LMFDB - Embedded newform 13.8.c.a.3.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,8,Mod(3,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.3"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	13.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.06100533129$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 796 x^{14} - 475 x^{13} + 449889 x^{12} - 92038 x^{11} + 116806037 x^{10} + \cdots + 11\!\cdots\!00 $ x^16 - x^15 + 796x^14 - 475x^13 + 449889x^12 - 92038x^11 + 116806037x^10 + 198490961x^9 + 21546318357x^8 + 32373621530x^7 + 2116860322049x^6 + 2147931692741x^5 + 148294262896076x^4 + 71847528967407x^3 + 4924011367741489x^2 - 2411116235274240x + 113340278793830400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{12}\cdot 3\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.2
Root			$8.10170 + 14.0326i$ of defining polynomial
Character	$\chi$	$=$	13.3
Dual form			13.8.c.a.9.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.60170 - 14.8986i) q^{2} +(-43.0086 - 74.4931i) q^{3} +(-83.9785 + 145.455i) q^{4} +289.904 q^{5} +(-739.895 + 1281.54i) q^{6} +(484.274 - 838.787i) q^{7} +687.398 q^{8} +(-2605.99 + 4513.70i) q^{9} +(-2493.67 - 4319.16i) q^{10} +(-536.447 - 929.153i) q^{11} +14447.2 q^{12} +(5291.92 - 5894.41i) q^{13} -16662.3 q^{14} +(-12468.4 - 21595.9i) q^{15} +(4836.46 + 8377.00i) q^{16} +(-9648.04 + 16710.9i) q^{17} +89663.7 q^{18} +(2342.02 - 4056.49i) q^{19} +(-24345.7 + 42168.0i) q^{20} -83311.9 q^{21} +(-9228.71 + 15984.6i) q^{22} +(-17524.1 - 30352.7i) q^{23} +(-29564.0 - 51206.4i) q^{24} +5919.34 q^{25} +(-133338. - 28140.2i) q^{26} +260200. q^{27} +(81337.3 + 140880. i) q^{28} +(-62785.3 - 108747. i) q^{29} +(-214499. + 371522. i) q^{30} +124054. q^{31} +(127197. - 220312. i) q^{32} +(-46143.7 + 79923.2i) q^{33} +331958. q^{34} +(140393. - 243168. i) q^{35} +(-437694. - 758108. i) q^{36} +(18025.4 + 31220.9i) q^{37} -80581.3 q^{38} +(-666692. - 140701. i) q^{39} +199279. q^{40} +(119806. + 207510. i) q^{41} +(716624. + 1.24123e6i) q^{42} +(356325. - 617172. i) q^{43} +180200. q^{44} +(-755486. + 1.30854e6i) q^{45} +(-301475. + 522170. i) q^{46} -1.15018e6 q^{47} +(416019. - 720567. i) q^{48} +(-57271.3 - 99196.7i) q^{49} +(-50916.4 - 88189.8i) q^{50} +1.65980e6 q^{51} +(412964. + 1.26474e6i) q^{52} +99663.5 q^{53} +(-2.23816e6 - 3.87661e6i) q^{54} +(-155518. - 269365. i) q^{55} +(332889. - 576580. i) q^{56} -402908. q^{57} +(-1.08012e6 + 1.87083e6i) q^{58} +(-449716. + 778932. i) q^{59} +4.18830e6 q^{60} +(1.18213e6 - 2.04750e6i) q^{61} +(-1.06707e6 - 1.84822e6i) q^{62} +(2.52402e6 + 4.37174e6i) q^{63} -3.13831e6 q^{64} +(1.53415e6 - 1.70881e6i) q^{65} +1.58766e6 q^{66} +(1.03560e6 + 1.79371e6i) q^{67} +(-1.62046e6 - 2.80671e6i) q^{68} +(-1.50738e6 + 2.61086e6i) q^{69} -4.83047e6 q^{70} +(1.78120e6 - 3.08513e6i) q^{71} +(-1.79135e6 + 3.10271e6i) q^{72} -340087. q^{73} +(310098. - 537106. i) q^{74} +(-254583. - 440950. i) q^{75} +(393358. + 681316. i) q^{76} -1.03915e6 q^{77} +(3.63843e6 + 1.11430e7i) q^{78} -641046. q^{79} +(1.40211e6 + 2.42853e6i) q^{80} +(-5.49155e6 - 9.51165e6i) q^{81} +(2.06107e6 - 3.56987e6i) q^{82} +1.03845e6 q^{83} +(6.99641e6 - 1.21181e7i) q^{84} +(-2.79701e6 + 4.84456e6i) q^{85} -1.22600e7 q^{86} +(-5.40062e6 + 9.35416e6i) q^{87} +(-368752. - 638698. i) q^{88} +(2.05873e6 + 3.56583e6i) q^{89} +2.59939e7 q^{90} +(-2.38142e6 - 7.29331e6i) q^{91} +5.88661e6 q^{92} +(-5.33538e6 - 9.24114e6i) q^{93} +(9.89350e6 + 1.71361e7i) q^{94} +(678960. - 1.17599e6i) q^{95} -2.18823e7 q^{96} +(5.12319e6 - 8.87362e6i) q^{97} +(-985261. + 1.70652e6i) q^{98} +5.59189e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 9 q^{2} - 28 q^{3} - 577 q^{4} + 384 q^{5} + 342 q^{6} + 196 q^{7} + 5922 q^{8} - 5988 q^{9} - 6813 q^{10} + 5052 q^{11} - 15816 q^{12} + 17064 q^{13} + 14484 q^{14} - 184 q^{15} - 61377 q^{16} - 22824 q^{17}+ \cdots + 27386736 q^{99}+O(q^{100}) $ 16 * q - 9 * q^2 - 28 * q^3 - 577 * q^4 + 384 * q^5 + 342 * q^6 + 196 * q^7 + 5922 * q^8 - 5988 * q^9 - 6813 * q^10 + 5052 * q^11 - 15816 * q^12 + 17064 * q^13 + 14484 * q^14 - 184 * q^15 - 61377 * q^16 - 22824 * q^17 + 226318 * q^18 + 63692 * q^19 - 121971 * q^20 - 271240 * q^21 - 73726 * q^22 - 72468 * q^23 + 224952 * q^24 + 58488 * q^25 + 154443 * q^26 + 358616 * q^27 - 172816 * q^28 - 221772 * q^29 - 258116 * q^30 + 58432 * q^31 + 77823 * q^32 - 352372 * q^33 + 643334 * q^34 + 31560 * q^35 - 1162993 * q^36 - 368884 * q^37 + 2364492 * q^38 - 672996 * q^39 + 766030 * q^40 - 385824 * q^41 + 1560954 * q^42 + 391492 * q^43 - 6149616 * q^44 + 232096 * q^45 - 2599078 * q^46 + 1089984 * q^47 + 4585712 * q^48 - 1108780 * q^49 + 1626894 * q^50 + 8040712 * q^51 - 1312478 * q^52 + 3329328 * q^53 - 5616702 * q^54 - 418216 * q^55 - 3609156 * q^56 - 12068664 * q^57 + 3685081 * q^58 - 6318924 * q^59 + 1448784 * q^60 + 1763548 * q^61 - 12998388 * q^62 + 6641128 * q^63 + 32227074 * q^64 + 9500508 * q^65 + 16245108 * q^66 - 8607964 * q^67 - 10118091 * q^68 - 4618492 * q^69 - 25381840 * q^70 + 9473220 * q^71 - 35174445 * q^72 + 5020888 * q^73 + 2206221 * q^74 - 21834988 * q^75 + 18702876 * q^76 + 35263992 * q^77 + 28395902 * q^78 + 12644416 * q^79 - 24671247 * q^80 - 9316272 * q^81 - 9347751 * q^82 - 22158432 * q^83 + 37532636 * q^84 - 36911824 * q^85 - 30103956 * q^86 + 5199988 * q^87 - 36676404 * q^88 + 18469860 * q^89 + 132263562 * q^90 - 9614540 * q^91 + 64127424 * q^92 - 26340696 * q^93 - 6026128 * q^94 - 16267080 * q^95 - 164216320 * q^96 + 19660916 * q^97 - 51546651 * q^98 + 27386736 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−8.60170	−	14.8986i	−0.760290	−	1.31686i	−0.942701	−	0.333639i	$-0.891723\pi$
$2$	−8.60170	−	14.8986i	−0.760290	−	1.31686i	0.182411	−	0.983222i	$-0.441610\pi$
$3$	−43.0086	−	74.4931i	−0.919669	−	1.59291i	−0.799919	−	0.600108i	$-0.795124\pi$
$3$	−43.0086	−	74.4931i	−0.919669	−	1.59291i	−0.119750	−	0.992804i	$-0.538209\pi$
$4$	−83.9785	+	145.455i	−0.656082	+	1.13637i
$5$	289.904			1.03719			0.518596	−	0.855019i	$-0.326455\pi$
$5$	289.904			1.03719			0.518596	+	0.855019i	$0.326455\pi$
$6$	−739.895	+	1281.54i	−1.39843	+	2.42215i
$7$	484.274	−	838.787i	0.533640	−	0.924291i	−0.465588	−	0.885001i	$-0.654157\pi$
$7$	484.274	−	838.787i	0.533640	−	0.924291i	0.999228	−	0.0392895i	$-0.0125095\pi$
$8$	687.398			0.474671
$9$	−2605.99	+	4513.70i	−1.19158	+	2.06388i
$10$	−2493.67	−	4319.16i	−0.788567	−	1.36584i
$11$	−536.447	−	929.153i	−0.121521	−	0.210481i	0.798846	−	0.601535i	$-0.205444\pi$
$11$	−536.447	−	929.153i	−0.121521	−	0.210481i	−0.920368	+	0.391054i	$0.872111\pi$
$12$	14447.2			2.41351
$13$	5291.92	−	5894.41i	0.668054	−	0.744113i
$13$	5291.92	−	5894.41i	0.668054	−	0.744113i
$14$	−16662.3			−1.62288
$15$	−12468.4	−	21595.9i	−0.953873	−	1.65216i
$16$	4836.46	+	8377.00i	0.295194	+	0.511292i
$17$	−9648.04	+	16710.9i	−0.476286	+	0.824952i	−0.999631	−	0.0271693i	$-0.991351\pi$
$17$	−9648.04	+	16710.9i	−0.476286	+	0.824952i	0.523345	+	0.852121i	$0.324684\pi$
$18$	89663.7			3.62379
$19$	2342.02	−	4056.49i	0.0783344	−	0.135679i	−0.824197	−	0.566303i	$-0.808373\pi$
$19$	2342.02	−	4056.49i	0.0783344	−	0.135679i	0.902531	+	0.430624i	$0.141706\pi$
$20$	−24345.7	+	42168.0i	−0.680483	+	1.17863i
$21$	−83311.9			−1.96309
$22$	−9228.71	+	15984.6i	−0.184783	+	0.320053i
$23$	−17524.1	−	30352.7i	−0.300324	−	0.520176i	0.675886	−	0.737006i	$-0.263761\pi$
$23$	−17524.1	−	30352.7i	−0.300324	−	0.520176i	−0.976209	+	0.216831i	$0.930428\pi$
$24$	−29564.0	−	51206.4i	−0.436540	−	0.756110i
$25$	5919.34			0.0757676
$26$	−133338.	−	28140.2i	−1.48781	−	0.313993i
$27$	260200.			2.54410
$28$	81337.3	+	140880.i	0.700223	+	1.21282i
$29$	−62785.3	−	108747.i	−0.478041	−	0.827992i	0.521642	−	0.853165i	$-0.325320\pi$
$29$	−62785.3	−	108747.i	−0.478041	−	0.827992i	−0.999683	+	0.0251729i	$0.991986\pi$
$30$	−214499.	+	371522.i	−1.45044	+	2.51224i
$31$	124054.			0.747900			0.373950	−	0.927449i	$-0.378003\pi$
$31$	124054.			0.747900			0.373950	+	0.927449i	$0.378003\pi$
$32$	127197.	−	220312.i	0.686202	−	1.18854i
$33$	−46143.7	+	79923.2i	−0.223519	+	0.387146i
$34$	331958.			1.44846
$35$	140393.	−	243168.i	0.553487	−	0.958667i
$36$	−437694.	−	758108.i	−1.56355	−	2.70815i
$37$	18025.4	+	31220.9i	0.0585031	+	0.101330i	0.893794	−	0.448478i	$-0.148034\pi$
$37$	18025.4	+	31220.9i	0.0585031	+	0.101330i	−0.835291	+	0.549809i	$0.814701\pi$
$38$	−80581.3			−0.238227
$39$	−666692.	−	140701.i	−1.79969	−	0.379815i
$40$	199279.			0.492326
$41$	119806.	+	207510.i	0.271478	+	0.470213i	0.969240	−	0.246116i	$-0.0791543\pi$
$41$	119806.	+	207510.i	0.271478	+	0.470213i	−0.697763	+	0.716329i	$0.745821\pi$
$42$	716624.	+	1.24123e6i	1.49252	+	2.58511i
$43$	356325.	−	617172.i	0.683449	−	1.18377i	−0.290472	−	0.956883i	$-0.593812\pi$
$43$	356325.	−	617172.i	0.683449	−	1.18377i	0.973921	−	0.226886i	$-0.0728543\pi$
$44$	180200.			0.318912
$45$	−755486.	+	1.30854e6i	−1.23590	+	2.14064i
$46$	−301475.	+	522170.i	−0.456666	+	0.790969i
$47$	−1.15018e6			−1.61593			−0.807966	−	0.589229i	$-0.799432\pi$
$47$	−1.15018e6			−1.61593			−0.807966	+	0.589229i	$0.799432\pi$
$48$	416019.	−	720567.i	0.542962	−	0.940437i
$49$	−57271.3	−	99196.7i	−0.0695425	−	0.120451i
$50$	−50916.4	−	88189.8i	−0.0576053	−	0.0997754i
$51$	1.65980e6			1.75210
$52$	412964.	+	1.26474e6i	0.407287	+	1.24735i
$53$	99663.5			0.0919540			0.0459770	−	0.998942i	$-0.485360\pi$
