226441i	$0.927291\pi$
$632$	−5.95489e7	−	8.31241e7i	−0.235897	−	0.329288i
$633$	−1.58510e8			−0.624951
$634$	6.49637e7	+	7.24734e7i	0.254920	+	0.284388i
$635$		−	5.72047e6i		−	0.0223414i
$636$	1.48119e8	+	1.62351e7i	0.575758	+	0.0631080i
$637$	−3.04738e6			−0.0117898
$638$	7.76043e7	−	6.95630e7i	0.298830	−	0.267865i
$639$		−	7.12311e7i		−	0.273003i
$640$	4.09601e8	−	1.74769e8i	1.56250	−	0.666690i
$641$	−9.87218e7			−0.374834			−0.187417	−	0.982280i	$-0.560012\pi$
$641$	−9.87218e7			−0.374834			−0.187417	+	0.982280i	$0.560012\pi$
$642$	2.09997e7	+	2.34272e7i	0.0793611	+	0.0885351i
$643$		−	2.84353e8i		−	1.06961i	−0.844976	−	0.534804i	$-0.820385\pi$
$643$		−	2.84353e8i		−	1.06961i	0.844976	−	0.534804i	$-0.179615\pi$
$644$	−8.52584e6	+	7.77844e7i	−0.0319212	+	0.291229i
$645$	2.76422e8			1.03013
$646$	1.58421e7	−	1.42005e7i	0.0587645	−	0.0526753i
$647$		−	4.63524e8i		−	1.71143i	−0.517446	−	0.855716i	$-0.673117\pi$
$647$		−	4.63524e8i		−	1.71143i	0.517446	−	0.855716i	$-0.326883\pi$
$648$	2.45772e7	−	1.76068e7i	0.0903250	−	0.0647076i
$649$	−7.38383e8			−2.70114
$650$	4.36014e6	+	4.86416e6i	0.0158767	+	0.0177120i
$651$			5.29510e7i			0.191925i
$652$	−5.01978e8	−	5.50212e7i	−1.81110	−	0.198512i
$653$	−9.73511e7			−0.349624			−0.174812	−	0.984602i	$-0.555932\pi$
$653$	−9.73511e7			−0.349624			−0.174812	+	0.984602i	$0.555932\pi$
$654$	−2.16988e8	+	1.94504e8i	−0.775716	+	0.695337i
$655$			3.39087e8i			1.20666i
$656$	2.03492e8	+	4.51514e7i	0.720834	+	0.159941i
$657$	1.06887e8			0.376903
$658$	−1.34527e7	−	1.50078e7i	−0.0472206	−	0.0526792i
$659$		−	2.18748e7i		−	0.0764343i	−0.999269	−	0.0382171i	$-0.987832\pi$
$659$		−	2.18748e7i		−	0.0764343i	0.999269	−	0.0382171i	$-0.0121679\pi$
$660$	−4.65539e7	+	4.24728e8i	−0.161929	+	1.47734i
$661$	−2.80594e8			−0.971570			−0.485785	−	0.874078i	$-0.661466\pi$
$661$	−2.80594e8			−0.971570			−0.485785	+	0.874078i	$0.661466\pi$
$662$	7.40216e7	−	6.63515e7i	0.255143	−	0.228706i
$663$		−	463953.i		−	0.00159197i
$664$	−1.40300e7	−	1.95844e7i	−0.0479239	−	0.0668968i
$665$	4.60639e7			0.156637
$666$	−5.15025e7	−	5.74561e7i	−0.174343	−	0.194497i
$667$		−	9.01418e7i		−	0.303773i
$668$	3.54020e8	+	3.88037e7i	1.18768	+	0.130180i
$669$	−9.98133e7			−0.333357
$670$	1.26522e8	−	1.13412e8i	0.420671	−	0.377082i
$671$			4.04724e8i			1.33965i
$672$	−2.19433e7	−	3.90033e7i	−0.0723092	−	0.128527i
$673$	2.53293e8			0.830957			0.415478	−	0.909603i	$-0.363614\pi$
$673$	2.53293e8			0.830957			0.415478	+	0.909603i	$0.363614\pi$
$674$	−7.60210e7	−	8.48089e7i	−0.248287	−	0.276988i
$675$			1.11621e8i			0.362939i
$676$	3.36529e7	−	3.07028e8i	0.108939	−	0.993888i
$677$	−1.05570e8			−0.340230			−0.170115	−	0.985424i	$-0.554414\pi$
$677$	−1.05570e8			−0.340230			−0.170115	+	0.985424i	$0.554414\pi$
$678$	−8.30453e7	+	7.44402e7i	−0.266456	+	0.238846i
$679$		−	2.91132e7i		−	0.0929995i
$680$	9.49297e7	−	6.80063e7i	0.301908	−	0.216283i
$681$	3.12110e8			0.988248
$682$	4.17547e8	+	4.65814e8i	1.31629	+	1.46845i
$683$		−	4.47968e8i		−	1.40600i	−0.711190	−	0.703000i	$-0.751843\pi$
$683$		−	4.47968e8i		−	1.40600i	0.711190	−	0.703000i	$-0.248157\pi$
$684$	−3.82773e7	−	4.19553e6i	−0.119612	−	0.0131105i
$685$	−1.71315e8			−0.532996
$686$	−1.18798e8	+	1.06488e8i	−0.367990	+	0.329859i
$687$		−	1.04729e8i		−	0.322994i
$688$	−7.40915e7	+	3.33922e8i	−0.227511	+	1.02537i
