LMFDB - Embedded newform 15.7.d.c.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,7,Mod(14,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("15.14");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	15.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:	$3.45081125430$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 60x^{6} + 7774x^{4} + 206220x^{2} + 5736025 $ x^8 + 60x^6 + 7774x^4 + 206220*x^2 + 5736025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.2
Root			$-2.84382 - 4.80492i$ of defining polynomial
Character	$\chi$	$=$	15.14
Dual form			15.7.d.c.14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.8944 q^{2} +(9.31012 + 25.3441i) q^{3} +77.4763 q^{4} +(-102.129 - 72.0738i) q^{5} +(-110.738 - 301.452i) q^{6} -553.145i q^{7} -160.292 q^{8} +(-555.643 + 471.913i) q^{9} +O(q^{10})$	\(q-11.8944 q^{2} +(9.31012 + 25.3441i) q^{3} +77.4763 q^{4} +(-102.129 - 72.0738i) q^{5} +(-110.738 - 301.452i) q^{6} -553.145i q^{7} -160.292 q^{8} +(-555.643 + 471.913i) q^{9} +(1214.76 + 857.274i) q^{10} -799.678i q^{11} +(721.314 + 1963.56i) q^{12} -1119.56i q^{13} +6579.32i q^{14} +(875.810 - 3259.38i) q^{15} -3051.91 q^{16} -2580.88 q^{17} +(6609.03 - 5613.11i) q^{18} -3496.52 q^{19} +(-7912.58 - 5584.01i) q^{20} +(14018.9 - 5149.85i) q^{21} +9511.67i q^{22} -5050.73 q^{23} +(-1492.34 - 4062.45i) q^{24} +(5235.72 + 14721.7i) q^{25} +13316.5i q^{26} +(-17133.3 - 9688.69i) q^{27} -42855.6i q^{28} -25414.6i q^{29} +(-10417.2 + 38768.3i) q^{30} -11931.1 q^{31} +46559.2 q^{32} +(20267.1 - 7445.10i) q^{33} +30697.9 q^{34} +(-39867.3 + 56492.2i) q^{35} +(-43049.2 + 36562.0i) q^{36} +28772.8i q^{37} +41589.0 q^{38} +(28374.3 - 10423.3i) q^{39} +(16370.5 + 11552.9i) q^{40} -55623.9i q^{41} +(-166747. + 61254.2i) q^{42} -38502.9i q^{43} -61956.0i q^{44} +(90759.9 - 8148.69i) q^{45} +60075.3 q^{46} +151747. q^{47} +(-28413.6 - 77347.8i) q^{48} -188320. q^{49} +(-62275.6 - 175105. i) q^{50} +(-24028.3 - 65409.9i) q^{51} -86739.6i q^{52} -143854. q^{53} +(203790. + 115241. i) q^{54} +(-57635.9 + 81670.4i) q^{55} +88664.7i q^{56} +(-32553.1 - 88616.1i) q^{57} +302291. i q^{58} +401125. i q^{59} +(67854.5 - 252525. i) q^{60} +309592. q^{61} +141913. q^{62} +(261036. + 307351. i) q^{63} -358471. q^{64} +(-80691.2 + 114340. i) q^{65} +(-241064. + 88554.8i) q^{66} -163390. i q^{67} -199957. q^{68} +(-47022.9 - 128006. i) q^{69} +(474197. - 671940. i) q^{70} -151582. i q^{71} +(89065.1 - 75643.8i) q^{72} +70173.6i q^{73} -342234. i q^{74} +(-324362. + 269755. i) q^{75} -270898. q^{76} -442338. q^{77} +(-337495. + 123978. i) q^{78} +437071. q^{79} +(311689. + 219963. i) q^{80} +(86037.8 - 524430. i) q^{81} +661612. i q^{82} -342935. q^{83} +(1.08614e6 - 398991. i) q^{84} +(263583. + 186014. i) q^{85} +457968. i q^{86} +(644110. - 236613. i) q^{87} +128182. i q^{88} -631196. i q^{89} +(-1.07953e6 + 96923.6i) q^{90} -619281. q^{91} -391311. q^{92} +(-111080. - 302383. i) q^{93} -1.80494e6 q^{94} +(357097. + 252008. i) q^{95} +(433472. + 1.18000e6i) q^{96} -1.55901e6i q^{97} +2.23995e6 q^{98} +(377378. + 444336. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 72 q^{4} - 612 q^{6} - 1980 q^{9}+O(q^{10}) $ 8 * q + 72 * q^4 - 612 * q^6 - 1980 * q^9	$ 8 q + 72 q^{4} - 612 q^{6} - 1980 q^{9} + 4240 q^{10} + 1980 q^{15} + 784 q^{16} - 28520 q^{19} + 24228 q^{21} + 14904 q^{24} + 800 q^{25} - 71100 q^{30} + 5896 q^{31} + 105344 q^{34} - 186624 q^{36} + 233568 q^{39} + 141920 q^{40} - 159300 q^{45} + 59336 q^{46} - 1041472 q^{49} + 66888 q^{51} + 917892 q^{54} + 442800 q^{55} - 638640 q^{60} + 1493416 q^{61} - 2063584 q^{64} - 1221840 q^{66} + 1502532 q^{69} + 2273400 q^{70} - 2574000 q^{75} - 219168 q^{76} - 1286360 q^{79} - 1752192 q^{81} + 6238728 q^{84} + 1651240 q^{85} - 2737440 q^{90} + 383616 q^{91} - 7641736 q^{94} - 151056 q^{96} + 6322320 q^{99}+O(q^{100}) $ 8 * q + 72 * q^4 - 612 * q^6 - 1980 * q^9 + 4240 * q^10 + 1980 * q^15 + 784 * q^16 - 28520 * q^19 + 24228 * q^21 + 14904 * q^24 + 800 * q^25 - 71100 * q^30 + 5896 * q^31 + 105344 * q^34 - 186624 * q^36 + 233568 * q^39 + 141920 * q^40 - 159300 * q^45 + 59336 * q^46 - 1041472 * q^49 + 66888 * q^51 + 917892 * q^54 + 442800 * q^55 - 638640 * q^60 + 1493416 * q^61 - 2063584 * q^64 - 1221840 * q^66 + 1502532 * q^69 + 2273400 * q^70 - 2574000 * q^75 - 219168 * q^76 - 1286360 * q^79 - 1752192 * q^81 + 6238728 * q^84 + 1651240 * q^85 - 2737440 * q^90 + 383616 * q^91 - 7641736 * q^94 - 151056 * q^96 + 6322320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−11.8944			−1.48680			−0.743399	−	0.668848i	$-0.766787\pi$
$2$	−11.8944			−1.48680			−0.743399	+	0.668848i	$0.766787\pi$
$3$	9.31012	+	25.3441i	0.344819	+	0.938669i
$3$	9.31012	+	25.3441i	0.344819	+	0.938669i
$4$	77.4763			1.21057
$5$	−102.129	−	72.0738i	−0.817033	−	0.576591i
$5$	−102.129	−	72.0738i	−0.817033	−	0.576591i
$6$	−110.738	−	301.452i	−0.512677	−	1.39561i
$7$		−	553.145i		−	1.61267i	−0.591461	−	0.806334i	$-0.701449\pi$
$7$		−	553.145i		−	1.61267i	0.591461	−	0.806334i	$-0.298551\pi$
$8$	−160.292			−0.313070
$9$	−555.643	+	471.913i	−0.762199	+	0.647343i
$10$	1214.76	+	857.274i	1.21476	+	0.857274i
$11$		−	799.678i		−	0.600810i	−0.953812	−	0.300405i	$-0.902878\pi$
$11$		−	799.678i		−	0.600810i	0.953812	−	0.300405i	$-0.0971218\pi$
$12$	721.314	+	1963.56i	0.417427	+	1.13632i
$13$		−	1119.56i		−	0.509587i	−0.966995	−	0.254794i	$-0.917992\pi$