$53$	99663.5			0.0919540			0.0459770	+	0.998942i	$0.485360\pi$
$54$	−2.23816e6	−	3.87661e6i	−1.93425	−	3.35022i
$55$	−155518.	−	269365.i	−0.126041	−	0.218309i
$56$	332889.	−	576580.i	0.253304	−	0.438735i
$57$	−402908.			−0.288167
$58$	−1.08012e6	+	1.87083e6i	−0.726900	+	1.25903i
$59$	−449716.	+	778932.i	−0.285073	+	0.493762i	−0.972627	−	0.232372i	$-0.925351\pi$
$59$	−449716.	+	778932.i	−0.285073	+	0.493762i	0.687554	+	0.726134i	$0.258685\pi$
$60$	4.18830e6			2.50328
$61$	1.18213e6	−	2.04750e6i	0.666821	−	1.15497i	−0.311967	−	0.950093i	$-0.600988\pi$
$61$	1.18213e6	−	2.04750e6i	0.666821	−	1.15497i	0.978788	−	0.204875i	$-0.0656787\pi$
$62$	−1.06707e6	−	1.84822e6i	−0.568621	−	0.984880i
$63$	2.52402e6	+	4.37174e6i	1.27175	+	2.20273i
$64$	−3.13831e6			−1.49646
$65$	1.53415e6	−	1.70881e6i	0.692900	−	0.771788i
$66$	1.58766e6			0.679756
$67$	1.03560e6	+	1.79371e6i	0.420658	+	0.728600i	0.996004	−	0.0893095i	$-0.0284660\pi$
$67$	1.03560e6	+	1.79371e6i	0.420658	+	0.728600i	−0.575346	+	0.817910i	$0.695133\pi$
$68$	−1.62046e6	−	2.80671e6i	−0.624966	−	1.08247i
$69$	−1.50738e6	+	2.61086e6i	−0.552396	+	0.956778i
$70$	−4.83047e6			−1.68324
$71$	1.78120e6	−	3.08513e6i	0.590620	−	1.02298i	−0.403529	−	0.914967i	$-0.632216\pi$
$71$	1.78120e6	−	3.08513e6i	0.590620	−	1.02298i	0.994149	−	0.108017i	$-0.0344502\pi$
$72$	−1.79135e6	+	3.10271e6i	−0.565609	+	0.979664i
$73$	−340087.			−0.102320			−0.0511599	−	0.998690i	$-0.516292\pi$
$73$	−340087.			−0.102320			−0.0511599	+	0.998690i	$0.516292\pi$
$74$	310098.	−	537106.i	0.0889586	−	0.154081i
$75$	−254583.	−	440950.i	−0.0696810	−	0.120691i
$76$	393358.	+	681316.i	0.102788	+	0.178033i
$77$	−1.03915e6			−0.259394
$78$	3.63843e6	+	1.11430e7i	0.868127	+	2.65872i
$79$	−641046.			−0.146283			−0.0731416	−	0.997322i	$-0.523302\pi$
$79$	−641046.			−0.146283			−0.0731416	+	0.997322i	$0.523302\pi$
$80$	1.40211e6	+	2.42853e6i	0.306173	+	0.530308i
$81$	−5.49155e6	−	9.51165e6i	−1.14815	−	1.98865i
$82$	2.06107e6	−	3.56987e6i	0.412804	−	0.714997i
$83$	1.03845e6			0.199347			0.0996737	−	0.995020i	$-0.468220\pi$
$83$	1.03845e6			0.199347			0.0996737	+	0.995020i	$0.468220\pi$
$84$	6.99641e6	−	1.21181e7i	1.28795	−	2.23079i
$85$	−2.79701e6	+	4.84456e6i	−0.494000	+	0.855634i
$86$	−1.22600e7			−2.07848
$87$	−5.40062e6	+	9.35416e6i	−0.879279	+	1.52296i
$88$	−368752.	−	638698.i	−0.0576827	−	0.0999093i
$89$	2.05873e6	+	3.56583e6i	0.309553	+	0.536162i	0.978265	−	0.207360i	$-0.0664873\pi$
$89$	2.05873e6	+	3.56583e6i	0.309553	+	0.536162i	−0.668712	+	0.743522i	$0.733154\pi$
$90$	2.59939e7			3.75856
$91$	−2.38142e6	−	7.29331e6i	−0.331277	−	1.01456i
$92$	5.88661e6			0.788148
$93$	−5.33538e6	−	9.24114e6i	−0.687820	−	1.19134i
$94$	9.89350e6	+	1.71361e7i	1.22858	+	2.12796i
$95$	678960.	−	1.17599e6i	0.0812478	−	0.140725i
$96$	−2.18823e7			−2.52431
$97$	5.12319e6	−	8.87362e6i	0.569953	−	0.987188i	−0.426617	−	0.904432i	$-0.640295\pi$
$97$	5.12319e6	−	8.87362e6i	0.569953	−	0.987188i	0.996570	−	0.0827551i	$-0.0263719\pi$
$98$	−985261.	+	1.70652e6i	−0.105745	+	0.183156i
$99$	5.59189e6			0.579210
$100$	−497098.	+	860998.i	−0.0497098	+	0.0860998i
$101$	46596.3	+	80707.2i	0.00450015	+	0.00779448i	0.868267	−	0.496098i	$-0.165234\pi$
$101$	46596.3	+	80707.2i	0.00450015	+	0.00779448i	−0.863767	+	0.503892i	$0.831901\pi$
$102$	−1.42771e7	−	2.47286e7i	−1.33211	−	2.30727i
$103$	1.92098e7			1.73218			0.866089	−	0.499890i	$-0.166626\pi$
$103$	1.92098e7			1.73218			0.866089	+	0.499890i	$0.166626\pi$
$104$	3.63765e6	−	4.05180e6i	0.317106	−	0.353209i
$105$	−2.41524e7			−2.03610
$106$	−857276.	−	1.48484e6i	−0.0699117	−	0.121091i
$107$	−896755.	−	1.55323e6i	−0.0707670	−	0.122572i	0.828471	−	0.560032i	$-0.189211\pi$
$107$	−896755.	−	1.55323e6i	−0.0707670	−	0.122572i	−0.899238	+	0.437460i	$0.855878\pi$
$108$	−2.18512e7	+	3.78474e7i	−1.66914	+	2.89103i
$109$	1.03829e7			0.767936			0.383968	−	0.923346i	$-0.374557\pi$
$109$	1.03829e7			0.767936			0.383968	+	0.923346i	$0.374557\pi$
$110$	−2.67544e6	+	4.63400e6i	−0.191655	+	0.331957i
$111$	1.55050e6	−	2.68554e6i	0.107607	−	0.186381i
$112$	9.36870e6			0.630109
$113$	−8.59251e6	+	1.48827e7i	−0.560203	+	0.970300i	0.437275	+	0.899328i	$0.355944\pi$
$113$	−8.59251e6	+	1.48827e7i	−0.560203	+	0.970300i	−0.997478	+	0.0709725i	$0.977390\pi$
$114$	3.46569e6	+	6.00275e6i	0.219090	+	0.379475i
$115$	−5.08032e6	−	8.79937e6i	−0.311493	−	0.539522i
$116$	2.10905e7			1.25454
$117$	1.28149e7	+	3.92469e7i	0.739717	+	2.26545i
$118$	1.54733e7			0.866954
$119$	9.34459e6	+	1.61853e7i	0.508330	+	0.880454i
$120$	−8.57073e6	−	1.48449e7i	−0.452776	−	0.784231i
$121$	9.16803e6	−	1.58795e7i	0.470465	−	0.814870i
$122$	−4.06732e7			−2.02791
$123$	1.03054e7	−	1.78494e7i	0.499339	−	0.864881i
$124$	−1.04178e7	+	1.80442e7i	−0.490684	+	0.849889i
$125$	−2.09327e7			−0.958607
$126$	4.34218e7	−	7.52087e7i	1.93380	−	3.34943i
$127$	−1.67606e7	−	2.90303e7i	−0.726069	−	1.25759i	−0.958533	−	0.284983i	$-0.908012\pi$
$127$	−1.67606e7	−	2.90303e7i	−0.726069	−	1.25759i	0.232464	−	0.972605i	$-0.425321\pi$
$128$	1.07136e7	+	1.85565e7i	0.451544	+	0.782097i
$129$	−6.13002e7			−2.51419
$130$	−3.86552e7	−	8.15795e6i	−1.54314	−	0.325671i
$131$	4.05156e7			1.57461			0.787305	−	0.616564i	$-0.211476\pi$
$131$	4.05156e7			1.57461			0.787305	+	0.616564i	$0.211476\pi$
$132$	−7.75016e6	−	1.34237e7i	−0.293293	−	0.507999i
$133$	−2.26836e6	−	3.92891e6i	−0.0836046	−	0.144807i
$134$	1.78158e7	−	3.08578e7i	0.639644	−	1.10790i
$135$	7.54330e7			2.63872
$136$	−6.63204e6	+	1.14870e7i	−0.226079	+	0.391581i
$137$	9.71519e6	−	1.68272e7i	0.322797	−	0.559100i	−0.658267	−	0.752784i	$-0.728710\pi$
$137$	9.71519e6	−	1.68272e7i	0.322797	−	0.559100i	0.981064	+	0.193684i	$0.0620436\pi$
$138$	5.18641e7			1.67993
$139$	−2.45346e7	+	4.24952e7i	−0.774867	+	1.34211i	0.160002	+	0.987117i	$0.448850\pi$
$139$	−2.45346e7	+	4.24952e7i	−0.774867	+	1.34211i	−0.934869	+	0.354992i	$0.884483\pi$
$140$	2.35800e7	+	4.08418e7i	0.726266	+	1.25793i
$141$	4.94677e7	+	8.56805e7i	1.48612	+	2.57404i
$142$	−6.12854e7			−1.79617
$143$	−8.31565e6	−	1.75497e6i	−0.237804	−	0.0501872i
$144$	−5.04150e7			−1.40699
$145$	−1.82017e7	−	3.15263e7i	−0.495821	−	0.858786i
$146$	2.92533e6	+	5.06681e6i	0.0777928	+	0.134741i
$147$	−4.92632e6	+	8.53263e6i	−0.127912	+	0.221550i
$148$	−6.05499e6			−0.153531
$149$	−2.80153e7	+	4.85239e7i	−0.693815	+	1.20172i	0.276764	+	0.960938i	$0.410738\pi$
$149$	−2.80153e7	+	4.85239e7i	−0.693815	+	1.20172i	−0.970579	+	0.240784i	$0.922595\pi$
$150$	−4.37969e6	+	7.58585e6i	−0.105956	+	0.183521i
$151$	−2.62118e7			−0.619551			−0.309776	−	0.950810i	$-0.600254\pi$
$151$	−2.62118e7			−0.619551			−0.309776	+	0.950810i	$0.600254\pi$
$152$	1.60990e6	−	2.78842e6i	0.0371831	−	0.0644030i
$153$	−5.02853e7	−	8.70967e7i	−1.13507	−	1.96599i
$154$	8.93845e6	+	1.54819e7i	0.197215	+	0.341586i
$155$	3.59636e7			0.775716
$156$	7.64535e7	−	8.51578e7i	1.61236	−	1.79593i
$157$	3.52510e7			0.726980			0.363490	−	0.931598i	$-0.381585\pi$
$157$	3.52510e7			0.726980			0.363490	+	0.931598i	$0.381585\pi$
$158$	5.51409e6	+	9.55068e6i	0.111218	+	0.192635i
$159$	−4.28639e6	−	7.42425e6i	−0.0845672	−	0.146475i
$160$	3.68749e7	−	6.38693e7i	0.711724	−	1.23274i
$161$	−3.39460e7			−0.641058
$162$	−9.44734e7	+	1.63633e8i	−1.74585	+	3.02390i
$163$	−1.38748e7	+	2.40319e7i	−0.250940	+	0.434641i	−0.963785	−	0.266681i	$-0.914073\pi$
$163$	−1.38748e7	+	2.40319e7i	−0.250940	+	0.434641i	0.712845	+	0.701322i	$0.247406\pi$
$164$	−4.02445e7			−0.712447
$165$	−1.33772e7	+	2.31701e7i	−0.231832	+	0.401544i
$166$	−8.93241e6	−	1.54714e7i	−0.151562	−	0.262513i
$167$	−1.75119e7	−	3.03314e7i	−0.290954	−	0.503948i	0.683081	−	0.730342i	$-0.260639\pi$
$167$	−1.75119e7	−	3.03314e7i	−0.290954	−	0.503948i	−0.974036	+	0.226395i	$0.927306\pi$
$168$	−5.72684e7			−0.931821
$169$	−6.73966e6	−	6.23855e7i	−0.107407	−	0.994215i
$170$	9.62360e7			1.50233
$171$	1.22065e7	+	2.11423e7i	0.186683	+	0.323345i
$172$	5.98473e7	+	1.03658e8i	0.896798	+	1.55330i
$173$	3.18005e7	−	5.50800e7i	0.466952	−	0.808784i	−0.532335	−	0.846534i	$-0.678685\pi$
$173$	3.18005e7	−	5.50800e7i	0.466952	−	0.808784i	0.999287	+	0.0377492i	$0.0120188\pi$
$174$	1.85818e8			2.67403
$175$	2.86658e6	−	4.96507e6i	0.0404326	−	0.0700313i
$176$	5.18901e6	−	8.98763e6i	0.0717448	−	0.124266i
$177$	7.73667e7			1.04869
$178$	3.54172e7	−	6.13444e7i	0.470700	−	0.815277i
$179$	3.20355e7	+	5.54872e7i	0.417490	+	0.723114i	0.995686	−	0.0927835i	$-0.0295765\pi$
$179$	3.20355e7	+	5.54872e7i	0.417490	+	0.723114i	−0.578196	+	0.815898i	$0.696243\pi$
$180$	−1.26889e8	−	2.19779e8i	−1.62170	−	2.80887i
$181$	−1.31039e6			−0.0164258			−0.00821290	−	0.999966i	$-0.502614\pi$
$181$	−1.31039e6			−0.0164258			−0.00821290	+	0.999966i	$0.502614\pi$
$182$	−8.81757e7	+	9.82146e7i	−1.08417	+	1.20761i
$183$	−2.03366e8			−2.45302
$184$	−1.20461e7	−	2.08644e7i	−0.142555	−	0.246913i
$185$	5.22563e6	+	9.05106e6i	0.0606789	+	0.105099i
$186$	−9.17866e7	+	1.58979e8i	−1.04589	+	1.81153i
$187$	2.07027e7			0.231516
$188$	9.65904e7	−	1.67300e8i	1.06018	−	1.83629i
$189$	1.26008e8	−	2.18252e8i	1.35763	−	2.35149i
$190$	−2.33608e7			−0.247088
$191$	1.74949e7	−	3.03020e7i	0.181675	−	0.314670i	−0.760776	−	0.649014i	$-0.775182\pi$
$191$	1.74949e7	−	3.03020e7i	0.181675	−	0.314670i	0.942451	+	0.334345i	$0.108515\pi$
$192$	1.34974e8	+	2.33783e8i	1.37625	+	2.38373i
$193$	9.89059e7	+	1.71310e8i	0.990311	+	1.71527i	0.615419	+	0.788200i	$0.288987\pi$