$689$	−4.13867e6			−0.0126533
$690$	2.46673e8	+	2.75188e8i	0.750887	+	0.837687i
$691$			1.39132e8i			0.421689i	0.977520	+	0.210844i	$0.0676213\pi$
$691$			1.39132e8i			0.421689i	−0.977520	+	0.210844i	$0.932379\pi$
$692$	3.39887e7	−	3.10091e8i	0.102569	−	0.935775i
$693$	4.29378e7			0.129015
$694$	2.43061e8	−	2.17875e8i	0.727172	−	0.651823i
$695$		−	6.05243e8i		−	1.80292i
$696$	3.00229e7	+	4.19089e7i	0.0890482	+	0.124302i
$697$	5.46581e7			0.161419
$698$	3.08408e8	+	3.44060e8i	0.906901	+	1.01174i
$699$		−	3.77514e8i		−	1.10535i
$700$	1.64242e8	+	1.80024e7i	0.478840	+	0.0524850i
$701$	−8.00717e7			−0.232448			−0.116224	−	0.993223i	$-0.537079\pi$
$701$	−8.00717e7			−0.232448			−0.116224	+	0.993223i	$0.537079\pi$
$702$	−625289.	+	560497.i	−0.00180746	+	0.00162018i
$703$			9.82758e7i			0.282866i
$704$	−5.00599e8	−	1.70081e8i	−1.43473	−	0.487458i
$705$	−9.51867e7			−0.271649
$706$	2.11650e8	+	2.36116e8i	0.601457	+	0.670984i
$707$			7.69916e7i			0.217864i
$708$	3.97965e7	−	3.63078e8i	0.112136	−	1.02306i
$709$	−6.76583e7			−0.189838			−0.0949189	−	0.995485i	$-0.530259\pi$
$709$	−6.76583e7			−0.189838			−0.0949189	+	0.995485i	$0.530259\pi$
$710$	−3.70805e8	+	3.32382e8i	−1.03602	+	0.928672i
$711$			4.85302e7i			0.135022i
$712$	2.29909e8	−	1.64703e8i	0.636965	−	0.456313i
$713$	5.41070e8			1.49274
$714$	−7.83287e6	−	8.73834e6i	−0.0215192	−	0.0240068i
$715$		−	1.18675e7i		−	0.0324670i
$716$	3.77135e8	+	4.13372e7i	1.02744	+	0.112617i
$717$	−2.95106e8			−0.800608
$718$	−2.19245e8	+	1.96527e8i	−0.592321	+	0.530945i
$719$			1.65088e8i			0.444150i	0.975030	+	0.222075i	$0.0712829\pi$
$719$			1.65088e8i			0.444150i	−0.975030	+	0.222075i	$0.928717\pi$
$720$	−2.06338e8	−	4.57830e7i	−0.552819	−	0.122661i
$721$	6.62512e7			0.176762
$722$	−2.18480e8	−	2.43735e8i	−0.580496	−	0.647600i
$723$			1.17181e8i			0.310058i
$724$	6.70480e7	−	6.11704e8i	0.176673	−	1.61185i
$725$	−1.90335e8			−0.499464
$726$	2.13218e8	−	1.91124e8i	0.557202	−	0.499465i
$727$			2.26579e8i			0.589681i	0.955546	+	0.294841i	$0.0952665\pi$
$727$			2.26579e8i			0.589681i	−0.955546	+	0.294841i	$0.904733\pi$
$728$	723884.	+	1.01047e6i	0.00187618	+	0.00261895i
$729$	−1.43489e7			−0.0370370
$730$	−4.98763e8	−	5.56419e8i	−1.28211	−	1.43032i
$731$			8.96916e7i			0.229615i
$732$	−1.99011e8	−	2.18134e7i	−0.507393	−	0.0556147i
$733$	5.77434e8			1.46619			0.733095	−	0.680126i	$-0.238075\pi$
$733$	5.77434e8			1.46619			0.733095	+	0.680126i	$0.238075\pi$
$734$	−3.56937e8	+	3.19951e8i	−0.902617	+	0.809088i
$735$			3.64032e8i			0.916807i
$736$	−3.98548e8	+	2.24223e8i	−0.999648	+	0.562403i
$737$	−2.01724e8			−0.503912
$738$	−6.60319e7	−	7.36650e7i	−0.164280	−	0.183270i
$739$			3.71248e8i			0.919879i	0.887950	+	0.459940i	$0.152129\pi$
$739$			3.71248e8i			0.919879i	−0.887950	+	0.459940i	$0.847871\pi$
$740$	−5.87731e7	+	5.36209e8i	−0.145039	+	1.32324i
$741$	1.06953e6			0.00262867
$742$	−7.79498e7	+	6.98727e7i	−0.190811	+	0.171039i
$743$			5.52868e8i			1.34789i	0.738780	+	0.673946i	$0.235402\pi$
$743$			5.52868e8i			1.34789i	−0.738780	+	0.673946i	$0.764598\pi$
$744$	−2.51555e8	+	1.80211e8i	−0.610821	+	0.437584i
$745$	−8.34738e8			−2.01874
$746$	−2.11584e8	−	2.36043e8i	−0.509644	−	0.568557i
$747$			1.14339e7i			0.0274305i
$748$	−1.37813e8	−	1.51055e7i	−0.329295	−	0.0360936i