$13$		−	1119.56i		−	0.509587i	0.966995	−	0.254794i	$-0.0820075\pi$
$14$			6579.32i			2.39771i
$15$	875.810	−	3259.38i	0.259499	−	0.965743i
$16$	−3051.91			−0.745095
$17$	−2580.88			−0.525316			−0.262658	−	0.964889i	$-0.584599\pi$
$17$	−2580.88			−0.525316			−0.262658	+	0.964889i	$0.584599\pi$
$18$	6609.03	−	5613.11i	1.13324	−	0.962467i
$19$	−3496.52			−0.509772			−0.254886	−	0.966971i	$-0.582038\pi$
$19$	−3496.52			−0.509772			−0.254886	+	0.966971i	$0.582038\pi$
$20$	−7912.58	−	5584.01i	−0.989073	−	0.698002i
$21$	14018.9	−	5149.85i	1.51376	−	0.556079i
$22$			9511.67i			0.893282i
$23$	−5050.73			−0.415117			−0.207558	−	0.978223i	$-0.566552\pi$
$23$	−5050.73			−0.415117			−0.207558	+	0.978223i	$0.566552\pi$
$24$	−1492.34	−	4062.45i	−0.107953	−	0.293869i
$25$	5235.72	+	14721.7i	0.335086	+	0.942188i
$26$			13316.5i			0.757653i
$27$	−17133.3	−	9688.69i	−0.870461	−	0.492237i
$28$		−	42855.6i		−	1.95224i
$29$		−	25414.6i		−	1.04205i	−0.853540	−	0.521027i	$-0.825549\pi$
$29$		−	25414.6i		−	1.04205i	0.853540	−	0.521027i	$-0.174451\pi$
$30$	−10417.2	+	38768.3i	−0.385823	+	1.43586i
$31$	−11931.1			−0.400494			−0.200247	−	0.979745i	$-0.564174\pi$
$31$	−11931.1			−0.400494			−0.200247	+	0.979745i	$0.564174\pi$
$32$	46559.2			1.42088
$33$	20267.1	−	7445.10i	0.563961	−	0.207171i
$34$	30697.9			0.781038
$35$	−39867.3	+	56492.2i	−0.929849	+	1.31760i
$36$	−43049.2	+	36562.0i	−0.922693	+	0.783651i
$37$			28772.8i			0.568037i	0.958819	+	0.284018i	$0.0916677\pi$
$37$			28772.8i			0.568037i	−0.958819	+	0.284018i	$0.908332\pi$
$38$	41589.0			0.757927
$39$	28374.3	−	10423.3i	0.478334	−	0.175716i
$40$	16370.5	+	11552.9i	0.255789	+	0.180513i
$41$		−	55623.9i		−	0.807067i	−0.914965	−	0.403534i	$-0.867782\pi$
$41$		−	55623.9i		−	0.807067i	0.914965	−	0.403534i	$-0.132218\pi$
$42$	−166747.	+	61254.2i	−2.25066	+	0.826777i
$43$		−	38502.9i		−	0.484270i	−0.970243	−	0.242135i	$-0.922152\pi$
$43$		−	38502.9i		−	0.484270i	0.970243	−	0.242135i	$-0.0778477\pi$
$44$		−	61956.0i		−	0.727320i
$45$	90759.9	−	8148.69i	0.995994	−	0.0894232i
$46$	60075.3			0.617195
$47$	151747.			1.46160			0.730798	−	0.682594i	$-0.239148\pi$
$47$	151747.			1.46160			0.730798	+	0.682594i	$0.239148\pi$
$48$	−28413.6	−	77347.8i	−0.256923	−	0.699397i
$49$	−188320.			−1.60070
$50$	−62275.6	−	175105.i	−0.498205	−	1.40084i
$51$	−24028.3	−	65409.9i	−0.181139	−	0.493098i
$52$		−	86739.6i		−	0.616889i
$53$	−143854.			−0.966258			−0.483129	−	0.875549i	$-0.660500\pi$
$53$	−143854.			−0.966258			−0.483129	+	0.875549i	$0.660500\pi$
$54$	203790.	+	115241.i	1.29420	+	0.731856i
$55$	−57635.9	+	81670.4i	−0.346421	+	0.490881i
$56$			88664.7i			0.504878i
$57$	−32553.1	−	88616.1i	−0.175779	−	0.478507i
$58$			302291.i			1.54932i