$193$	9.89059e7	+	1.71310e8i	0.990311	+	1.71527i	0.374892	+	0.927068i	$0.377680\pi$
$194$	−1.76272e8			−1.73332
$195$	−1.93277e8	−	4.07899e7i	−1.86663	−	0.393941i
$196$	1.92382e7			0.182503
$197$	6.17840e7	+	1.07013e8i	0.575763	+	0.997251i	0.995958	+	0.0898176i	$0.0286284\pi$
$197$	6.17840e7	+	1.07013e8i	0.575763	+	0.997251i	−0.420195	+	0.907434i	$0.638038\pi$
$198$	−4.80998e7	−	8.33113e7i	−0.440367	−	0.762739i
$199$	−4.01412e7	+	6.95266e7i	−0.361081	+	0.625410i	−0.988139	−	0.153562i	$-0.950925\pi$
$199$	−4.01412e7	+	6.95266e7i	−0.361081	+	0.625410i	0.627058	+	0.778972i	$0.284259\pi$
$200$	4.06894e6			0.0359647
$201$	8.90792e7	−	1.54290e8i	0.773731	−	1.34014i
$202$	801615.	−	1.38844e6i	0.00684283	−	0.0118521i
$203$	−1.21621e8			−1.02041
$204$	−1.39387e8	+	2.41426e8i	−1.14952	+	1.99103i
$205$	3.47322e7	+	6.01579e7i	0.281575	+	0.487701i
$206$	−1.65237e8	−	2.86199e8i	−1.31696	−	2.28104i
$207$	1.82671e8			1.43144
$208$	7.49717e7	+	1.58223e7i	0.577664	+	0.121913i
$209$	−5.02547e6			−0.0380772
$210$	2.07752e8	+	3.59837e8i	1.54803	+	2.68126i
$211$	3.53037e7	+	6.11477e7i	0.258721	+	0.448117i	0.965899	−	0.258917i	$-0.0833657\pi$
$211$	3.53037e7	+	6.11477e7i	0.258721	+	0.448117i	−0.707179	+	0.707035i	$0.750032\pi$
$212$	−8.36959e6	+	1.44966e7i	−0.0603294	+	0.104494i
$213$	−3.06428e8			−2.17270
$214$	−1.54272e7	+	2.67208e7i	−0.107607	+	0.186381i
$215$	1.03300e8	−	1.78921e8i	0.708868	−	1.22780i
$216$	1.78861e8			1.20761
$217$	6.00759e7	−	1.04055e8i	0.399109	−	0.691277i
$218$	−8.93104e7	−	1.54690e8i	−0.583854	−	1.01127i
$219$	1.46267e7	+	2.53341e7i	0.0941003	+	0.162987i
$220$	5.22407e7			0.330773
$221$	4.74442e7	+	1.45302e8i	0.295672	+	0.905523i
$222$	−5.33476e7			−0.327250
$223$	−7.92138e7	−	1.37202e8i	−0.478337	−	0.828504i	0.521355	−	0.853340i	$-0.325427\pi$
$223$	−7.92138e7	−	1.37202e8i	−0.478337	−	0.828504i	−0.999692	+	0.0248364i	$0.992094\pi$
$224$	−1.23196e8	−	2.13383e8i	−0.732370	−	1.26850i
$225$	−1.54257e7	+	2.67181e7i	−0.0902831	+	0.156375i
$226$	2.95641e8			1.70367
$227$	−8.26816e7	+	1.43209e8i	−0.469157	+	0.812605i	−0.999378	−	0.0352550i	$-0.988776\pi$
$227$	−8.26816e7	+	1.43209e8i	−0.469157	+	0.812605i	0.530221	+	0.847860i	$0.322109\pi$
$228$	3.38356e7	−	5.86050e7i	0.189061	−	0.327463i
$229$	−1.59724e8			−0.878916			−0.439458	−	0.898263i	$-0.644829\pi$
$229$	−1.59724e8			−0.878916			−0.439458	+	0.898263i	$0.644829\pi$
$230$	−8.73988e7	+	1.51379e8i	−0.473650	+	0.820387i
$231$	4.46924e7	+	7.74095e7i	0.238557	+	0.413192i
$232$	−4.31585e7	−	7.47527e7i	−0.226912	−	0.393024i
$233$	1.58511e8			0.820944			0.410472	−	0.911873i	$-0.365364\pi$
$233$	1.58511e8			0.820944			0.410472	+	0.911873i	$0.365364\pi$
$234$	4.74493e8	−	5.28515e8i	2.42089	−	2.69651i
$235$	−3.33442e8			−1.67603
$236$	−7.55330e7	−	1.30827e8i	−0.374063	−	0.647896i
$237$	2.75705e7	+	4.77535e7i	0.134532	+	0.233016i
$238$	1.60759e8	−	2.78442e8i	0.772957	−	1.33880i
$239$	1.94610e8			0.922089			0.461045	−	0.887377i	$-0.347475\pi$
$239$	1.94610e8			0.922089			0.461045	+	0.887377i	$0.347475\pi$
$240$	1.20606e8	−	2.08895e8i	0.563156	−	0.975414i
$241$	−1.47330e8	+	2.55182e8i	−0.678001	+	1.17433i	0.297581	+	0.954697i	$0.403820\pi$
$241$	−1.47330e8	+	2.55182e8i	−0.678001	+	1.17433i	−0.975582	+	0.219635i	$0.929513\pi$
$242$	−3.15443e8			−1.43076
$243$	−1.87840e8	+	3.25348e8i	−0.839780	+	1.45454i
$244$	1.98546e8	+	3.43892e8i	0.874979	+	1.51551i
$245$	−1.66032e7	−	2.87575e7i	−0.0721290	−	0.124931i
$246$	−3.54575e8			−1.51857
$247$	−1.15169e7	−	3.52714e7i	−0.0486289	−	0.148931i
$248$	8.52741e7			0.355007
$249$	−4.46622e7	−	7.73571e7i	−0.183334	−	0.317543i
$250$	1.80057e8	+	3.11868e8i	0.728819	+	1.26235i
$251$	2.17660e8	−	3.76998e8i	0.868800	−	1.50481i	0.00557667	−	0.999984i	$-0.498225\pi$
$251$	2.17660e8	−	3.76998e8i	0.868800	−	1.50481i	0.863224	−	0.504822i	$-0.168442\pi$
$252$	−8.47855e8			−3.33749
$253$	−1.88015e7	+	3.25652e7i	−0.0729914	+	0.126425i
$254$	−2.88340e8	+	4.99420e8i	−1.10405	+	1.91226i
$255$	4.81182e8			1.81727
$256$	−1.65418e7	+	2.86512e7i	−0.0616228	+	0.106734i
$257$	1.75799e8	+	3.04492e8i	0.646026	+	1.11895i	0.984064	+	0.177817i	$0.0569035\pi$
$257$	1.75799e8	+	3.04492e8i	0.646026	+	1.11895i	−0.338038	+	0.941133i	$0.609763\pi$
$258$	5.27286e8	+	9.13286e8i	1.91151	+	3.31084i
$259$	3.49169e7			0.124878
$260$	1.19720e8	+	3.66653e8i	0.422435	+	1.29375i
$261$	6.54471e8			2.27850
$262$	−3.48503e8	−	6.03625e8i	−1.19716	−	2.07354i
$263$	−1.99248e8	−	3.45108e8i	−0.675382	−	1.16980i	−0.976357	−	0.216164i	$-0.930645\pi$
$263$	−1.99248e8	−	3.45108e8i	−0.675382	−	1.16980i	0.300975	−	0.953632i	$-0.402688\pi$
$264$	−3.17191e7	+	5.49391e7i	−0.106098	+	0.183767i
$265$	2.88928e7			0.0953739
$266$	−3.90234e7	+	6.75906e7i	−0.127128	+	0.220191i
$267$	1.77087e8	−	3.06723e8i	0.569372	−	0.986182i
$268$	−3.47872e8			−1.10394
$269$	1.05501e8	−	1.82732e8i	0.330462	−	0.572377i	−0.652140	−	0.758098i	$-0.726129\pi$
$269$	1.05501e8	−	1.82732e8i	0.330462	−	0.572377i	0.982603	+	0.185721i	$0.0594621\pi$
$270$	−6.48852e8	−	1.12384e9i	−2.00619	−	3.47483i
$271$	−1.83698e8	−	3.18175e8i	−0.560677	−	0.971121i	−0.997438	−	0.0715430i	$-0.977208\pi$
$271$	−1.83698e8	−	3.18175e8i	−0.560677	−	0.971121i	0.436761	−	0.899578i	$-0.356126\pi$
$272$	−1.86650e8			−0.562388
$273$	−4.40880e8	+	4.91074e8i	−1.31145	+	1.46076i
$274$	−3.34269e8			−0.981677
$275$	−3.17541e6	−	5.49998e6i	−0.00920737	−	0.0159476i
$276$	−2.53175e8	−	4.38512e8i	−0.724835	−	1.25545i
$277$	−1.40187e8	+	2.42811e8i	−0.396304	+	0.686419i	−0.993267	−	0.115850i	$-0.963041\pi$
$277$	−1.40187e8	+	2.42811e8i	−0.396304	+	0.686419i	0.596962	+	0.802269i	$0.296374\pi$
$278$	8.44157e8			2.35649
$279$	−3.23282e8	+	5.59941e8i	−0.891183	+	1.54357i
$280$	9.65058e7	−	1.67153e8i	0.262724	−	0.455052i
$281$	6.51288e8			1.75106			0.875530	−	0.483163i	$-0.160512\pi$
$281$	6.51288e8			1.75106			0.875530	+	0.483163i	$0.160512\pi$
$282$	8.51012e8	−	1.47400e9i	2.25977	−	3.91403i
$283$	−7.80018e6	−	1.35103e7i	−0.0204575	−	0.0354334i	0.855615	−	0.517612i	$-0.173179\pi$
$283$	−7.80018e6	−	1.35103e7i	−0.0204575	−	0.0354334i	−0.876073	+	0.482179i	$0.839846\pi$
$284$	2.99165e8	+	5.18169e8i	0.774991	+	1.34232i
$285$	−1.16805e8			−0.298884
$286$	4.53822e7	+	1.38987e8i	0.114711	+	0.351312i
$287$	2.32075e8			0.579485
$288$	6.62948e8	+	1.14826e9i	1.63533	+	2.83248i
$289$	1.89999e7	+	3.29088e7i	0.0463030	+	0.0801991i
$290$	−3.13132e8	+	5.42360e8i	−0.753935	+	1.30585i
$291$	−8.81365e8			−2.09667
$292$	2.85600e7	−	4.94674e7i	0.0671302	−	0.116273i
$293$	1.68184e8	−	2.91304e8i	0.390615	−	0.676565i	−0.601916	−	0.798559i	$-0.705596\pi$
$293$	1.68184e8	−	2.91304e8i	0.390615	−	0.676565i	0.992531	+	0.121995i	$0.0389291\pi$
$294$	1.69499e8			0.389001
$295$	−1.30375e8	+	2.25815e8i	−0.295676	+	0.512126i
$296$	1.23906e7	+	2.14612e7i	0.0277697	+	0.0480986i
$297$	−1.39583e8	−	2.41766e8i	−0.309162	−	0.535485i
$298$	9.63917e8			2.11000
$299$	−2.71648e8	−	5.73296e7i	−0.587702	−	0.124031i
$300$	8.55180e7			0.182866
$301$	−3.45118e8	−	5.97761e8i	−0.729431	−	1.26341i
$302$	2.25466e8	+	3.90518e8i	0.471039	+	0.815863i
$303$	4.00809e6	−	6.94221e6i	0.00827729	−	0.0143367i
$304$	4.53083e7			0.0924954
$305$	3.42703e8	−	5.93579e8i	0.691621	−	1.19792i
$306$	−8.65079e8	+	1.49836e9i	−1.72596	+	2.98945i
$307$	3.13460e8			0.618298			0.309149	−	0.951014i	$-0.399956\pi$
$307$	3.13460e8			0.618298			0.309149	+	0.951014i	$0.399956\pi$
$308$	8.72662e7	−	1.51150e8i	0.170184	−	0.294767i
$309$	−8.26187e8	−	1.43100e9i	−1.59303	−	2.75921i
$310$	−3.09348e8	−	5.35807e8i	−0.589769	−	1.02151i
$311$	−7.59259e8			−1.43129			−0.715646	−	0.698463i	$-0.753868\pi$
$311$	−7.59259e8			−1.43129			−0.715646	+	0.698463i	$0.753868\pi$
$312$	−4.58282e8	−	9.67177e7i	−0.854264	−	0.180287i
$313$	−1.21815e8			−0.224542			−0.112271	−	0.993678i	$-0.535812\pi$
$313$	−1.21815e8			−0.224542			−0.112271	+	0.993678i	$0.535812\pi$
$314$	−3.03218e8	−	5.25189e8i	−0.552715	−	0.957331i
$315$	7.31724e8	+	1.26738e9i	1.31905	+	2.28466i
$316$	5.38341e7	−	9.32434e7i	0.0959738	−	0.166232i
$317$	1.57120e8			0.277028			0.138514	−	0.990361i	$-0.455767\pi$
$317$	1.57120e8			0.277028			0.138514	+	0.990361i	$0.455767\pi$
$318$	−7.37405e7	+	1.27722e8i	−0.128591	+	0.222726i
$319$	−6.73620e7	+	1.16674e8i	−0.116184	+	0.201237i
$320$	−9.09809e8			−1.55212
$321$	−7.71364e7	+	1.33604e8i	−0.130164	+	0.225451i
$322$	2.91993e8	+	5.05747e8i	0.487390	+	0.844185i
$323$	4.51917e7	+	7.82744e7i	0.0746191	+	0.129244i
$324$	1.84469e9			3.01312
$325$	3.13247e7	−	3.48910e7i	0.0506168	−	0.0563796i
$326$	4.77388e8			0.763150
$327$	−4.46554e8	−	7.73454e8i	−0.706247	−	1.22326i
$328$	8.23542e7	+	1.42642e8i	0.128863	+	0.223197i
$329$	−5.57002e8	+	9.64756e8i	−0.862326	+	1.49359i
$330$	4.60268e8			0.705038
$331$	−3.58254e8	+	6.20513e8i	−0.542991	+	0.940488i	0.455740	+	0.890113i	$0.349375\pi$
$331$	−3.58254e8	+	6.20513e8i	−0.542991	+	0.940488i	−0.998730	+	0.0503746i	$0.983958\pi$
$332$	−8.72072e7	+	1.51047e8i	−0.130788	+	0.226532i
$333$	−1.87896e8			−0.278845
$334$	−3.01264e8	+	5.21804e8i	−0.442419	+	0.766293i
$335$	3.00224e8	+	5.20003e8i	0.436303	+	0.755699i
$336$	−4.02935e8	−	6.97904e8i	−0.579492	−	1.00371i
$337$	1.21201e9			1.72505			0.862523	−	0.506018i	$-0.168883\pi$
$337$	1.21201e9			1.72505			0.862523	+	0.506018i	$0.168883\pi$
$338$	−8.71483e8	+	6.37033e8i	−1.22758	+	0.897333i
$339$	1.47821e9			2.06080