$749$	−2.21028e7			−0.0526019
$750$	2.72951e8	−	2.44668e8i	0.646994	−	0.579953i
$751$		−	6.10327e8i		−	1.44093i	−0.693491	−	0.720465i	$-0.743928\pi$
$751$		−	6.10327e8i		−	1.44093i	0.693491	−	0.720465i	$-0.256072\pi$
$752$	2.55136e7	−	1.14987e8i	0.0599954	−	0.270392i
$753$	3.30549e6			0.00774196
$754$	−955755.	−	1.06624e6i	−0.00222963	−	0.00248737i
$755$			6.38003e8i			1.48246i
$756$	−2.31421e6	+	2.11134e7i	−0.00535596	+	0.0488644i
$757$	6.28508e8			1.44885			0.724424	−	0.689354i	$-0.242106\pi$
$757$	6.28508e8			1.44885			0.724424	+	0.689354i	$0.242106\pi$
$758$	4.96026e8	−	4.44628e8i	1.13893	−	1.02091i
$759$		−	4.38752e8i		−	1.00344i
$760$	1.56771e8	+	2.18836e8i	0.357129	+	0.498515i
$761$	4.85991e8			1.10274			0.551372	−	0.834260i	$-0.314105\pi$
$761$	4.85991e8			1.10274			0.551372	+	0.834260i	$0.314105\pi$
$762$	−2.24238e6	−	2.50160e6i	−0.00506809	−	0.00565396i
$763$		−	2.04721e8i		−	0.460881i
$764$	5.33434e8	+	5.84689e7i	1.19619	+	0.131113i
$765$	−5.54227e7			−0.123795
$766$	−2.10937e8	+	1.89080e8i	−0.469317	+	0.420686i
$767$			1.01449e7i			0.0224835i
$768$	1.10613e8	−	2.36988e8i	0.244187	−	0.523169i
$769$	2.04116e8			0.448846			0.224423	−	0.974492i	$-0.427950\pi$
$769$	2.04116e8			0.448846			0.224423	+	0.974492i	$0.427950\pi$
$770$	−2.00358e8	−	2.23519e8i	−0.438870	−	0.489602i
$771$		−	1.12345e8i		−	0.245128i
$772$	−5.83118e7	+	5.32001e8i	−0.126737	+	1.15627i
$773$	−1.62938e8			−0.352764			−0.176382	−	0.984322i	$-0.556439\pi$
$773$	−1.62938e8			−0.352764			−0.176382	+	0.984322i	$0.556439\pi$
$774$	1.20881e8	−	1.08356e8i	0.260697	−	0.233684i
$775$		−	1.14247e9i		−	2.45437i
$776$	1.38308e8	−	9.90822e7i	0.295981	−	0.212036i
$777$	5.42079e7			0.115558
$778$	−1.05007e8	−	1.17146e8i	−0.222987	−	0.248764i
$779$			1.26000e8i			0.266538i
$780$	5.83551e6	+	639623.i	0.0122969	+	0.00134785i
$781$	5.91200e8			1.24103
$782$	−8.92910e7	+	8.00388e7i	−0.186719	+	0.167371i
$783$		−	2.44676e7i		−	0.0509690i
$784$	−4.39755e8	−	9.75742e7i	−0.912563	−	0.202482i
$785$	−1.01698e8			−0.210234
$786$	1.32919e8	+	1.48285e8i	0.273729	+	0.305371i
$787$			5.35030e8i			1.09763i	0.835945	+	0.548813i	$0.184920\pi$
$787$			5.35030e8i			1.09763i	−0.835945	+	0.548813i	$0.815080\pi$
$788$	6.44222e7	−	5.87747e8i	0.131661	−	1.20119i
$789$	3.73677e8			0.760791
$790$	2.52632e8	−	2.26454e8i	0.512397	−	0.459303i
$791$		−	7.83505e7i		−	0.158311i
$792$	1.46132e8	+	2.03985e8i	0.294151	+	0.410604i
$793$	5.56067e6			0.0111508
$794$	2.10597e8	+	2.34941e8i	0.420717	+	0.469351i
$795$			4.94395e8i			0.983950i
$796$	−2.04897e8	−	2.24585e7i	−0.406252	−	0.0445288i
$797$	−6.24633e8			−1.23381			−0.616907	−	0.787036i	$-0.711615\pi$
$797$	−6.24633e8			−1.23381			−0.616907	+	0.787036i	$0.711615\pi$
$798$	2.01440e7	−	1.80567e7i	0.0396403	−	0.0355328i
$799$		−	3.08855e7i		−	0.0605500i
$800$	4.73449e8	+	8.41535e8i	0.924704	+	1.64362i
$801$	−1.34227e8			−0.261182
$802$	3.28676e8	+	3.66670e8i	0.637154	+	0.710808i
$803$			8.87138e8i			1.71334i
$804$	1.08723e7	−	9.91917e7i	0.0209195	−	0.190857i
$805$	−2.59631e8			−0.497701
$806$	6.40002e6	−	5.73685e6i	0.0122229	−	0.0109564i
$807$			4.27532e8i			0.813482i
$808$	−3.65765e8	+	2.62029e8i	−0.693375	+	0.496724i
$809$	3.14376e8			0.593751			0.296875	−	0.954916i	$-0.404055\pi$
$809$	3.14376e8			0.593751			0.296875	+	0.954916i	$0.404055\pi$