$59$			401125.i			1.95310i	0.215294	+	0.976549i	$0.430929\pi$
$59$			401125.i			1.95310i	−0.215294	+	0.976549i	$0.569071\pi$
$60$	67854.5	−	252525.i	0.314141	−	1.16910i
$61$	309592.			1.36396			0.681978	−	0.731373i	$-0.261120\pi$
$61$	309592.			1.36396			0.681978	+	0.731373i	$0.261120\pi$
$62$	141913.			0.595453
$63$	261036.	+	307351.i	1.04395	+	1.22917i
$64$	−358471.			−1.36746
$65$	−80691.2	+	114340.i	−0.293823	+	0.416350i
$66$	−241064.	+	88554.8i	−0.838497	+	0.308021i
$67$		−	163390.i		−	0.543252i	−0.962403	−	0.271626i	$-0.912439\pi$
$67$		−	163390.i		−	0.543252i	0.962403	−	0.271626i	$-0.0875614\pi$
$68$	−199957.			−0.635930
$69$	−47022.9	−	128006.i	−0.143140	−	0.389657i
$70$	474197.	−	671940.i	1.38250	−	1.95901i
$71$		−	151582.i		−	0.423518i	−0.977322	−	0.211759i	$-0.932081\pi$
$71$		−	151582.i		−	0.423518i	0.977322	−	0.211759i	$-0.0679192\pi$
$72$	89065.1	−	75643.8i	0.238622	−	0.202664i
$73$			70173.6i			0.180387i	0.995924	+	0.0901935i	$0.0287485\pi$
$73$			70173.6i			0.180387i	−0.995924	+	0.0901935i	$0.971251\pi$
$74$		−	342234.i		−	0.844556i
$75$	−324362.	+	269755.i	−0.768858	+	0.639419i
$76$	−270898.			−0.617113
$77$	−442338.			−0.968906
$78$	−337495.	+	123978.i	−0.711186	+	0.261253i
$79$	437071.			0.886484			0.443242	−	0.896402i	$-0.353828\pi$
$79$	437071.			0.886484			0.443242	+	0.896402i	$0.353828\pi$
$80$	311689.	+	219963.i	0.608767	+	0.429615i
$81$	86037.8	−	524430.i	0.161895	−	0.986808i
$82$			661612.i			1.19995i
$83$	−342935.			−0.599761			−0.299880	−	0.953977i	$-0.596947\pi$
$83$	−342935.			−0.599761			−0.299880	+	0.953977i	$0.596947\pi$
$84$	1.08614e6	−	398991.i	1.83251	−	0.673171i
$85$	263583.	+	186014.i	0.429200	+	0.302892i
$86$			457968.i			0.720012i
$87$	644110.	−	236613.i	0.978143	−	0.359320i
$88$			128182.i			0.188096i
$89$		−	631196.i		−	0.895352i	−0.894196	−	0.447676i	$-0.852252\pi$
$89$		−	631196.i		−	0.895352i	0.894196	−	0.447676i	$-0.147748\pi$
$90$	−1.07953e6	+	96923.6i	−1.48084	+	0.132954i
$91$	−619281.			−0.821795
$92$	−391311.			−0.502527
$93$	−111080.	−	302383.i	−0.138098	−	0.375931i
$94$	−1.80494e6			−2.17310
$95$	357097.	+	252008.i	0.416500	+	0.293930i
$96$	433472.	+	1.18000e6i	0.489945	+	1.33373i
$97$		−	1.55901e6i		−	1.70818i	−0.520129	−	0.854088i	$-0.674116\pi$
$97$		−	1.55901e6i		−	1.70818i	0.520129	−	0.854088i	$-0.325884\pi$
$98$	2.23995e6			2.37991
$99$	377378.	+	444336.i	0.388930	+	0.457937i
$100$	405644.	+	1.14058e6i	0.405644	+	1.14058i
$101$		−	96149.6i		−	0.0933218i	−0.998911	−	0.0466609i	$-0.985142\pi$
$101$		−	96149.6i		−	0.0933218i	0.998911	−	0.0466609i	$-0.0148580\pi$
$102$	285801.	+	778010.i	0.269317	+	0.733136i
$103$			364316.i			0.333401i	0.986008	+	0.166701i	$0.0533113\pi$