$340$	−4.69777e8	−	8.13678e8i	−0.648210	−	1.12273i
$341$	−6.65482e7	−	1.15265e8i	−0.0908857	−	0.157419i
$342$	2.09994e8	−	3.63720e8i	0.283867	−	0.491672i
$343$	6.86701e8			0.918837
$344$	2.44937e8	−	4.24243e8i	0.324414	−	0.561901i
$345$	−4.36995e8	+	7.56898e8i	−0.572941	+	0.992363i
$346$	−1.09415e9			−1.42008
$347$	−2.27893e8	+	3.94722e8i	−0.292804	+	0.507152i	−0.974472	−	0.224510i	$-0.927922\pi$
$347$	−2.27893e8	+	3.94722e8i	−0.292804	+	0.507152i	0.681668	+	0.731662i	$0.261255\pi$
$348$	−9.07073e8	−	1.57110e9i	−1.15376	−	1.99837i
$349$	9.00399e7	+	1.55954e8i	0.113382	+	0.196384i	0.917132	−	0.398584i	$-0.130498\pi$
$349$	9.00399e7	+	1.55954e8i	0.113382	+	0.196384i	−0.803750	+	0.594968i	$0.797165\pi$
$350$	−9.86300e7			−0.122962
$351$	1.37696e9	−	1.53373e9i	1.69960	−	1.89310i
$352$	−2.72938e8			−0.333553
$353$	4.63948e8	+	8.03582e8i	0.561381	+	0.972341i	0.997376	+	0.0723920i	$0.0230633\pi$
$353$	4.63948e8	+	8.03582e8i	0.561381	+	0.972341i	−0.435995	+	0.899949i	$0.643603\pi$
$354$	−6.65486e8	−	1.15266e9i	−0.797310	−	1.38098i
$355$	5.16377e8	−	8.94391e8i	0.612587	−	1.06103i
$356$	−6.91558e8			−0.812369
$357$	8.03796e8	−	1.39222e9i	0.934991	−	1.61945i
$358$	5.51120e8	−	9.54568e8i	0.634827	−	1.09955i
$359$	6.38744e7			0.0728612			0.0364306	−	0.999336i	$-0.488401\pi$
$359$	6.38744e7			0.0728612			0.0364306	+	0.999336i	$0.488401\pi$
$360$	−5.19319e8	+	8.99487e8i	−0.586645	+	1.01610i
$361$	4.35966e8	+	7.55115e8i	0.487727	+	0.844769i
$362$	1.12716e7	+	1.95230e7i	0.0124884	+	0.0216305i
$363$	−1.57722e9			−1.73069
$364$	1.26084e9	+	2.66092e8i	1.37026	+	0.289186i
$365$	−9.85926e7			−0.106125
$366$	1.74930e9	+	3.02987e9i	1.86500	+	3.23028i
$367$	−5.33531e8	−	9.24103e8i	−0.563415	−	0.975864i	−0.997195	−	0.0748448i	$-0.976154\pi$
$367$	−5.33531e8	−	9.24103e8i	−0.563415	−	0.975864i	0.433780	−	0.901019i	$-0.357179\pi$
$368$	1.69510e8	−	2.93599e8i	0.177308	−	0.307106i
$369$	−1.24885e9			−1.29395
$370$	8.98987e7	−	1.55709e8i	0.0922672	−	0.159811i
$371$	4.82644e7	−	8.35965e7i	0.0490703	−	0.0849922i
$372$	1.79223e9			1.80507
$373$	−3.15985e8	+	5.47302e8i	−0.315272	+	0.546068i	−0.979495	−	0.201467i	$-0.935429\pi$
$373$	−3.15985e8	+	5.47302e8i	−0.315272	+	0.546068i	0.664223	+	0.747534i	$0.268763\pi$
$374$	−1.78078e8	−	3.08440e8i	−0.176019	−	0.304874i
$375$	9.00287e8	+	1.55934e9i	0.881600	+	1.52698i
$376$	−7.90631e8			−0.767037
$377$	−9.73257e8	−	2.05400e8i	−0.935476	−	0.197427i
$378$	−4.33553e9			−4.12878
$379$	−2.70088e8	−	4.67806e8i	−0.254840	−	0.441396i	0.710012	−	0.704190i	$-0.248690\pi$
$379$	−2.70088e8	−	4.67806e8i	−0.254840	−	0.441396i	−0.964852	+	0.262794i	$0.915356\pi$
$380$	1.14036e8	+	1.97516e8i	0.106610	+	0.184655i
$381$	−1.44171e9	+	2.49711e9i	−1.33548	+	2.31313i
$382$	−6.01943e8			−0.552502
$383$	6.00254e8	−	1.03967e9i	0.545933	−	0.945584i	−0.452615	−	0.891706i	$-0.649509\pi$
$383$	6.00254e8	−	1.03967e9i	0.545933	−	0.945584i	0.998548	−	0.0538774i	$-0.0171580\pi$
$384$	9.21553e8	−	1.59618e9i	0.830541	−	1.43854i
$385$	−3.01254e8			−0.269042
$386$	1.70152e9	−	2.94712e9i	1.50585	−	2.60820i
$387$	1.85715e9	+	3.21669e9i	1.62877	+	2.82111i
$388$	8.60475e8	+	1.49039e9i	0.747872	+	1.29535i
$389$	4.20919e8			0.362556			0.181278	−	0.983432i	$-0.441977\pi$
$389$	4.20919e8			0.362556			0.181278	+	0.983432i	$0.441977\pi$
$390$	1.05480e9	+	3.23041e9i	0.900414	+	2.75760i
$391$	6.76295e8			0.572160
$392$	−3.93681e7	−	6.81876e7i	−0.0330099	−	0.0571747i
$393$	−1.74252e9	−	3.01813e9i	−1.44812	−	2.50821i
$394$	1.06289e9	−	1.84099e9i	0.875495	−	1.51640i
$395$	−1.85842e8			−0.151724
$396$	−4.69599e8	+	8.13369e8i	−0.380009	+	0.658195i
$397$	−8.97765e8	+	1.55497e9i	−0.720105	+	1.24726i	0.240853	+	0.970562i	$0.422573\pi$
$397$	−8.97765e8	+	1.55497e9i	−0.720105	+	1.24726i	−0.960957	+	0.276696i	$0.910760\pi$
$398$	1.38113e9			1.09810
$399$	−1.95118e8	+	3.37954e8i	−0.153777	+	0.266350i
$400$	2.86287e7	+	4.95863e7i	0.0223662	+	0.0387393i
$401$	−1.60421e8	−	2.77857e8i	−0.124238	−	0.215187i	0.797197	−	0.603720i	$-0.206315\pi$
$401$	−1.60421e8	−	2.77857e8i	−0.124238	−	0.215187i	−0.921435	+	0.388533i	$0.872982\pi$
$402$	−3.06493e9			−2.35304
$403$	6.56482e8	−	7.31223e8i	0.499638	−	0.556522i
$404$	−1.56524e7			−0.0118099
$405$	−1.59202e9	−	2.75746e9i	−1.19085	−	2.06261i
$406$	1.04615e9	+	1.81198e9i	0.775805	+	1.34373i
$407$	1.93393e7	−	3.34967e7i	0.0142187	−	0.0246276i
$408$	1.14094e9			0.831673
$409$	−9.05875e8	+	1.56902e9i	−0.654692	+	1.13396i	0.327279	+	0.944928i	$0.393868\pi$
$409$	−9.05875e8	+	1.56902e9i	−0.654692	+	1.13396i	−0.981971	+	0.189032i	$0.939465\pi$
$410$	5.97512e8	−	1.03492e9i	0.428157	−	0.741589i
$411$	−1.67135e9			−1.18746
$412$	−1.61321e9	+	2.79416e9i	−1.13645	+	1.96839i
$413$	4.35572e8	+	7.54433e8i	0.304253	+	0.526981i
$414$	−1.57128e9	−	2.72153e9i	−1.08831	−	1.88501i
$415$	3.01050e8			0.206762
$416$	−6.25492e8	−	1.91562e9i	−0.425985	−	1.30462i
$417$	4.22080e9			2.85048
$418$	4.32276e7	+	7.48724e7i	0.0289497	+	0.0501423i
$419$	3.08709e8	+	5.34700e8i	0.205022	+	0.355108i	0.950140	−	0.311825i	$-0.100940\pi$
$419$	3.08709e8	+	5.34700e8i	0.205022	+	0.355108i	−0.745118	+	0.666933i	$0.767607\pi$
$420$	2.02829e9	−	3.51310e9i	1.33585	−	2.31376i
$421$	−1.43462e9			−0.937023			−0.468511	−	0.883457i	$-0.655210\pi$
$421$	−1.43462e9			−0.937023			−0.468511	+	0.883457i	$0.655210\pi$
$422$	6.07343e8	−	1.05195e9i	0.393406	−	0.681398i
$423$	2.99735e9	−	5.19157e9i	1.92551	−	3.33509i
$424$	6.85085e7			0.0436479
$425$	−5.71101e7	+	9.89175e7i	−0.0360870	+	0.0625046i
$426$	2.63580e9	+	4.56534e9i	1.65188	+	2.86114i
$427$	−1.14495e9	−	1.98310e9i	−0.711684	−	1.23267i
$428$	3.01233e8			0.185716
$429$	2.26912e8	+	6.94938e8i	0.138757	+	0.424957i
$430$	−3.55422e9			−2.15578
$431$	7.83089e8	+	1.35635e9i	0.471130	+	0.816021i	0.999455	−	0.0330211i	$-0.0105129\pi$
$431$	7.83089e8	+	1.35635e9i	0.471130	+	0.816021i	−0.528324	+	0.849043i	$0.677180\pi$
$432$	1.25845e9	+	2.17969e9i	0.751003	+	1.30078i
$433$	1.16115e9	−	2.01117e9i	0.687354	−	1.19053i	−0.285336	−	0.958427i	$-0.592105\pi$
$433$	1.16115e9	−	2.01117e9i	0.687354	−	1.19053i	0.972691	−	0.232105i	$-0.0745614\pi$
$434$	−2.06702e9			−1.21375
$435$	−1.56566e9	+	2.71181e9i	−0.911981	+	1.57960i
$436$	−8.71939e8	+	1.51024e9i	−0.503829	+	0.872658i
$437$	−1.64167e8			−0.0941026
$438$	2.51629e8	−	4.35833e8i	0.143087	−	0.247834i
$439$	−8.56638e8	−	1.48374e9i	−0.483250	−	0.837013i	0.516565	−	0.856248i	$-0.327210\pi$
$439$	−8.56638e8	−	1.48374e9i	−0.483250	−	0.837013i	−0.999815	+	0.0192346i	$0.993877\pi$
$440$	−1.06903e8	−	1.85161e8i	−0.0598280	−	0.103625i
$441$	5.96993e8			0.331462
$442$	1.75670e9	−	1.95670e9i	0.967651	−	1.07782i
$443$	−3.57631e9			−1.95444			−0.977220	−	0.212231i	$-0.931927\pi$
$443$	−3.57631e9			−1.95444			−0.977220	+	0.212231i	$0.931927\pi$
$444$	2.60417e8	+	4.51055e8i	0.141198	+	0.244562i
$445$	5.96835e8	+	1.03375e9i	0.321066	+	0.556103i
$446$	−1.36275e9	+	2.36035e9i	−0.727350	+	1.25981i
$447$	4.81960e9			2.55232
$448$	−1.51980e9	+	2.63238e9i	−0.798572	+	1.38317i
$449$	−1.58206e9	+	2.74022e9i	−0.824825	+	1.42864i	0.0772279	+	0.997013i	$0.475393\pi$
$449$	−1.58206e9	+	2.74022e9i	−0.824825	+	1.42864i	−0.902053	+	0.431625i	$0.857940\pi$
$450$	5.30750e8			0.274566
$451$	1.28539e8	−	2.22636e8i	0.0659807	−	0.114282i
$452$	−1.44317e9	−	2.49965e9i	−0.735079	−	1.27319i
$453$	1.12733e9	+	1.95260e9i	0.569782	+	0.986891i
$454$	2.84481e9			1.42678
$455$	−6.90382e8	−	2.11436e9i	−0.343597	−	1.05230i
$456$	−2.76958e8			−0.136784
$457$	−7.31837e8	−	1.26758e9i	−0.358680	−	0.621253i	0.629060	−	0.777357i	$-0.283440\pi$
$457$	−7.31837e8	−	1.26758e9i	−0.358680	−	0.621253i	−0.987741	+	0.156104i	$0.950107\pi$
$458$	1.37390e9	+	2.37967e9i	0.668231	+	1.15741i
$459$	−2.51042e9	+	4.34817e9i	−1.21172	+	2.09876i
$460$	1.70655e9			0.817461
$461$	9.41849e8	−	1.63133e9i	0.447742	−	0.775512i	−0.550497	−	0.834837i	$-0.685562\pi$
$461$	9.41849e8	−	1.63133e9i	0.447742	−	0.775512i	0.998239	+	0.0593254i	$0.0188950\pi$
$462$	7.68861e8	−	1.33171e9i	0.362745	−	0.628292i
$463$	1.10589e9			0.517819			0.258910	−	0.965902i	$-0.416637\pi$
$463$	1.10589e9			0.517819			0.258910	+	0.965902i	$0.416637\pi$
$464$	6.07318e8	−	1.05191e9i	0.282230	−	0.488837i
$465$	−1.54675e9	−	2.67904e9i	−0.713401	−	1.23565i
$466$	−1.36346e9	−	2.36159e9i	−0.624156	−	1.08107i
$467$	−2.36571e9			−1.07486			−0.537431	−	0.843308i	$-0.680605\pi$
$467$	−2.36571e9			−1.07486			−0.537431	+	0.843308i	$0.680605\pi$
$468$	−6.78484e9	−	1.43190e9i	−3.05970	−	0.645732i
$469$	2.00605e9			0.897918
$470$	2.86817e9	+	4.96781e9i	1.27427	+	2.20710i
$471$	−1.51610e9	−	2.62596e9i	−0.668580	−	1.15801i
$472$	−3.09134e8	+	5.35436e8i	−0.135316	+	0.234374i
$473$	−7.64597e8			−0.332215
$474$	4.74307e8	−	8.21523e8i	0.204567	−	0.354320i
$475$	1.38632e7	−	2.40118e7i	0.00593520	−	0.0102801i
$476$	−3.13898e9			−1.33403
$477$	−2.59722e8	+	4.49851e8i	−0.109571	+	0.189782i
$478$	−1.67398e9	−	2.89942e9i	−0.701055	−	1.21426i
$479$	−7.54950e7	−	1.30761e8i	−0.0313866	−	0.0543632i	0.849905	−	0.526935i	$-0.176659\pi$
$479$	−7.54950e7	−	1.30761e8i	−0.0313866	−	0.0543632i	−0.881292	+	0.472572i	$0.843326\pi$
$480$	−6.34376e9			−2.61820
$481$	2.79418e8	+	5.89694e7i	0.114484	+	0.0241612i
$482$	5.06914e9			2.06191
$483$	1.45997e9	+	2.52874e9i	0.589561	+	1.02115i
$484$	1.53984e9	+	2.66707e9i	0.617328	+	1.06924i
$485$	1.48523e9	−	2.57250e9i	0.591151	−	1.02390i
$486$	6.46297e9			2.55391