$810$	6.69556e7	+	7.46955e7i	0.125989	+	0.140553i
$811$		−	8.24389e8i		−	1.54550i	−0.634710	−	0.772751i	$-0.718880\pi$
$811$		−	8.24389e8i		−	1.54550i	0.634710	−	0.772751i	$-0.281120\pi$
$812$	−3.60023e7	−	3.94617e6i	−0.0672454	−	0.00737068i
$813$	−2.93264e8			−0.545741
$814$	4.76871e8	−	4.27458e8i	0.884154	−	0.792539i
$815$		−	1.67551e9i		−	3.09510i
$816$	1.48553e7	−	6.69513e7i	0.0273409	−	0.123222i
$817$	−2.06761e8			−0.379143
$818$	−2.69773e8	−	3.00958e8i	−0.492876	−	0.549852i
$819$		−	589940.i		−	0.00107388i
$820$	−7.53536e7	+	6.87479e8i	−0.136667	+	1.24686i
$821$	−8.10319e8			−1.46429			−0.732144	−	0.681150i	$-0.761480\pi$
$821$	−8.10319e8			−1.46429			−0.732144	+	0.681150i	$0.761480\pi$
$822$	−7.49171e7	+	6.71542e7i	−0.134886	+	0.120909i
$823$		−	4.13830e7i		−	0.0742374i	−0.999311	−	0.0371187i	$-0.988182\pi$
$823$		−	4.13830e7i		−	0.0742374i	0.999311	−	0.0371187i	$-0.0118180\pi$
$824$	2.25476e8	+	3.14740e8i	0.403012	+	0.562563i
$825$	−9.26426e8			−1.64987
$826$	1.71276e8	+	1.91075e8i	0.303918	+	0.339050i
$827$		−	4.96913e8i		−	0.878545i	−0.898354	−	0.439273i	$-0.855236\pi$
$827$		−	4.96913e8i		−	0.878545i	0.898354	−	0.439273i	$-0.144764\pi$
$828$	2.15743e8	+	2.36473e7i	0.380055	+	0.0416573i
$829$	−4.12898e8			−0.724736			−0.362368	−	0.932035i	$-0.618032\pi$
$829$	−4.12898e8			−0.724736			−0.362368	+	0.932035i	$0.618032\pi$
$830$	5.95211e7	−	5.33535e7i	0.104097	−	0.0933102i
$831$		−	5.13223e7i		−	0.0894340i
$832$	−2.33681e6	+	6.87793e6i	−0.00405745	+	0.0119423i
$833$	−1.18119e8			−0.204354
$834$	−2.37251e8	−	2.64676e8i	−0.408987	−	0.456265i
$835$			1.18166e9i			2.02970i
$836$	3.48218e7	−	3.17692e8i	0.0595982	−	0.543736i
$837$	1.46865e8			0.250462
$838$	−2.51331e8	+	2.25288e8i	−0.427085	+	0.382831i
$839$		−	2.94684e8i		−	0.498966i	−0.968379	−	0.249483i	$-0.919739\pi$
$839$		−	2.94684e8i		−	0.498966i	0.968379	−	0.249483i	$-0.0802606\pi$
$840$	1.20708e8	−	8.64734e7i	0.203656	−	0.145896i
$841$	−5.53101e8			−0.929858
$842$	−5.64507e8	−	6.29763e8i	−0.945656	−	1.05497i
$843$		−	3.53891e7i		−	0.0590727i
$844$	6.46905e8	+	7.09064e7i	1.07600	+	0.117939i
$845$	1.02480e9			1.69852
$846$	−4.16257e7	+	3.73125e7i	−0.0687465	+	0.0616230i
$847$			2.01164e8i			0.331054i
$848$	−5.97235e8	−	1.32516e8i	−0.979395	−	0.217311i
$849$	4.12938e8			0.674780
$850$	1.69002e8	+	1.88538e8i	0.275192	+	0.307003i
$851$		−	5.53913e8i		−	0.898779i
$852$	−3.18638e7	+	2.90705e8i	−0.0515204	+	0.470039i
$853$	1.00716e9			1.62274			0.811371	−	0.584532i	$-0.198722\pi$
$853$	1.00716e9			1.62274			0.811371	+	0.584532i	$0.198722\pi$
$854$	1.04733e8	−	9.38803e7i	0.168154	−	0.150730i
$855$		−	1.27763e8i		−	0.204412i
$856$	−7.52234e7	−	1.05004e8i	−0.119931	−	0.167411i
$857$	5.70733e6			0.00906757			0.00453378	−	0.999990i	$-0.498557\pi$
$857$	5.70733e6			0.00906757			0.00453378	+	0.999990i	$0.498557\pi$
$858$	−4.65199e6	−	5.18975e6i	−0.00736507	−	0.00821645i
$859$			1.59005e8i			0.250860i	0.992102	+	0.125430i	$0.0400311\pi$
$859$			1.59005e8i			0.250860i	−0.992102	+	0.125430i	$0.959969\pi$
$860$	−1.12812e9	−	1.23652e8i	−1.77362	−	0.194404i
$861$	6.95004e7			0.108888
$862$	−4.84885e8	+	4.34641e8i	−0.757036	+	0.678592i
$863$			1.00726e9i			1.56715i	0.621299	+	0.783574i	$0.286605\pi$
$863$			1.00726e9i			1.56715i	−0.621299	+	0.783574i	$0.713395\pi$
$864$	−1.08180e8	+	6.08620e7i	−0.167728	+	0.0943637i