$103$			364316.i			0.333401i	−0.986008	+	0.166701i	$0.946689\pi$
$104$			179457.i			0.159537i
$105$	−1.80291e6	−	484450.i	−1.55742	−	0.418486i
$106$	1.71105e6			1.43663
$107$	43747.4			0.0357109			0.0178555	−	0.999841i	$-0.494316\pi$
$107$	43747.4			0.0357109			0.0178555	+	0.999841i	$0.494316\pi$
$108$	−1.32742e6	−	750644.i	−1.05375	−	0.595885i
$109$	−157763.			−0.121822			−0.0609109	−	0.998143i	$-0.519401\pi$
$109$	−157763.			−0.121822			−0.0609109	+	0.998143i	$0.519401\pi$
$110$	685543.	−	971419.i	0.515058	−	0.729841i
$111$	−729219.	+	267878.i	−0.533199	+	0.195870i
$112$			1.68815e6i			1.20159i
$113$	−811828.			−0.562637			−0.281319	−	0.959614i	$-0.590772\pi$
$113$	−811828.			−0.562637			−0.281319	+	0.959614i	$0.590772\pi$
$114$	387199.	+	1.05403e6i	0.261348	+	0.711443i
$115$	515826.	+	364025.i	0.339164	+	0.239353i
$116$		−	1.96903e6i		−	1.26147i
$117$	528336.	+	622078.i	0.329878	+	0.388407i
$118$		−	4.77114e6i		−	2.90386i
$119$			1.42760e6i			0.847160i
$120$	−140385.	+	522453.i	−0.0812414	+	0.302345i
$121$	1.13208e6			0.639028
$122$	−3.68240e6			−2.02793
$123$	1.40974e6	−	517865.i	0.757569	−	0.278292i
$124$	−924378.			−0.484824
$125$	526329.	−	1.88087e6i	0.269480	−	0.963006i
$126$	−3.10486e6	−	3.65575e6i	−1.55214	−	1.82753i
$127$			705580.i			0.344457i	0.985057	+	0.172229i	$0.0550968\pi$
$127$			705580.i			0.344457i	−0.985057	+	0.172229i	$0.944903\pi$
$128$	1.28400e6			0.612259
$129$	975819.	−	358466.i	0.454570	−	0.166986i
$130$	959772.	−	1.36000e6i	0.436856	−	0.619028i
$131$			2.35922e6i			1.04943i	0.851277	+	0.524716i	$0.175829\pi$
$131$			2.35922e6i			1.04943i	−0.851277	+	0.524716i	$0.824171\pi$
$132$	1.57022e6	−	576818.i	0.682713	−	0.250794i
$133$			1.93408e6i			0.822092i
$134$			1.94342e6i			0.807706i
$135$	1.05151e6	+	2.22436e6i	0.427377	+	0.904074i
$136$	413694.			0.164461
$137$	2.73309e6			1.06290			0.531450	−	0.847090i	$-0.321647\pi$
$137$	2.73309e6			1.06290			0.531450	+	0.847090i	$0.321647\pi$
$138$	559308.	+	1.52255e6i	0.212821	+	0.579341i
$139$	−2.86791e6			−1.06788			−0.533939	−	0.845523i	$-0.679289\pi$
$139$	−2.86791e6			−1.06788			−0.533939	+	0.845523i	$0.679289\pi$
$140$	−3.08877e6	+	4.37681e6i	−1.12564	+	1.59505i
$141$	1.41279e6	+	3.84589e6i	0.503986	+	1.37195i
$142$			1.80297e6i			0.629686i
$143$	−895290.			−0.306165
$144$	1.69577e6	−	1.44023e6i	0.567911	−	0.482332i
$145$	−1.83173e6	+	2.59557e6i	−0.600838	+	0.851392i
$146$		−	834671.i		−	0.268199i
$147$	−1.75329e6	−	4.77280e6i	−0.551951	−	1.50252i
$148$			2.22921e6i			0.687647i
$149$		−	3.71980e6i		−	1.12450i	−0.826966	−	0.562252i	$-0.809935\pi$
$149$		−	3.71980e6i		−	1.12450i	0.826966	−	0.562252i	$-0.190065\pi$
$150$	3.85808e6	−	3.20857e6i	1.14314	−	0.950687i