$487$	−5.38511e7	+	9.32728e7i	−0.0211273	+	0.0365935i	−0.876396	−	0.481592i	$-0.840059\pi$
$487$	−5.38511e7	+	9.32728e7i	−0.0211273	+	0.0365935i	0.855268	+	0.518185i	$0.173392\pi$
$488$	8.12590e8	−	1.40745e9i	0.316521	−	0.548230i
$489$	2.38695e9			0.923128
$490$	−2.85631e8	+	4.94727e8i	−0.109678	+	0.189968i
$491$	−2.48626e8	−	4.30633e8i	−0.0947899	−	0.164181i	0.814731	−	0.579839i	$-0.196885\pi$
$491$	−2.48626e8	−	4.30633e8i	−0.0947899	−	0.164181i	−0.909521	+	0.415658i	$0.863551\pi$
$492$	1.73086e9	+	2.99794e9i	0.655215	+	1.13487i
$493$	2.42302e9			0.910738
$494$	−4.26430e8	+	4.74979e8i	−0.159149	+	0.177268i
$495$	1.62111e9			0.600752
$496$	5.99981e8	+	1.03920e9i	0.220776	+	0.382395i
$497$	−1.72518e9	−	2.98810e9i	−0.630357	−	1.09181i
$498$	−7.68341e8	+	1.33081e9i	−0.278773	+	0.482850i
$499$	1.84373e9			0.664272			0.332136	−	0.943231i	$-0.392231\pi$
$499$	1.84373e9			0.664272			0.332136	+	0.943231i	$0.392231\pi$
$500$	1.75790e9	−	3.04477e9i	0.628925	−	1.08933i
$501$	−1.50632e9	+	2.60903e9i	−0.535163	+	0.926929i
$502$	−7.48897e9			−2.64216
$503$	−2.53159e9	+	4.38484e9i	−0.886963	+	1.53626i	−0.0435159	+	0.999053i	$0.513856\pi$
$503$	−2.53159e9	+	4.38484e9i	−0.886963	+	1.53626i	−0.843447	+	0.537212i	$0.819477\pi$
$504$	1.73501e9	+	3.00512e9i	0.603663	+	1.04557i
$505$	1.35085e7	+	2.33973e7i	0.00466752	+	0.00808438i
$506$	6.46901e8			0.221979
$507$	−4.35743e9	+	3.18517e9i	−1.48492	+	1.08544i
$508$	5.63014e9			1.90544
$509$	−7.27907e8	−	1.26077e9i	−0.244660	−	0.423764i	0.717376	−	0.696687i	$-0.245343\pi$
$509$	−7.27907e8	−	1.26077e9i	−0.244660	−	0.423764i	−0.962036	+	0.272922i	$0.912010\pi$
$510$	−4.13898e9	−	7.16893e9i	−1.38165	−	2.39309i
$511$	−1.64695e8	+	2.85261e8i	−0.0546019	+	0.0945733i
$512$	3.31183e9			1.09049
$513$	6.09392e8	−	1.05550e9i	0.199290	−	0.345181i
$514$	3.02434e9	−	5.23831e9i	0.982334	−	1.70145i
$515$	5.56900e9			1.79660
$516$	5.14790e9	−	8.91642e9i	1.64951	−	2.85704i
$517$	6.17010e8	+	1.06869e9i	0.196370	+	0.340123i
$518$	−3.00345e8	−	5.20213e8i	−0.0949437	−	0.164447i
$519$	−5.47078e9			−1.71776
$520$	1.05457e9	−	1.17463e9i	0.328900	−	0.366346i
$521$	−3.76381e9			−1.16599			−0.582996	−	0.812475i	$-0.698120\pi$
$521$	−3.76381e9			−1.16599			−0.582996	+	0.812475i	$0.698120\pi$
$522$	−5.62956e9	−	9.75069e9i	−1.73232	−	3.00047i
$523$	2.75444e9	+	4.77084e9i	0.841934	+	1.45827i	0.888257	+	0.459346i	$0.151916\pi$
$523$	2.75444e9	+	4.77084e9i	0.841934	+	1.45827i	−0.0463231	+	0.998927i	$0.514750\pi$
$524$	−3.40244e9	+	5.89320e9i	−1.03307	+	1.78934i
$525$	−4.93151e8			−0.148738
$526$	−3.42775e9	+	5.93703e9i	−1.02697	+	1.77877i
$527$	−1.19687e9	+	2.07305e9i	−0.356214	+	0.616981i
$528$	−8.92689e8			−0.263926
$529$	1.08822e9	−	1.88486e9i	0.319612	−	0.553583i
$530$	−2.48528e8	−	4.30462e8i	−0.0725119	−	0.125594i
$531$	−2.34391e9	−	4.05977e9i	−0.679376	−	1.17671i
$532$	7.61973e8			0.219406
$533$	1.85715e9	+	3.91940e8i	0.531253	+	0.112118i
$534$	−6.09298e9			−1.73155
$535$	−2.59973e8	−	4.50286e8i	−0.0733990	−	0.127131i
$536$	7.11867e8	+	1.23299e9i	0.199674	+	0.345846i
$537$	2.75561e9	−	4.77286e9i	0.767905	−	1.33005i
$538$	−3.62994e9			−1.00499
$539$	−6.14460e7	+	1.06428e8i	−0.0169018	+	0.0292748i
$540$	−6.33475e9	+	1.09721e10i	−1.73122	+	2.99856i
$541$	5.39173e9			1.46399			0.731994	−	0.681311i	$-0.238590\pi$
$541$	5.39173e9			1.46399			0.731994	+	0.681311i	$0.238590\pi$
$542$	−3.16024e9	+	5.47369e9i	−0.852554	+	1.47667i
$543$	5.63582e7	+	9.76153e7i	0.0151063	+	0.0261649i
$544$	2.45441e9	+	4.25116e9i	0.653657	+	1.13217i
$545$	3.01004e9			0.796497
$546$	1.11086e10	+	2.34441e9i	2.92070	+	0.616395i
$547$	−2.68552e9			−0.701574			−0.350787	−	0.936455i	$-0.614086\pi$
$547$	−2.68552e9			−0.701574			−0.350787	+	0.936455i	$0.614086\pi$
$548$	1.63173e9	+	2.82625e9i	0.423562	+	0.733632i
$549$	6.16120e9	+	1.06715e10i	1.58914	+	2.75247i
$550$	−5.46279e7	+	9.46183e7i	−0.0140006	+	0.0242497i
$551$	−5.88177e8			−0.149788
$552$	−1.03617e9	+	1.79470e9i	−0.262207	+	0.454155i
$553$	−3.10442e8	+	5.37701e8i	−0.0780625	+	0.135208i
$554$	4.82339e9			1.20522
$555$	4.49495e8	−	7.78548e8i	0.111609	−	0.193312i
$556$	−4.12076e9	−	7.13736e9i	−1.01675	−	1.76107i
$557$	1.82610e9	+	3.16290e9i	0.447746	+	0.775518i	0.998239	−	0.0593215i	$-0.0188937\pi$
$557$	1.82610e9	+	3.16290e9i	0.447746	+	0.775518i	−0.550493	+	0.834840i	$0.685560\pi$
$558$	1.11231e10			2.71023
$559$	−1.75223e9	−	5.36635e9i	−0.424276	−	1.29939i
$560$	2.71602e9			0.653545
$561$	−8.90393e8	−	1.54221e9i	−0.212918	−	0.368784i
$562$	−5.60219e9	−	9.70327e9i	−1.33131	−	2.30590i
$563$	3.19629e8	−	5.53613e8i	0.0754860	−	0.130746i	−0.825811	−	0.563946i	$-0.809283\pi$
$563$	3.19629e8	−	5.53613e8i	0.0754860	−	0.130746i	0.901298	+	0.433201i	$0.142616\pi$
$564$	−1.66169e10			−3.90007
$565$	−2.49100e9	+	4.31454e9i	−0.581038	+	1.00639i
$566$	−1.34190e8	+	2.32423e8i	−0.0311072	+	0.0538793i
$567$	−1.06377e10			−2.45079
$568$	1.22439e9	−	2.12071e9i	0.280351	−	0.485581i
$569$	−1.30009e9	−	2.25182e9i	−0.295855	−	0.512437i	0.679328	−	0.733835i	$-0.262271\pi$
$569$	−1.30009e9	−	2.25182e9i	−0.295855	−	0.512437i	−0.975184	+	0.221398i	$0.928938\pi$
$570$	1.00472e9	+	1.74022e9i	0.227239	+	0.393589i
$571$	6.94810e8			0.156185			0.0780926	−	0.996946i	$-0.475117\pi$
$571$	6.94810e8			0.156185			0.0780926	+	0.996946i	$0.475117\pi$
$572$	9.53605e8	−	1.06217e9i	0.213050	−	0.237306i
$573$	−3.00972e9			−0.668321
$574$	−1.99624e9	−	3.45759e9i	−0.440577	−	0.763102i
$575$	−1.03731e8	−	1.79668e8i	−0.0227548	−	0.0394124i
$576$	8.17839e9	−	1.41654e10i	1.78316	−	3.08852i
$577$	−7.49430e9			−1.62411			−0.812056	−	0.583580i	$-0.801652\pi$
$577$	−7.49430e9			−1.62411			−0.812056	+	0.583580i	$0.801652\pi$
$578$	3.26863e8	−	5.66143e8i	0.0704074	−	0.121949i
$579$	8.50762e9	−	1.47356e10i	1.82152	−	3.15496i
$580$	6.11422e9			1.30120
$581$	5.02893e8	−	8.71036e8i	0.106380	−	0.184255i
$582$	7.58124e9	+	1.31311e10i	1.59408	+	2.76102i
$583$	−5.34642e7	−	9.26027e7i	−0.0111744	−	0.0193546i
$584$	−2.33775e8			−0.0485683
$585$	3.71510e9	+	1.13778e10i	0.767229	+	2.34971i
$586$	−5.78668e9			−1.18792
$587$	1.11394e9	+	1.92939e9i	0.227314	+	0.393720i	0.957011	−	0.290051i	$-0.0936722\pi$
$587$	1.11394e9	+	1.92939e9i	0.227314	+	0.393720i	−0.729697	+	0.683771i	$0.760339\pi$
$588$	−8.27410e8	−	1.43312e9i	−0.167842	−	0.290711i
$589$	2.90536e8	−	5.03222e8i	0.0585862	−	0.101474i
$590$	4.48577e9			0.899198
$591$	5.31449e9	−	9.20497e9i	1.05902	−	1.83428i
$592$	−1.74358e8	+	3.01997e8i	−0.0345396	+	0.0598243i
$593$	−2.90402e9			−0.571884			−0.285942	−	0.958247i	$-0.592306\pi$
$593$	−2.90402e9			−0.571884			−0.285942	+	0.958247i	$0.592306\pi$
$594$	−2.40131e9	+	4.15919e9i	−0.470106	+	0.814247i
$595$	2.70904e9	+	4.69219e9i	0.527236	+	0.913200i
$596$	−4.70537e9	−	8.14994e9i	−0.910399	−	1.57686i
$597$	6.90567e9			1.32830
$598$	1.48250e9	+	4.54030e9i	0.283492	+	0.868221i
$599$	2.97978e9			0.566487			0.283244	−	0.959048i	$-0.408590\pi$
$599$	2.97978e9			0.566487			0.283244	+	0.959048i	$0.408590\pi$
$600$	−1.75000e8	−	3.03108e8i	−0.0330756	−	0.0572886i
$601$	−1.25707e9	−	2.17732e9i	−0.236211	−	0.409130i	0.723413	−	0.690416i	$-0.242572\pi$
$601$	−1.25707e9	−	2.17732e9i	−0.236211	−	0.409130i	−0.959624	+	0.281286i	$0.909239\pi$
$602$	−5.93720e9	+	1.02835e10i	−1.10916	+	1.92112i
$603$	−1.07950e10			−2.00499
$604$	2.20123e9	−	3.81264e9i	0.406477	−	0.704038i
$605$	2.65785e9	−	4.60353e9i	0.487963	−	0.845176i
$606$	−1.37905e8			−0.0251726
$607$	3.99877e8	−	6.92608e8i	0.0725715	−	0.125698i	−0.827456	−	0.561530i	$-0.810213\pi$
$607$	3.99877e8	−	6.92608e8i	0.0725715	−	0.125698i	0.900028	+	0.435833i	$0.143546\pi$
$608$	−5.95795e8	−	1.03195e9i	−0.107506	−	0.186207i
$609$	5.23077e9	+	9.05995e9i	0.938436	+	1.62542i
$610$	−1.17913e10			−2.10333
$611$	−6.08666e9	+	6.77963e9i	−1.07953	+	1.20244i
$612$	1.68916e10			2.97879
$613$	−1.71337e9	−	2.96764e9i	−0.300427	−	0.520354i	0.675806	−	0.737080i	$-0.263796\pi$
$613$	−1.71337e9	−	2.96764e9i	−0.300427	−	0.520354i	−0.976233	+	0.216725i	$0.930462\pi$
$614$	−2.69629e9	−	4.67011e9i	−0.470086	−	0.814213i
$615$	2.98757e9	−	5.17462e9i	0.517911	−	0.897047i
$616$	−7.14309e8			−0.123127
$617$	3.17926e9	−	5.50664e9i	0.544914	−	0.943818i	−0.453699	−	0.891155i	$-0.649896\pi$
$617$	3.17926e9	−	5.50664e9i	0.544914	−	0.943818i	0.998612	−	0.0526631i	$-0.0167710\pi$
$618$	−1.42132e10	+	2.46180e10i	−2.42233	+	4.19560i
$619$	3.14173e9			0.532417			0.266209	−	0.963915i	$-0.414229\pi$
$619$	3.14173e9			0.532417			0.266209	+	0.963915i	$0.414229\pi$
$620$	−3.02017e9	+	5.23109e9i	−0.508933	+	0.881499i
$621$	−4.55978e9	−	7.89777e9i	−0.764053	−	1.32338i
$622$	6.53092e9	+	1.13119e10i	1.08820	+	1.88481i
$623$	3.98796e9			0.660759
$624$	−2.04578e9	−	6.26537e9i	−0.337064	−	1.03229i
$625$	−6.53093e9			−1.07003
$626$	1.04782e9	+	1.81488e9i	0.170717	+	0.295690i
$627$	2.16139e8	+	3.74363e8i	0.0350184	+	0.0606536i
$628$	−2.96032e9	+	5.12743e9i	−0.476958	+	0.826116i
$629$	−6.95639e8			−0.111457
$630$	1.25882e10	−	2.18033e10i	2.00572	−	3.47401i
$631$	−3.95935e9	+	6.85779e9i	−0.627366	+	1.08663i	0.360712	+	0.932677i	$0.382534\pi$
$631$	−3.95935e9	+	6.85779e9i	−0.627366	+	1.08663i	−0.988078	+	0.153953i	$0.950800\pi$
$632$	−4.40654e8			−0.0694364
$633$	3.03672e9	−	5.25976e9i	0.475875	−	0.824239i
$634$	−1.35150e9	−	2.34086e9i	−0.210621	−	0.364807i
$635$	−4.85898e9	−	8.41600e9i	−0.753073	−	1.30436i
$636$	1.43986e9			0.221932
$637$	−8.87782e8	−	1.87361e8i	−0.136087	−	0.0287204i