$865$	1.03503e9			1.59921
$866$	5.07965e8	+	5.66685e8i	0.782132	+	0.872545i
$867$			3.58284e8i			0.549757i
$868$	2.36866e7	−	2.16102e8i	0.0362196	−	0.330445i
$869$	−4.02789e8			−0.613788
$870$	−1.27370e8	+	1.14172e8i	−0.193424	+	0.173381i
$871$			2.77156e6i			0.00419441i
$872$	9.72571e8	−	6.96736e8i	1.46680	−	1.05080i
$873$	−8.07485e7			−0.121364
$874$	−1.84509e8	−	2.05838e8i	−0.276365	−	0.308312i
$875$			2.57520e8i			0.384403i
$876$	−4.36224e8	−	4.78139e7i	−0.648929	−	0.0711283i
$877$	−9.30502e8			−1.37949			−0.689745	−	0.724053i	$-0.742277\pi$
$877$	−9.30502e8			−1.37949			−0.689745	+	0.724053i	$0.742277\pi$
$878$	−2.70771e8	+	2.42713e8i	−0.400053	+	0.358600i
$879$		−	4.97996e8i		−	0.733262i
$880$	3.79988e8	−	1.71256e9i	0.557598	−	2.51303i
$881$	−3.18226e8			−0.465381			−0.232690	−	0.972551i	$-0.574753\pi$
$881$	−3.18226e8			−0.465381			−0.232690	+	0.972551i	$0.574753\pi$
$882$	1.42698e8	+	1.59193e8i	0.207975	+	0.232017i
$883$		−	5.91320e8i		−	0.858895i	−0.903092	−	0.429448i	$-0.858708\pi$
$883$		−	5.91320e8i		−	0.858895i	0.903092	−	0.429448i	$-0.141292\pi$
$884$	−207540.	+	1.89347e6i	−0.000300432	+	0.00274095i
$885$	1.21189e9			1.74837
$886$	−1.55693e8	+	1.39560e8i	−0.223855	+	0.200659i
$887$			2.51524e8i			0.360420i	0.983628	+	0.180210i	$0.0576777\pi$
$887$			2.51524e8i			0.360420i	−0.983628	+	0.180210i	$0.942322\pi$
$888$	1.84488e8	+	2.57526e8i	0.263469	+	0.367775i
$889$	2.36017e6			0.00335922
$890$	6.26339e8	+	6.98742e8i	0.888463	+	0.991167i
$891$		−	1.19092e8i		−	0.168365i
$892$	4.07354e8	+	4.46495e7i	0.573954	+	0.0629104i
$893$	7.11987e7			0.0999810
$894$	−3.65036e8	+	3.27211e8i	−0.510885	+	0.457947i
$895$			1.25881e9i			1.75586i
$896$	7.21067e7	+	1.68995e8i	0.100242	+	0.234935i
$897$	−6.02819e6			−0.00835237
$898$	−5.83780e8	−	6.51264e8i	−0.806159	−	0.899349i
$899$			2.50433e8i			0.344677i
$900$	4.99314e7	−	4.55543e8i	0.0684930	−	0.624887i
$901$	−1.60418e8			−0.219320
$902$	6.11401e8	−	5.48048e8i	0.833118	−	0.746791i
$903$			1.14047e8i			0.154890i
$904$	3.72221e8	−	2.66654e8i	0.503843	−	0.360946i
$905$	2.04176e9			2.75460
$906$	2.50092e8	+	2.79002e8i	0.336291	+	0.375166i
$907$		−	7.02548e8i		−	0.941574i	−0.882247	−	0.470787i	$-0.843970\pi$
$907$		−	7.02548e8i		−	0.941574i	0.882247	−	0.470787i	$-0.156030\pi$
$908$	−1.27377e9	−	1.39616e8i	−1.70151	−	0.186500i
$909$	2.13544e8			0.284313
$910$	−3.07102e6	+	2.75281e6i	−0.00407530	+	0.00365302i
$911$			5.39123e8i			0.713071i	0.934282	+	0.356535i	$0.116042\pi$
$911$			5.39123e8i			0.713071i	−0.934282	+	0.356535i	$0.883958\pi$
$912$	1.54339e8	+	3.42452e7i	0.203466	+	0.0451456i
$913$	−9.48987e7			−0.124695
$914$	6.63613e8	+	7.40326e8i	0.869114	+	0.969581i
$915$		−	6.64264e8i		−	0.867117i
$916$	−4.68483e7	+	4.27414e8i	−0.0609547	+	0.556112i
$917$	−1.39902e8			−0.181432
$918$	−2.42367e7	+	2.17253e7i	−0.0313289	+	0.0280826i
$919$			9.44553e8i			1.21697i	0.793565	+	0.608485i	$0.208222\pi$
$919$			9.44553e8i			1.21697i	−0.793565	+	0.608485i	$0.791778\pi$
$920$	−8.83612e8	−	1.23343e9i	−1.13474	−	1.58398i
$921$	−8.80483e8			−1.12705
$922$	−6.15491e8	−	6.86641e8i	−0.785288	−	0.876066i
$923$		−	8.12274e6i		−	0.0103299i
$924$	−1.75236e8	−	1.92074e7i	−0.222130	−	0.0243474i
$925$	−1.16959e9			−1.47778
$926$	−4.08905e8	+	3.66534e8i	−0.514979	+	0.461617i
$927$		−	1.83755e8i		−	0.230674i
$928$	−1.03781e8	−	1.84467e8i	−0.129860	−	0.230821i
$929$	2.39618e8			0.298864			0.149432	−	0.988772i	$-0.452256\pi$
$929$	2.39618e8			0.298864			0.149432	+	0.988772i	$0.452256\pi$
$930$	−6.85310e8	−	7.64530e8i	−0.851997	−	0.950486i
$931$		−	2.72292e8i		−	0.337432i
$932$	−1.68874e8	+	1.54070e9i	−0.208600	+	1.90313i
$933$	1.37357e8			0.169124
$934$	8.21780e8	−	7.36628e8i	1.00859	−	0.904081i
$935$		−	4.59995e8i		−	0.562753i
$936$	2.80263e6	−	2.00777e6i	0.00341774	−	0.00244842i
$937$	−6.62445e8			−0.805251			−0.402625	−	0.915365i	$-0.631902\pi$
$937$	−6.62445e8			−0.805251			−0.402625	+	0.915365i	$0.631902\pi$
$938$	4.67920e7	+	5.22011e7i	0.0566974	+	0.0632515i
$939$		−	2.59055e8i		−	0.312892i
$940$	3.88472e8	+	4.25799e7i	0.467709	+	0.0512650i
$941$	−2.80539e8			−0.336686			−0.168343	−	0.985728i	$-0.553842\pi$
$941$	−2.80539e8			−0.336686			−0.168343	+	0.985728i	$0.553842\pi$
$942$	−4.44730e7	+	3.98647e7i	−0.0532039	+	0.0476910i
$943$		−	7.10177e8i		−	0.846899i
$944$	−3.24832e8	+	1.46398e9i	−0.386138	+	1.74028i
$945$	−7.04727e7			−0.0835075
$946$	8.99324e8	+	1.00328e9i	1.06229	+	1.18509i
$947$		−	1.29621e9i		−	1.52625i	−0.646254	−	0.763123i	$-0.723665\pi$
$947$		−	1.29621e9i		−	1.52625i	0.646254	−	0.763123i	$-0.276335\pi$
$948$	2.17090e7	−	1.98060e8i	0.0254810	−	0.232472i
$949$	1.21888e7			0.0142614
$950$	−4.34627e8	+	3.89591e8i	−0.506928	+	0.454400i
$951$			1.89649e8i			0.220500i
$952$	2.80583e7	+	3.91664e7i	0.0325200	+	0.0453945i
$953$	−8.23943e8			−0.951959			−0.475980	−	0.879456i	$-0.657906\pi$
$953$	−8.23943e8			−0.951959			−0.475980	+	0.879456i	$0.657906\pi$
$954$	1.93799e8	+	2.16202e8i	0.223207	+	0.249009i
$955$			1.78051e9i			2.04425i
$956$	1.20437e9	+	1.32010e8i	1.37844	+	0.151089i
$957$	2.03075e8			0.231697
$958$	−7.23507e8	+	6.48538e8i	−0.822899	+	0.737630i
$959$		−	7.06818e7i		−	0.0801404i
$960$	8.21620e8	+	2.79149e8i	0.928661	+	0.315517i
$961$	−6.15703e8			−0.693747
$962$	−5.87302e6	−	6.55193e6i	−0.00659685	−	0.00735943i
$963$			6.13044e7i			0.0686456i
$964$	5.24187e7	−	4.78235e8i	0.0585134	−	0.533839i
$965$	−1.77572e9			−1.97603
$966$	−1.13538e8	+	1.01773e8i	−0.125953	+	0.112902i
$967$		−	1.24892e9i		−	1.38120i	−0.723236	−	0.690600i	$-0.757346\pi$
$967$		−	1.24892e9i		−	1.38120i	0.723236	−	0.690600i	$-0.242654\pi$
$968$	−9.55670e8	+	6.84629e8i	−1.05362	+	0.754795i
$969$	4.14556e7			0.0455630
$970$	3.76793e8	+	4.20349e8i	0.412845	+	0.460569i
$971$			3.08066e7i			0.0336501i	0.999858	+	0.0168251i	$0.00535583\pi$
$971$			3.08066e7i			0.0336501i	−0.999858	+	0.0168251i	$0.994644\pi$
$972$	5.85602e7	+	6.41870e6i	0.0637681	+	0.00698954i
$973$	2.49713e8			0.271084
$974$	5.35455e8	−	4.79971e8i	0.579490	−	0.519443i
$975$			1.27285e7i			0.0137330i
$976$	8.02439e8	+	1.78048e8i	0.863103	+	0.191508i
$977$	7.02342e8			0.753121			0.376561	−	0.926392i	$-0.377107\pi$
$977$	7.02342e8			0.753121			0.376561	+	0.926392i	$0.377107\pi$
$978$	−6.56789e8	−	7.32712e8i	−0.702117	−	0.783280i
$979$		−	1.11405e9i		−	1.18729i
$980$	1.62843e8	−	1.48567e9i	0.173017	−	1.57850i
$981$	−5.67815e8			−0.601451
$982$	9.81868e8	−	8.80127e8i	1.03686	−	0.929418i
$983$			1.21645e9i			1.28066i	0.768100	+	0.640330i	$0.221202\pi$
$983$			1.21645e9i			1.28066i	−0.768100	+	0.640330i	$0.778798\pi$
$984$	2.36534e8	+	3.30177e8i	0.248261	+	0.346546i
$985$	1.96180e9			2.05279