$638$	2.31771e9			0.353335
$639$	9.28356e9	+	1.60796e10i	1.40754	+	2.43794i
$640$	3.10591e9	+	5.37960e9i	0.468338	+	0.811185i
$641$	−3.40788e9	+	5.90262e9i	−0.511071	+	0.885201i	0.488847	+	0.872370i	$0.337418\pi$
$641$	−3.40788e9	+	5.90262e9i	−0.511071	+	0.885201i	−0.999918	+	0.0128313i	$0.995916\pi$
$642$	2.65402e9			0.395851
$643$	−3.11981e9	+	5.40368e9i	−0.462797	+	0.801588i	−0.999099	−	0.0424383i	$-0.986487\pi$
$643$	−3.11981e9	+	5.40368e9i	−0.462797	+	0.801588i	0.536302	+	0.844026i	$0.319821\pi$
$644$	2.85073e9	−	4.93761e9i	0.420587	−	0.728478i
$645$	−1.77712e10			−2.60770
$646$	7.77452e8	−	1.34659e9i	0.113464	−	0.196526i
$647$	−3.96320e8	−	6.86446e8i	−0.0575282	−	0.0996418i	0.835827	−	0.548993i	$-0.184989\pi$
$647$	−3.96320e8	−	6.86446e8i	−0.0575282	−	0.0996418i	−0.893355	+	0.449351i	$0.851655\pi$
$648$	−3.77488e9	−	6.53828e9i	−0.544993	−	0.943955i
$649$	9.64996e8			0.138570
$650$	−7.89273e8	−	1.66571e8i	−0.112728	−	0.0237905i
$651$	−1.03351e10			−1.46819
$652$	−2.33037e9	−	4.03632e9i	−0.329275	−	0.570321i
$653$	−6.27854e9	−	1.08748e10i	−0.882394	−	1.52835i	−0.848671	−	0.528921i	$-0.822597\pi$
$653$	−6.27854e9	−	1.08748e10i	−0.882394	−	1.52835i	−0.0337229	−	0.999431i	$-0.510736\pi$
$654$	−7.68224e9	+	1.33060e10i	−1.07390	+	1.86006i
$655$	1.17456e10			1.63317
$656$	−1.15887e9	+	2.00723e9i	−0.160277	+	0.277609i
$657$	8.86262e8	−	1.53505e9i	0.121922	−	0.211176i
$658$	1.91647e10			2.62247
$659$	2.45714e9	−	4.25588e9i	0.334449	−	0.579283i	−0.648930	−	0.760848i	$-0.724783\pi$
$659$	2.45714e9	−	4.25588e9i	0.334449	−	0.579283i	0.983379	+	0.181565i	$0.0581164\pi$
$660$	−2.24680e9	−	3.89158e9i	−0.304201	−	0.526892i
$661$	−1.83473e9	−	3.17784e9i	−0.247096	−	0.427983i	0.715623	−	0.698487i	$-0.246143\pi$
$661$	−1.83473e9	−	3.17784e9i	−0.247096	−	0.427983i	−0.962719	+	0.270504i	$0.912810\pi$
$662$	1.23264e10			1.65132
$663$	8.78351e9	−	9.78352e9i	1.17050	−	1.30376i
$664$	7.13826e8			0.0946246
$665$	−6.57605e8	−	1.13901e9i	−0.0867141	−	0.150193i
$666$	1.61622e9	+	2.79938e9i	0.212003	+	0.367200i
$667$	−2.20052e9	+	3.81141e9i	−0.287134	+	0.497331i
$668$	5.88248e9			0.763560
$669$	−6.81375e9	+	1.18018e10i	−0.879823	+	1.52390i
$670$	5.16487e9	−	8.94581e9i	0.663434	−	1.14910i
$671$	−2.53659e9			−0.324132
$672$	−1.05970e10	+	1.83546e10i	−1.34707	+	2.33320i
$673$	4.03822e9	+	6.99440e9i	0.510666	+	0.884499i	0.999924	+	0.0123600i	$0.00393440\pi$
$673$	4.03822e9	+	6.99440e9i	0.510666	+	0.884499i	−0.489258	+	0.872139i	$0.662732\pi$
$674$	−1.04253e10	−	1.80572e10i	−1.31154	−	2.27165i
$675$	1.54021e9			0.192760
$676$	9.64028e9	+	4.25873e9i	1.20026	+	0.530233i
$677$	−1.20647e8			−0.0149437			−0.00747183	−	0.999972i	$-0.502378\pi$
$677$	−1.20647e8			−0.0149437			−0.00747183	+	0.999972i	$0.502378\pi$
$678$	−1.27151e10	−	2.20232e10i	−1.56681	−	2.71379i
$679$	−4.96205e9	−	8.59453e9i	−0.608299	−	1.05360i
$680$	−1.92266e9	+	3.33014e9i	−0.234488	+	0.406145i
$681$	1.42241e10			1.72588
$682$	−1.14485e9	+	1.98295e9i	−0.138199	+	0.239368i
$683$	−4.24151e8	+	7.34651e8i	−0.0509387	+	0.0882285i	−0.890370	−	0.455237i	$-0.849555\pi$
$683$	−4.24151e8	+	7.34651e8i	−0.0509387	+	0.0882285i	0.839432	+	0.543465i	$0.182888\pi$
$684$	−4.10034e9			−0.489919
$685$	2.81647e9	−	4.87827e9i	0.334802	−	0.579894i
$686$	−5.90680e9	−	1.02309e10i	−0.698582	−	1.20998i
$687$	6.86953e9	+	1.18984e10i	0.808311	+	1.40004i
$688$	6.89341e9			0.807001
$689$	5.27411e8	−	5.87458e8i	0.0614302	−	0.0684241i
$690$	1.50356e10			1.74241
$691$	5.44807e9	+	9.43634e9i	0.628159	+	1.08800i	0.987921	+	0.154959i	$0.0495247\pi$
$691$	5.44807e9	+	9.43634e9i	0.628159	+	1.08800i	−0.359762	+	0.933044i	$0.617142\pi$
$692$	5.34111e9	+	9.25108e9i	0.612718	+	1.06126i
$693$	2.70801e9	−	4.69041e9i	0.309089	−	0.535358i
$694$	7.84106e9			0.890464
$695$	−7.11268e9	+	1.23195e10i	−0.803686	+	1.39202i
$696$	−3.71238e9	+	6.43003e9i	−0.417369	+	0.722904i
$697$	−4.62356e9			−0.517204
$698$	1.54899e9	−	2.68293e9i	0.172407	−	0.298618i
$699$	−6.81734e9	−	1.18080e10i	−0.754997	−	1.30769i
$700$	4.81463e8	+	8.33918e8i	0.0530542	+	0.0918926i
$701$	1.65855e10			1.81851			0.909254	−	0.416241i	$-0.136653\pi$
$701$	1.65855e10			1.81851			0.909254	+	0.416241i	$0.136653\pi$
$702$	−3.46945e10	−	7.32207e9i	−3.78513	−	0.798829i
$703$	1.68863e8			0.0183312
$704$	1.68354e9	+	2.91597e9i	0.181852	+	0.314977i
$705$	1.43409e10	+	2.48391e10i	1.54139	+	2.66977i
$706$	7.98149e9	−	1.38243e10i	0.853626	−	1.47852i
$707$	9.02615e7			0.00960583
$708$	−6.49715e9	+	1.12534e10i	−0.688028	+	1.19170i
$709$	−1.80022e9	+	3.11807e9i	−0.189698	+	0.328567i	−0.945150	−	0.326638i	$-0.894084\pi$
$709$	−1.80022e9	+	3.11807e9i	−0.189698	+	0.328567i	0.755451	+	0.655205i	$0.227418\pi$
$710$	−1.77669e10			−1.86297
$711$	1.67056e9	−	2.89349e9i	0.174308	−	0.301911i
$712$	1.41517e9	+	2.45114e9i	0.146936	+	0.254501i
$713$	−2.17393e9	−	3.76536e9i	−0.224612	−	0.389039i
$714$	−2.76561e10			−2.84346
$715$	−2.41074e9	−	5.08772e8i	−0.246649	−	0.0520538i
$716$	−1.07612e10			−1.09563
$717$	−8.36992e9	−	1.44971e10i	−0.848016	−	1.46881i
$718$	−5.49428e8	−	9.51638e8i	−0.0553956	−	0.0959481i
$719$	−1.54699e9	+	2.67946e9i	−0.155216	+	0.268841i	−0.933138	−	0.359520i	$-0.882941\pi$
$719$	−1.54699e9	+	2.67946e9i	−0.155216	+	0.268841i	0.777922	+	0.628361i	$0.216274\pi$
$720$	−1.46155e10			−1.45932
$721$	9.30280e9	−	1.61129e10i	0.924358	−	1.60104i
$722$	7.50010e9	−	1.29905e10i	0.741629	−	1.28454i
$723$	2.53458e10			2.49414
$724$	1.10045e8	−	1.90603e8i	0.0107767	−	0.0186657i
$725$	−3.71648e8	−	6.43713e8i	−0.0362200	−	0.0627349i
$726$	1.35668e10	+	2.34983e10i	1.31583	+	2.27908i
$727$	−1.53270e10			−1.47940			−0.739700	−	0.672937i	$-0.765032\pi$
$727$	−1.53270e10			−1.47940			−0.739700	+	0.672937i	$0.765032\pi$
$728$	−1.63698e9	−	5.01340e9i	−0.157247	−	0.481585i
$729$	8.29488e9			0.792983
$730$	8.48064e8	+	1.46889e9i	0.0806861	+	0.139752i
$731$	6.87567e9	+	1.19090e10i	0.651035	+	1.12763i
$732$	1.70784e10	−	2.95807e10i	1.60938	−	2.78753i
$733$	−1.32913e9			−0.124654			−0.0623268	−	0.998056i	$-0.519852\pi$
$733$	−1.32913e9			−0.124654			−0.0623268	+	0.998056i	$0.519852\pi$
$734$	−9.17855e9	+	1.58977e10i	−0.856718	+	1.48388i
$735$	−1.42816e9	+	2.47365e9i	−0.132669	+	0.229790i
$736$	−8.91608e9			−0.824331
$737$	1.11109e9	−	1.92446e9i	0.102238	−	0.177081i
$738$	1.07422e10	+	1.86061e10i	0.983778	+	1.70395i
$739$	7.61695e9	+	1.31929e10i	0.694265	+	1.20250i	0.970428	+	0.241392i	$0.0776038\pi$
$739$	7.61695e9	+	1.31929e10i	0.694265	+	1.20250i	−0.276163	+	0.961111i	$0.589063\pi$
$740$	−1.75536e9			−0.159242
$741$	−2.13216e9	+	2.37490e9i	−0.192511	+	0.214428i
$742$	−1.66063e9			−0.149231
$743$	−1.23089e9	−	2.13196e9i	−0.110092	−	0.190686i	0.805715	−	0.592303i	$-0.201781\pi$
$743$	−1.23089e9	−	2.13196e9i	−0.110092	−	0.190686i	−0.915807	+	0.401618i	$0.868448\pi$
$744$	−3.66753e9	−	6.35234e9i	−0.326488	−	0.565495i
$745$	−8.12175e9	+	1.40673e10i	−0.719619	+	1.24642i
$746$	1.08720e10			0.958794
$747$	−2.70618e9	+	4.68724e9i	−0.237539	+	0.411429i
$748$	−1.73858e9	+	3.01131e9i	−0.151893	+	0.263087i
$749$	−1.73710e9			−0.151056
$750$	1.54880e10	−	2.68260e10i	1.34054	−	2.32189i
$751$	−1.17502e9	−	2.03520e9i	−0.101229	−	0.175335i	0.810962	−	0.585099i	$-0.198944\pi$
$751$	−1.17502e9	−	2.03520e9i	−0.101229	−	0.175335i	−0.912191	+	0.409764i	$0.865611\pi$
$752$	−5.56280e9	−	9.63506e9i	−0.477014	−	0.826213i
$753$	−3.74450e10			−3.19603
$754$	5.31150e9	+	1.62669e10i	0.451250	+	1.38199i
$755$	−7.59890e9			−0.642594
$756$	2.11639e10	+	3.66570e10i	1.78144	+	3.08554i
$757$	−3.93756e9	−	6.82005e9i	−0.329907	−	0.571416i	0.652586	−	0.757715i	$-0.273684\pi$
$757$	−3.93756e9	−	6.82005e9i	−0.329907	−	0.571416i	−0.982493	+	0.186299i	$0.940351\pi$
$758$	−4.64643e9	+	8.04785e9i	−0.387505	+	0.671178i
$759$	3.23452e9			0.268512
$760$	4.66715e8	−	8.08375e8i	0.0385660	−	0.0667983i
$761$	−4.81110e9	+	8.33306e9i	−0.395729	+	0.685423i	−0.993194	−	0.116472i	$-0.962841\pi$
$761$	−4.81110e9	+	8.33306e9i	−0.395729	+	0.685423i	0.597465	+	0.801895i	$0.296175\pi$
$762$	4.96045e10			4.06142
$763$	5.02816e9	−	8.70903e9i	0.409801	−	0.709796i
$764$	2.93839e9	+	5.08944e9i	0.238387	+	0.412898i
$765$	−1.45779e10	−	2.52497e10i	−1.17728	−	2.03911i
$766$	−2.06528e10			−1.66027
$767$	2.21148e9	+	6.77286e9i	0.176970	+	0.541986i
$768$	2.84575e9			0.226690
$769$	8.34716e9	+	1.44577e10i	0.661906	+	1.14646i	0.980114	+	0.198435i	$0.0635858\pi$
$769$	8.34716e9	+	1.44577e10i	0.661906	+	1.14646i	−0.318208	+	0.948021i	$0.603081\pi$
$770$	2.59129e9	+	4.48825e9i	0.204550	+	0.354291i
$771$	1.51217e10	−	2.61916e10i	1.18826	−	2.05813i
$772$	−3.32239e10			−2.59890
$773$	5.24643e9	−	9.08708e9i	0.408541	−	0.707613i	−0.586186	−	0.810177i	$-0.699371\pi$
$773$	5.24643e9	−	9.08708e9i	0.408541	−	0.707613i	0.994726	+	0.102563i	$0.0327045\pi$
$774$	3.19494e10	−	5.53379e10i	2.47668	−	4.28973i
$775$	7.34316e8			0.0566665
$776$	3.52167e9	−	6.09970e9i	0.270540	−	0.468590i
$777$	−1.50173e9	−	2.60107e9i	−0.114847	−	0.198920i
$778$	−3.62062e9	−	6.27110e9i	−0.275648	−	0.477436i
$779$	1.12235e9			0.0850641
$780$	2.21642e10	−	2.46876e10i	1.67232	−	1.86272i
$781$	−3.82208e9			−0.287092
$782$	−5.81728e9	−	1.00758e10i	−0.435007	−	0.753455i
$783$	−1.63367e10	−	2.82961e10i	−1.21618	−	2.10649i
$784$	5.53981e8	−	9.59523e8i	0.0410571	−	0.0711130i
$785$	1.02194e10			0.754018
$786$	−2.99773e10	+	5.19222e10i	−2.20198	+	3.81394i