$986$	−3.70458e7	−	4.13282e7i	−0.0386463	−	0.0431137i
$987$		−	3.92725e7i		−	0.0408448i
$988$	−4.36491e6	−	478431.i	−0.00452589	−	0.000496077i
$989$	1.16537e9			1.20469
$990$	−6.19954e8	+	5.55715e8i	−0.638931	+	0.572725i
$991$			5.87815e8i			0.603976i	0.953312	+	0.301988i	$0.0976502\pi$
$991$			5.87815e8i			0.603976i	−0.953312	+	0.301988i	$0.902350\pi$
$992$	1.10725e9	−	6.22940e8i	1.13425	−	0.638133i
$993$	1.93700e8			0.197825
$994$	−1.37135e8	−	1.52988e8i	−0.139634	−	0.155775i
$995$		−	6.83909e8i		−	0.694271i
$996$	5.11474e6	−	4.66636e7i	0.00517661	−	0.0472281i
$997$	9.61156e8			0.969859			0.484929	−	0.874553i	$-0.338845\pi$
$997$	9.61156e8			0.969859			0.484929	+	0.874553i	$0.338845\pi$
$998$	1.43495e9	−	1.28626e9i	1.44359	−	1.29401i
$999$		−	1.50351e8i		−	0.150803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.7.d.a.7.3	✓	6
3.2	odd	2		36.7.d.e.19.4		6
4.3	odd	2	inner	12.7.d.a.7.4	yes	6
8.3	odd	2		192.7.g.e.127.3		6
8.5	even	2		192.7.g.e.127.6		6
12.11	even	2		36.7.d.e.19.3		6
16.3	odd	4		768.7.b.h.127.6		12
16.5	even	4		768.7.b.h.127.1		12
16.11	odd	4		768.7.b.h.127.7		12
16.13	even	4		768.7.b.h.127.12		12
24.5	odd	2		576.7.g.p.127.1		6
24.11	even	2		576.7.g.p.127.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.7.d.a.7.3	✓	6	1.1	even	1	trivial
12.7.d.a.7.4	yes	6	4.3	odd	2	inner
36.7.d.e.19.3		6	12.11	even	2
36.7.d.e.19.4		6	3.2	odd	2
192.7.g.e.127.3		6	8.3	odd	2
192.7.g.e.127.6		6	8.5	even	2
576.7.g.p.127.1		6	24.5	odd	2
576.7.g.p.127.2		6	24.11	even	2
768.7.b.h.127.1		12	16.5	even	4
768.7.b.h.127.6		12	16.3	odd	4
768.7.b.h.127.7		12	16.11	odd	4
768.7.b.h.127.12		12	16.13	even	4

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.33979 - 5.95706i) q^{2} -15.5885i q^{3} +(-6.97319 + 63.6190i) q^{4} -212.349 q^{5} +(-92.8614 + 83.2392i) q^{6} -87.6116i q^{7} +(416.218 - 298.173i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(-5.33979 - 5.95706i) q^{2} -15.5885i q^{3} +(-6.97319 + 63.6190i) q^{4} -212.349 q^{5} +(-92.8614 + 83.2392i) q^{6} -87.6116i q^{7} +(416.218 - 298.173i) q^{8} -243.000 q^{9} +(1133.90 + 1264.98i) q^{10} -2016.84i q^{11} +(991.722 + 108.701i) q^{12} -27.7102 q^{13} +(-521.908 + 467.828i) q^{14} +3310.19i q^{15} +(-3998.75 - 887.254i) q^{16} -1074.07 q^{17} +(1297.57 + 1447.57i) q^{18} -2475.99i q^{19} +(1480.75 - 13509.4i) q^{20} -1365.73 q^{21} +(-12014.4 + 10769.5i) q^{22} +13955.5i q^{23} +(-4648.05 - 6488.19i) q^{24} +29467.0 q^{25} +(147.967 + 165.071i) q^{26} +3788.00i q^{27} +(5573.76 + 610.932i) q^{28} -6459.25 q^{29} +(19719.0 - 17675.7i) q^{30} -38771.2i q^{31} +(16067.1 + 28558.6i) q^{32} -31439.4 q^{33} +(5735.30 + 6398.29i) q^{34} +18604.2i q^{35} +(1694.48 - 15459.4i) q^{36} -39691.5 q^{37} +(-14749.6 + 13221.3i) q^{38} +431.959i q^{39} +(-88383.3 + 63316.6i) q^{40} -50888.9 q^{41} +(7292.72 + 8135.74i) q^{42} -83506.5i q^{43} +(128309. + 14063.8i) q^{44} +51600.8 q^{45} +(83133.5 - 74519.3i) q^{46} +28755.6i q^{47} +(-13830.9 + 62334.3i) q^{48} +109973. q^{49} +(-157348. - 175537. i) q^{50} +16743.1i q^{51} +(193.228 - 1762.89i) q^{52} +149356. q^{53} +(22565.3 - 20227.1i) q^{54} +428274. i q^{55} +(-26123.4 - 36465.5i) q^{56} -38596.9 q^{57} +(34491.1 + 38478.2i) q^{58} -366109. i q^{59} +(-210591. - 23082.6i) q^{60} -200673. q^{61} +(-230962. + 