$787$	−2.95328e9	+	5.11523e9i	−0.215970	+	0.374071i	−0.953572	−	0.301165i	$-0.902625\pi$
$787$	−2.95328e9	+	5.11523e9i	−0.215970	+	0.374071i	0.737602	+	0.675235i	$0.235958\pi$
$788$	−2.07541e10			−1.51099
$789$	−1.71388e10	+	2.96853e10i	−1.24225	+	2.15165i
$790$	1.59856e9	+	2.76878e9i	0.115354	+	0.199799i
$791$	8.32226e9	+	1.44146e10i	0.597893	+	1.03558i
$792$	3.84385e9			0.274934
$793$	−5.81310e9	−	1.78031e10i	−0.413954	−	1.26777i
$794$	3.08892e10			2.18995
$795$	−1.24264e9	−	2.15232e9i	−0.0877124	−	0.151922i
$796$	−6.74199e9	−	1.16775e10i	−0.473797	−	0.820641i
$797$	7.90143e9	−	1.36857e10i	0.552843	−	0.957552i	−0.445225	−	0.895419i	$-0.646876\pi$
$797$	7.90143e9	−	1.36857e10i	0.552843	−	0.957552i	0.998068	−	0.0621332i	$-0.0197904\pi$
$798$	6.71338e9			0.467661
$799$	1.10970e10	−	1.92205e10i	0.769646	−	1.33307i
$800$	7.52923e8	−	1.30410e9i	0.0519919	−	0.0900526i
$801$	−2.14601e10			−1.47543
$802$	−2.75979e9	+	4.78009e9i	−0.188915	+	0.327210i
$803$	1.82439e8	+	3.15993e8i	0.0124340	+	0.0215364i
$804$	1.49615e10	+	2.59140e10i	1.01526	+	1.75849i
$805$	−9.84107e9			−0.664900
$806$	−1.65410e10	−	3.49089e9i	−1.11273	−	0.234835i
$807$	−1.81497e10			−1.21566
$808$	3.20302e7	+	5.54779e7i	0.00213609	+	0.00369982i
$809$	5.09883e9	+	8.83143e9i	0.338572	+	0.586423i	0.984164	−	0.177259i	$-0.0567230\pi$
$809$	5.09883e9	+	8.83143e9i	0.338572	+	0.586423i	−0.645593	+	0.763682i	$0.723390\pi$
$810$	−2.73882e10	+	4.74378e10i	−1.81078	+	3.13637i
$811$	2.34048e8			0.0154075			0.00770375	−	0.999970i	$-0.497548\pi$
$811$	2.34048e8			0.0154075			0.00770375	+	0.999970i	$0.497548\pi$
$812$	1.02136e10	−	1.76904e10i	0.669471	−	1.15956i
$813$	−1.58012e10	+	2.73685e10i	−1.03127	+	1.78622i
$814$	−6.65405e8			−0.0432415
$815$	−4.02236e9	+	6.96694e9i	−0.260273	+	0.450807i
$816$	8.02755e9	+	1.39041e10i	0.517210	+	0.895835i
$817$	−1.66904e9	−	2.89086e9i	−0.107075	−	0.185460i
$818$	3.11683e10			1.99102
$819$	3.91257e10	+	8.25725e9i	2.48868	+	0.525221i
$820$	−1.16670e10			−0.738944
$821$	4.46483e9	+	7.73332e9i	0.281581	+	0.487713i	0.971774	−	0.235912i	$-0.0758077\pi$
$821$	4.46483e9	+	7.73332e9i	0.281581	+	0.487713i	−0.690193	+	0.723625i	$0.742474\pi$
$822$	1.43764e10	+	2.49007e10i	0.902817	+	1.56373i
$823$	3.53313e9	−	6.11957e9i	0.220933	−	0.382667i	−0.734159	−	0.678978i	$-0.762423\pi$
$823$	3.53313e9	−	6.11957e9i	0.220933	−	0.382667i	0.955092	+	0.296311i	$0.0957565\pi$
$824$	1.32048e10			0.822215
$825$	−2.73140e8	+	4.73093e8i	−0.0169355	+	0.0293331i
$826$	7.49332e9	−	1.29788e10i	0.462641	−	0.801318i
$827$	1.30769e10			0.803965			0.401982	−	0.915647i	$-0.368321\pi$
$827$	1.30769e10			0.803965			0.401982	+	0.915647i	$0.368321\pi$
$828$	−1.53404e10	+	2.65704e10i	−0.939141	+	1.62664i
$829$	8.89000e9	+	1.53979e10i	0.541952	+	0.938689i	0.998792	+	0.0491399i	$0.0156480\pi$
$829$	8.89000e9	+	1.53979e10i	0.541952	+	0.938689i	−0.456840	+	0.889549i	$0.651019\pi$
$830$	−2.58954e9	−	4.48522e9i	−0.157199	−	0.272276i
$831$	2.41170e10			1.45787
$832$	−1.66077e10	+	1.84985e10i	−0.999718	+	1.11354i
$833$	2.21022e9			0.132489
$834$	−3.63061e10	−	6.28839e10i	−2.16719	−	3.75369i
$835$	−5.07676e9	−	8.79321e9i	−0.301775	−	0.522690i
$836$	4.22032e8	−	7.30980e8i	0.0249818	−	0.0432697i
$837$	3.22787e10			1.90273
$838$	5.31084e9	−	9.19865e9i	0.311752	−	0.539971i
$839$	−1.50434e10	+	2.60559e10i	−0.879385	+	1.52314i	−0.0273674	+	0.999625i	$0.508712\pi$
$839$	−1.50434e10	+	2.60559e10i	−0.879385	+	1.52314i	−0.852017	+	0.523514i	$0.824621\pi$
$840$	−1.66023e10			−0.966477
$841$	7.40939e8	−	1.28334e9i	0.0429533	−	0.0743972i
$842$	1.23402e10	+	2.13738e10i	0.712409	+	1.23393i
$843$	−2.80110e10	−	4.85165e10i	−1.61040	−	2.78929i
$844$	−1.18590e10			−0.678968
$845$	−1.95385e9	−	1.80858e10i	−0.111402	−	1.03119i
$846$	−1.03129e11			−5.85580
$847$	−8.87968e9	−	1.53801e10i	−0.502118	−	0.869693i
$848$	4.82019e8	+	8.34881e8i	0.0271443	+	0.0470153i
$849$	−6.70950e8	+	1.16212e9i	−0.0376282	+	0.0651739i
$850$	1.96497e9			0.109746
$851$	6.31759e8	−	1.09424e9i	0.0351397	−	0.0608638i
$852$	2.57334e10	−	4.45715e10i	1.42547	−	2.46899i
$853$	3.19904e9			0.176481			0.0882405	−	0.996099i	$-0.471876\pi$
$853$	3.19904e9			0.176481			0.0882405	+	0.996099i	$0.471876\pi$
$854$	−1.96970e10	+	3.41161e10i	−1.08217	+	1.87438i
$855$	3.53872e9	+	6.12924e9i	0.193627	+	0.335371i
$856$	−6.16427e8	−	1.06768e9i	−0.0335911	−	0.0581814i
$857$	−2.71025e9			−0.147088			−0.0735440	−	0.997292i	$-0.523431\pi$
$857$	−2.71025e9			−0.147088			−0.0735440	+	0.997292i	$0.523431\pi$
$858$	8.40176e9	−	9.35831e9i	0.454114	−	0.505815i
$859$	3.46967e10			1.86772			0.933860	−	0.357640i	$-0.116418\pi$
$859$	3.46967e10			1.86772			0.933860	+	0.357640i	$0.116418\pi$
$860$	1.73500e10	+	3.00510e10i	0.930152	+	1.61107i
$861$	−9.98124e9	−	1.72880e10i	−0.532934	−	0.923069i
$862$	1.34718e10	−	2.33338e10i	0.716391	−	1.24083i
$863$	9.27631e9			0.491289			0.245645	−	0.969360i	$-0.421000\pi$
$863$	9.27631e9			0.491289			0.245645	+	0.969360i	$0.421000\pi$
$864$	3.30967e10	−	5.73251e10i	1.74577	−	3.02376i
$865$	9.21908e9	−	1.59679e10i	0.484319	−	0.838865i
$866$	−3.99515e10			−2.09036
$867$	1.63432e9	−	2.83073e9i	0.0851668	−	0.147513i
$868$	1.00902e10	+	1.74767e10i	0.523697	+	0.907069i
$869$	3.43887e8	+	5.95630e8i	0.0177765	+	0.0307898i
$870$	5.38695e10			2.77348
$871$	1.60531e10	+	3.38792e9i	0.823183	+	0.173728i
$872$	7.13717e9			0.364517
$873$	2.67019e10	+	4.62491e10i	1.35829	+	2.35263i
$874$	1.41212e9	+	2.44586e9i	0.0715453	+	0.123920i
$875$	−1.01372e10	+	1.75581e10i	−0.511550	+	0.886031i
$876$	−4.91331e9			−0.246950
$877$	2.24440e9	−	3.88742e9i	0.112358	−	0.194609i	−0.804363	−	0.594138i	$-0.797493\pi$
$877$	2.24440e9	−	3.88742e9i	0.112358	−	0.194609i	0.916720	+	0.399529i	$0.130826\pi$
$878$	−1.47371e10	+	2.55254e10i	−0.734820	+	1.27275i
$879$	−2.89335e10			−1.43694
$880$	1.50432e9	−	2.60555e9i	0.0744131	−	0.128887i
$881$	−7.54359e9	−	1.30659e10i	−0.371674	−	0.643758i	0.618149	−	0.786061i	$-0.287883\pi$
$881$	−7.54359e9	−	1.30659e10i	−0.371674	−	0.643758i	−0.989823	+	0.142302i	$0.954549\pi$
$882$	−5.13515e9	−	8.89434e9i	−0.252007	−	0.436490i
$883$	−1.92130e10			−0.939147			−0.469573	−	0.882893i	$-0.655592\pi$
$883$	−1.92130e10			−0.939147			−0.469573	+	0.882893i	$0.655592\pi$
$884$	−2.51193e10	−	5.30127e9i	−1.22299	−	0.258105i
$885$	2.24289e10			1.08770
$886$	3.07624e10	+	5.32820e10i	1.48594	+	2.57372i
$887$	5.60414e9	+	9.70665e9i	0.269635	+	0.467021i	0.968768	−	0.247971i	$-0.0797637\pi$
$887$	5.60414e9	+	9.70665e9i	0.269635	+	0.467021i	−0.699133	+	0.714992i	$0.746430\pi$
$888$	1.06581e9	−	1.84603e9i	0.0510779	−	0.0884695i
$889$	−3.24670e10			−1.54984
$890$	1.02676e10	−	1.77840e10i	0.488207	−	0.845599i
$891$	−5.89185e9	+	1.02050e10i	−0.279049	+	0.483326i
$892$	2.66090e10			1.25531
$893$	−2.69374e9	+	4.66569e9i	−0.126583	+	0.219248i
$894$	−4.14568e10	−	7.18052e10i	−1.94050	−	3.36105i
$895$	9.28723e9	+	1.60860e10i	0.433018	+	0.750009i
$896$	2.07532e10			0.963847
$897$	7.41254e9	+	2.27016e10i	0.342920	+	1.05022i
$898$	5.44338e10			2.50843
$899$	−7.78875e9	−	1.34905e10i	−0.357527	−	0.619255i
$900$	−2.59086e9	−	4.48750e9i	−0.118466	−	0.205190i
$901$	−9.61558e8	+	1.66547e9i	−0.0437964	+	0.0758576i
$902$	−4.42261e9			−0.200658
$903$	−2.96861e10	+	5.14178e10i	−1.34167	+	2.32384i
$904$	−5.90647e9	+	1.02303e10i	−0.265912	+	0.460574i
$905$	−3.79888e8			−0.0170367
$906$	1.93940e10	−	3.35913e10i	0.866399	−	1.50065i
$907$	−7.29029e9	−	1.26271e10i	−0.324429	−	0.561927i	0.656968	−	0.753918i	$-0.271839\pi$
$907$	−7.29029e9	−	1.26271e10i	−0.324429	−	0.561927i	−0.981397	+	0.191992i	$0.938505\pi$
$908$	−1.38870e10	−	2.40529e10i	−0.615612	−	1.06627i
$909$	−4.85717e8			−0.0214491
$910$	−2.55625e10	+	2.84728e10i	−1.12450	+	1.25252i
$911$	8.97962e9			0.393499			0.196749	−	0.980454i	$-0.436961\pi$
$911$	8.97962e9			0.393499			0.196749	+	0.980454i	$0.436961\pi$
$912$	−1.94865e9	−	3.37516e9i	−0.0850651	−	0.147337i
$913$	−5.57071e8	−	9.64876e8i	−0.0242250	−	0.0419589i
$914$	−1.25901e10	+	2.18067e10i	−0.545402	+	0.944665i
$915$	−5.89567e10			−2.54425
$916$	1.34134e10	−	2.32327e10i	0.576641	−	0.998772i
$917$	1.96207e10	−	3.39840e10i	0.840274	−	1.45540i
$918$	8.63755e10			3.68503
$919$	1.23401e10	−	2.13737e10i	0.524464	−	0.908398i	−0.475130	−	0.879915i	$-0.657599\pi$
$919$	1.23401e10	−	2.13737e10i	0.524464	−	0.908398i	0.999594	−	0.0284828i	$-0.00906757\pi$
$920$	−3.49220e9	−	6.04867e9i	−0.147857	−	0.256096i
$921$	−1.34815e10	−	2.33506e10i	−0.568629	−	0.984895i
$922$	−3.24060e10			−1.36166
$923$	−8.75905e9	−	2.68254e10i	−0.366649	−	1.12290i
$924$	−1.50128e10			−0.626052
$925$	1.06698e8	+	1.84807e8i	0.00443264	+	0.00767755i
$926$	−9.51253e9	−	1.64762e10i	−0.393693	−	0.681896i
$927$	−5.00604e10	+	8.67072e10i	−2.06403	+	3.57500i
$928$	−3.19445e10			−1.31213
$929$	1.65131e10	−	2.86014e10i	0.675729	−	1.17040i	−0.300527	−	0.953773i	$-0.597162\pi$
$929$	1.65131e10	−	2.86014e10i	0.675729	−	1.17040i	0.976255	−	0.216623i	$-0.0695042\pi$
$930$	−2.66093e10	+	4.60887e10i	−1.08478	+	1.87890i
$931$	−5.36521e8			−0.0217903
$932$	−1.33115e10	+	2.30562e10i	−0.538607	+	0.932895i
$933$	3.26547e10	+	5.65596e10i	1.31631	+	2.27992i
$934$	2.03492e10	+	3.52458e10i	0.817207	+	1.41544i
$935$	6.00178e9			0.240126
$936$	8.80896e9	+	2.69782e10i	0.351123	+	1.07535i
$937$	−7.49732e9			−0.297727			−0.148863	−	0.988858i	$-0.547561\pi$
$937$	−7.49732e9			−0.297727			−0.148863	+	0.988858i	$0.547561\pi$
$938$	−1.72554e10	−	2.98873e10i	−0.682679	−	1.18243i
$939$	5.23911e9	+	9.07441e9i	0.206504	+	0.357675i
$940$	2.80020e10	−	4.85008e10i	1.09962	−	1.90459i
$941$	1.60185e10			0.626697			0.313349	−	0.949638i	$-0.398549\pi$
$941$	1.60185e10			0.626697			0.313349	+	0.949638i	$0.398549\pi$
$942$	−2.60820e10	+	4.51754e10i	−1.01663	+	1.76085i
$943$	4.19899e9	−	7.27286e9i	0.163062	−	0.282432i
$944$	−8.70015e9			−0.336608
$945$	3.65302e10	−	6.32722e10i	1.40813	−	2.43894i
$946$	6.57684e9	+	1.13914e10i	0.252579	+	0.437481i
$947$	1.20737e9	+	2.09123e9i	0.0461973	+	0.0800160i	0.888199	−	0.459458i	$-0.151956\pi$
$947$	1.20737e9	+	2.09123e9i	0.0461973	+	0.0800160i	−0.842002	+	0.539474i	$0.818623\pi$
$948$	−9.26133e9			−0.353056
$949$	−1.79971e9	+	2.00461e9i	−0.0683552	+	0.0761375i
$950$	−4.76988e8			−0.0180499
$951$	−6.75750e9	−	1.17043e10i	−0.254774	−	0.441281i
$952$	6.42345e9	+	1.11257e10i	0.241290	+	0.417926i
$953$	1.78096e10	−	3.08471e10i	0.666543	−	1.15449i	−0.312322	−	0.949976i	$-0.601107\pi$
$953$	1.78096e10	−	3.08471e10i	0.666543	−	1.15449i	0.978865	−	0.204509i	$-0.0655599\pi$
$954$	8.93619e9			0.333222
$955$	5.07184e9	−	8.78468e9i	0.188431	−	0.326373i
$956$	−1.63431e10	+	2.83070e10i	−0.604966	+	1.04783i
$957$	1.15886e10			0.427404
$958$	−1.29877e9	+	2.24954e9i	−0.0477258	+	0.0826636i
$959$	−9.40963e9	−	1.62979e10i	−0.344514	−	0.596716i
$960$	3.91296e10	+	6.77745e10i	1.42744	+	2.47239i
$961$	−1.21233e10			−0.440646
$962$	−1.52491e9	−	4.67017e9i	−0.0552244	−	0.169130i
$963$	9.34773e9			0.337298
$964$	−2.47450e10	−	4.28597e10i	−0.889649	−	1.54092i
$965$	2.86732e10	+	4.96635e10i	1.02714	+	1.77906i
$966$	2.51164e10	−	4.35029e10i	0.896475	−	1.55274i
$967$	−3.92427e10			−1.39562			−0.697808	−	0.716285i	$-0.745841\pi$
$967$	−3.92427e10			−1.39562			−0.697808	+	0.716285i	$0.745841\pi$
$968$	6.30209e9	−	1.09155e10i	0.223316	−	0.386795i
$969$	3.88727e9	−	6.73295e9i	0.137250	−	0.237724i
$970$	−5.11021e10			−1.79778
$971$	−3.61767e9	+	6.26599e9i	−0.126813	+	0.219646i	−0.922440	−	0.386141i	$-0.873808\pi$
$971$	−3.61767e9	+	6.26599e9i	−0.126813	+	0.219646i	0.795627	+	0.605786i	$0.207141\pi$
$972$	−3.15490e10	−	5.46445e10i	−1.10193	−	1.90860i
$973$	2.37629e10	+	4.11586e10i	0.826999	+	1.43241i
$974$	1.85284e9			0.0642514
$975$	−3.94638e9	−	8.32859e8i	−0.136358	−	0.0287776i
$976$	2.28692e10			0.787367
$977$	−1.65391e10	−	2.86466e10i	−0.567391	−	0.982749i	−0.996823	−	0.0796503i	$-0.974620\pi$
$977$	−1.65391e10	−	2.86466e10i	−0.567391	−	0.982749i	0.429432	−	0.903099i	$-0.358714\pi$
$978$	−2.05318e10	−	3.55621e10i	−0.701845	−	1.21563i
$979$	2.20880e9	−	3.82576e9i	0.0752346	−	0.130310i
$980$	5.57724e9			0.189290
$981$	−2.70576e10	+	4.68652e10i	−0.915058	+	1.58493i
$982$	−4.27722e9	+	7.40836e9i	−0.144136	+	0.249650i
$983$	4.64468e9			0.155962			0.0779809	−	0.996955i	$-0.475153\pi$
$983$	4.64468e9			0.155962			0.0779809	+	0.996955i	$0.475153\pi$
$984$	7.08388e9	−	1.22696e10i	0.237022	−	0.410534i
$985$	1.79114e10	+	3.10235e10i	0.597177	+	1.03434i
$986$	−2.08421e10	−	3.60996e10i	−0.692425	−	1.19932i
$987$	9.58236e10			3.17222
$988$	6.09758e9	+	1.28686e9i	0.201145	+	0.0424503i
$989$	−2.49771e10			−0.821024
$990$	−1.39443e10	−	2.41523e10i	−0.456746	−	0.791106i
$991$	3.88362e9	+	6.72663e9i	0.126759	+	0.219553i	0.922419	−	0.386190i	$-0.126209\pi$
$991$	3.88362e9	+	6.72663e9i	0.126759	+	0.219553i	−0.795660	+	0.605743i	$0.792876\pi$
$992$	1.57793e10	−	2.73305e10i	0.513211	−	0.888907i
$993$	6.16320e10			1.99749
$994$	−2.96789e10	+	5.14054e10i	−0.958508	+	1.66018i
$995$	−1.16371e10	+	2.01560e10i	−0.374510	+	0.648671i
$996$	1.50027e10			0.481128
$997$	1.66431e10	−	2.88266e10i	0.531864	−	0.921215i	−0.467444	−	0.884023i	$-0.654825\pi$
$997$	1.66431e10	−	2.88266e10i	0.531864	−	0.921215i	0.999308	−	0.0371926i	$-0.0118415\pi$
$998$	−1.58592e10	−	2.74690e10i	−0.505040	−	0.874754i
$999$	4.69021e9	+	8.12368e9i	0.148838	+	0.257794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.8.c.a.3.2	✓	16
3.2	odd	2		117.8.g.d.55.7		16
4.3	odd	2		208.8.i.d.81.8		16
13.2	odd	12		169.8.b.e.168.3		16
13.3	even	3		169.8.a.f.1.7		8
13.9	even	3	inner	13.8.c.a.9.2	yes	16
13.10	even	6		169.8.a.e.1.2		8
13.11	odd	12		169.8.b.e.168.14		16
39.35	odd	6		117.8.g.d.100.7		16
52.35	odd	6		208.8.i.d.113.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.c.a.3.2	✓	16	1.1	even	1	trivial
13.8.c.a.9.2	yes	16	13.9	even	3	inner
117.8.g.d.55.7		16	3.2	odd	2
117.8.g.d.100.7		16	39.35	odd	6
169.8.a.e.1.2		8	13.10	even	6
169.8.a.f.1.7		8	13.3	even	3
169.8.b.e.168.3		16	13.2	odd	12
169.8.b.e.168.14		16	13.11	odd	12
208.8.i.d.81.8		16	4.3	odd	2
208.8.i.d.113.8		16	52.35	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	13.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.60170 - 14.8986i) q^{2} +(-43.0086 - 74.4931i) q^{3} +(-83.9785 + 145.455i) q^{4} +289.904 q^{5} +(-739.895 + 1281.54i) q^{6} +(484.274 - 838.787i) q^{7} +687.398 q^{8} +(-2605.99 + 4513.70i) q^{9} +(-2493.67 - 4319.16i) q^{10} +(-536.447 - 929.153i) q^{11} +14447.2 q^{12} +(5291.92 - 5894.41i) q^{13} -16662.3 q^{14} +(-12468.4 - 21595.9i) q^{15} +(4836.46 + 8377.00i) q^{16} +(-9648.04 + 16710.9i) q^{17} +89663.7 q^{18} +(2342.02 - 4056.49i) q^{19} +(-24345.7 + 42168.0i) q^{20} -83311.9 q^{21} +(-9228.71 + 15984.6i) q^{22} +(-17524.1 - 30352.7i) q^{23} +(-29564.0 - 51206.4i) q^{24} +5919.34 q^{25} +(-133338. - 28140.2i) q^{26} +260200. q^{27} +(81337.3 + 140880. i) q^{28} +(-62785.3 - 108747. i) q^{29} +(-214499. + 371522. i) q^{30} +124054. q^{31} +(127197. - 220312. i) q^{32} +(-46143.7 + 79923.2i) q^{33} +331958. q^{34} +(140393. - 243168. i) q^{35} +(-437694. - 758108. i) q^{36} +(18025.4 + 31220.9i) q^{37} -80581.3 q^{38} +(-666692. - 140701. i) q^{39} +199279. q^{40} +(119806. + 207510. i) q^{41} +(716624. + 1.24123e6i) q^{42} +(356325. - 617172. i) q^{43} +180200. q^{44} +(-755486. + 1.30854e6i) q^{45} +(-301475. + 522170. i) q^{46} -1.15018e6 q^{47} +(416019. - 720567. i) q^{48} +(-57271.3 - 99196.7i) q^{49} +(-50916.4 - 88189.8i) q^{50} +1.65980e6 q^{51} +(412964. + 1.26474e6i) q^{52} +99663.5 q^{53} +(-2.23816e6 - 3.87661e6i) q^{54} +(-155518. - 269365. i) q^{55} +(332889. - 576580. i) q^{56} -402908. q^{57} +(-1.08012e6 + 1.87083e6i) q^{58} +(-449716. + 778932. i) q^{59} +4.18830e6 q^{60} +(1.18213e6 - 2.04750e6i) q^{61} +(-1.06707e6 - 1.84822e6i) q^{62} +(2.52402e6 + 4.37174e6i) q^{63} -3.13831e6 q^{64} +(1.53415e6 - 1.70881e6i) q^{65} +1.58766e6 q^{66} +(1.03560e6 + 1.79371e6i) q^{67} +(-1.62046e6 - 2.80671e6i) q^{68} +(-1.50738e6 + 2.61086e6i) q^{69} -4.83047e6 q^{70} +(1.78120e6 - 3.08513e6i) q^{71} +(-1.79135e6 + 3.10271e6i) q^{72} -340087. q^{73} +(310098. - 537106. i) q^{74} +(-254583. - 440950. i) q^{75} +(393358. + 681316. i) q^{76} -1.03915e6 q^{77} +(3.63843e6 + 1.11430e7i) q^{78} -641046. q^{79} +(1.40211e6 + 2.42853e6i) q^{80} +(-5.49155e6 - 9.51165e6i) q^{81} +(2.06107e6 - 3.56987e6i) q^{82} +1.03845e6 q^{83} +(6.99641e6 - 1.21181e7i) q^{84} +(-2.79701e6 + 4.84456e6i) q^{85} -1.22600e7 q^{86} +(-5.40062e6 + 9.35416e6i) q^{87} +(-368752. - 638698. i) q^{88} +(2.05873e6 + 3.56583e6i) q^{89} +2.59939e7 q^{90} +(-2.38142e6 - 7.29331e6i) q^{91} +5.88661e6 q^{92} +(-5.33538e6 - 9.24114e6i) q^{93} +(9.89350e6 + 1.71361e7i) q^{94} +(678960. - 1.17599e6i) q^{95} -2.18823e7 q^{96} +(5.12319e6 - 8.87362e6i) q^{97} +(-985261. + 1.70652e6i) q^{98} +5.59189e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 9 q^{2} - 28 q^{3} - 577 q^{4} + 384 q^{5} + 342 q^{6} + 196 q^{7} + 5922 q^{8} - 5988 q^{9} - 6813 q^{10} + 5052 q^{11} - 15816 q^{12} + 17064 q^{13} + 14484 q^{14} - 184 q^{15} - 61377 q^{16} - 22824 q^{17}+ \cdots + 27386736 q^{99}+O(q^{100}) \) 16 * q - 9 * q^2 - 28 * q^3 - 577 * q^4 + 384 * q^5 + 342 * q^6 + 196 * q^7 + 5922 * q^8 - 5988 * q^9 - 6813 * q^10 + 5052 * q^11 - 15816 * q^12 + 17064 * q^13 + 14484 * q^14 - 184 * q^15 - 61377 * q^16 - 22824 * q^17 + 226318 * q^18 + 63692 * q^19 - 121971 * q^20 - 271240 * q^21 - 73726 * q^22 - 72468 * q^23 + 224952 * q^24 + 58488 * q^25 + 154443 * q^26 + 358616 * q^27 - 172816 * q^28 - 221772 * q^29 - 258116 * q^30 + 58432 * q^31 + 77823 * q^32 - 352372 * q^33 + 643334 * q^34 + 31560 * q^35 - 1162993 * q^36 - 368884 * q^37 + 2364492 * q^38 - 672996 * q^39 + 766030 * q^40 - 385824 * q^41 + 1560954 * q^42 + 391492 * q^43 - 6149616 * q^44 + 232096 * q^45 - 2599078 * q^46 + 1089984 * q^47 + 4585712 * q^48 - 1108780 * q^49 + 1626894 * q^50 + 8040712 * q^51 - 1312478 * q^52 + 3329328 * q^53 - 5616702 * q^54 - 418216 * q^55 - 3609156 * q^56 - 12068664 * q^57 + 3685081 * q^58 - 6318924 * q^59 + 1448784 * q^60 + 1763548 * q^61 - 12998388 * q^62 + 6641128 * q^63 + 32227074 * q^64 + 9500508 * q^65 + 16245108 * q^66 - 8607964 * q^67 - 10118091 * q^68 - 4618492 * q^69 - 25381840 * q^70 + 9473220 * q^71 - 35174445 * q^72 + 5020888 * q^73 + 2206221 * q^74 - 21834988 * q^75 + 18702876 * q^76 + 35263992 * q^77 + 28395902 * q^78 + 12644416 * q^79 - 24671247 * q^80 - 9316272 * q^81 - 9347751 * q^82 - 22158432 * q^83 + 37532636 * q^84 - 36911824 * q^85 - 30103956 * q^86 + 5199988 * q^87 - 36676404 * q^88 + 18469860 * q^89 + 132263562 * q^90 - 9614540 * q^91 + 64127424 * q^92 - 26340696 * q^93 - 6026128 * q^94 - 16267080 * q^95 - 164216320 * q^96 + 19660916 * q^97 - 51546651 * q^98 + 27386736 * q^99

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