207030. i) q^{62} +21289.6i q^{63} +(84330.2 - 248209. i) q^{64} +5884.23 q^{65} +(167880. + 187287. i) q^{66} -100020. i q^{67} +(7489.68 - 68331.1i) q^{68} +217544. q^{69} +(110827. - 99342.7i) q^{70} +293132. i q^{71} +(-101141. + 72455.9i) q^{72} -439866. q^{73} +(211945. + 236445. i) q^{74} -459345. i q^{75} +(157520. + 17265.5i) q^{76} -176699. q^{77} +(2573.21 - 2306.57i) q^{78} -199713. i q^{79} +(849130. + 188407. i) q^{80} +59049.0 q^{81} +(271736. + 303148. i) q^{82} -47053.2i q^{83} +(9523.49 - 86886.4i) q^{84} +228077. q^{85} +(-497453. + 445908. i) q^{86} +100690. i q^{87} +(-601366. - 839444. i) q^{88} +552376. q^{89} +(-275537. - 307389. i) q^{90} +2427.74i q^{91} +(-887832. - 97314.1i) q^{92} -604383. q^{93} +(171299. - 153549. i) q^{94} +525773. i q^{95} +(445184. - 250461. i) q^{96} +332298. q^{97} +(-587234. - 655117. i) q^{98} +490092. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9}+O(q^{10}) \) 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9	\( 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9} + 84 q^{10} - 972 q^{12} - 3348 q^{13} + 4776 q^{14} - 9744 q^{16} + 12220 q^{17} + 2430 q^{18} + 17608 q^{20} - 9720 q^{21} - 13512 q^{22} - 7776 q^{24} + 56418 q^{25} - 59252 q^{26} - 17808 q^{28} - 84860 q^{29} + 57348 q^{30} + 61280 q^{32} + 4536 q^{33} + 109404 q^{34} - 37908 q^{36} + 20796 q^{37} - 128088 q^{38} - 195552 q^{40} - 65252 q^{41} + 210600 q^{42} + 445008 q^{44} + 10692 q^{45} + 81120 q^{46} - 276048 q^{48} - 111546 q^{49} - 743118 q^{50} - 179592 q^{52} + 470308 q^{53} + 39366 q^{54} + 793728 q^{56} - 204120 q^{57} + 529860 q^{58} - 723816 q^{60} + 12924 q^{61} - 513384 q^{62} - 642432 q^{64} + 321512 q^{65} + 771768 q^{66} + 690328 q^{68} + 541728 q^{69} + 938928 q^{70} - 276048 q^{72} - 1283412 q^{73} - 1522916 q^{74} + 67824 q^{76} - 1487328 q^{77} + 396252 q^{78} + 1272352 q^{80} + 354294 q^{81} + 240444 q^{82} - 143856 q^{84} + 814920 q^{85} - 1154568 q^{86} + 489600 q^{88} + 730924 q^{89} - 20412 q^{90} - 1338816 q^{92} - 83592 q^{93} - 390288 q^{94} + 624672 q^{96} + 3249420 q^{97} + 1604918 q^{98}+O(q^{100}) \) 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9 + 84 * q^10 - 972 * q^12 - 3348 * q^13 + 4776 * q^14 - 9744 * q^16 + 12220 * q^17 + 2430 * q^18 + 17608 * q^20 - 9720 * q^21 - 13512 * q^22 - 7776 * q^24 + 56418 * q^25 - 59252 * q^26 - 17808 * q^28 - 84860 * q^29 + 57348 * q^30 + 61280 * q^32 + 4536 * q^33 + 109404 * q^34 - 37908 * q^36 + 20796 * q^37 - 128088 * q^38 - 195552 * q^40 - 65252 * q^41 + 210600 * q^42 + 445008 * q^44 + 10692 * q^45 + 81120 * q^46 - 276048 * q^48 - 111546 * q^49 - 743118 * q^50 - 179592 * q^52 + 470308 * q^53 + 39366 * q^54 + 793728 * q^56 - 204120 * q^57 + 529860 * q^58 - 723816 * q^60 + 12924 * q^61 - 513384 * q^62 - 642432 * q^64 + 321512 * q^65 + 771768 * q^66 + 690328 * q^68 + 541728 * q^69 + 938928 * q^70 - 276048 * q^72 - 1283412 * q^73 - 1522916 * q^74 + 67824 * q^76 - 1487328 * q^77 + 396252 * q^78 + 1272352 * q^80 + 354294 * q^81 + 240444 * q^82 - 143856 * q^84 + 814920 * q^85 - 1154568 * q^86 + 489600 * q^88 + 730924 * q^89 - 20412 * q^90 - 1338816 * q^92 - 83592 * q^93 - 390288 * q^94 + 624672 * q^96 + 3249420 * q^97 + 1604918 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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