$151$	−4.26236e6			−1.23800			−0.618998	−	0.785392i	$-0.712461\pi$
$151$	−4.26236e6			−1.23800			−0.618998	+	0.785392i	$0.712461\pi$
$152$	560464.			0.159594
$153$	1.43405e6	−	1.21795e6i	0.400395	−	0.340059i
$154$	5.26133e6			1.44057
$155$	1.21851e6	+	859921.i	0.327217	+	0.230921i
$156$	2.19833e6	−	807556.i	0.579055	−	0.212715i
$157$		−	5.22753e6i		−	1.35082i	−0.737442	−	0.675410i	$-0.763966\pi$
$157$		−	5.22753e6i		−	1.35082i	0.737442	−	0.675410i	$-0.236034\pi$
$158$	−5.19869e6			−1.31802
$159$	−1.33929e6	−	3.64584e6i	−0.333185	−	0.906997i
$160$	−4.75506e6	−	3.35570e6i	−1.16090	−	0.819264i
$161$			2.79378e6i			0.669445i
$162$	−1.02337e6	+	6.23777e6i	−0.240706	+	1.46718i
$163$			1.86579e6i			0.430825i	0.976523	+	0.215413i	$0.0691096\pi$
$163$			1.86579e6i			0.430825i	−0.976523	+	0.215413i	$0.930890\pi$
$164$		−	4.30953e6i		−	0.977009i
$165$	−2.60646e6	−	700365.i	−0.580228	−	0.155910i
$166$	4.07900e6			0.891723
$167$	3.82949e6			0.822227			0.411114	−	0.911584i	$-0.365140\pi$
$167$	3.82949e6			0.822227			0.411114	+	0.911584i	$0.365140\pi$
$168$	−2.24712e6	+	825479.i	−0.473913	+	0.174092i
$169$	3.57339e6			0.740321
$170$	−3.13515e6	−	2.21252e6i	−0.638134	−	0.450339i
$171$	1.94282e6	−	1.65005e6i	0.388548	−	0.329997i
$172$		−	2.98306e6i		−	0.586241i
$173$	−3.03786e6			−0.586717			−0.293359	−	0.956002i	$-0.594773\pi$
$173$	−3.03786e6			−0.586717			−0.293359	+	0.956002i	$0.594773\pi$
$174$	−7.66129e6	+	2.81437e6i	−1.45430	+	0.534236i
$175$	8.14322e6	−	2.89611e6i	1.51944	−	0.540382i
$176$			2.44054e6i			0.447660i
$177$	−1.01661e7	+	3.73453e6i	−1.83331	+	0.673466i
$178$			7.50768e6i			1.33121i
$179$		−	2.06795e6i		−	0.360563i	−0.983615	−	0.180282i	$-0.942299\pi$
$179$		−	2.06795e6i		−	0.360563i	0.983615	−	0.180282i	$-0.0577009\pi$
$180$	7.03174e6	−	631330.i	1.20572	−	0.108253i
$181$	−2.88344e6			−0.486267			−0.243133	−	0.969993i	$-0.578175\pi$
$181$	−2.88344e6			−0.486267			−0.243133	+	0.969993i	$0.578175\pi$
$182$	7.36596e6			1.22184
$183$	2.88234e6	+	7.84632e6i	0.470318	+	1.28030i
$184$	809591.			0.129961
$185$	2.07376e6	−	2.93854e6i	0.327525	−	0.464105i
$186$	1.32123e6	+	3.59666e6i	0.205324	+	0.558933i
$187$			2.06387e6i			0.315615i
$188$	1.17568e7			1.76936
$189$	−5.35925e6	+	9.47719e6i	−0.793814	+	1.40376i
$190$	−4.24745e6	−	2.99748e6i	−0.619252	−	0.437014i
$191$		−	1.15389e7i		−	1.65601i	−0.560720	−	0.828005i	$-0.689476\pi$
$191$		−	1.15389e7i		−	1.65601i	0.560720	−	0.828005i	$-0.310524\pi$
$192$	−3.33741e6	−	9.08512e6i	−0.471526	−	1.28359i
$193$		−	5.52092e6i		−	0.767961i	−0.923341	−	0.383981i	$-0.874553\pi$
$193$		−	5.52092e6i		−	0.767961i	0.923341	−	0.383981i	$-0.125447\pi$
$194$			1.85434e7i			2.53971i
$195$	−3.64909e6	−	980524.i	−0.492131	−	0.132237i
$196$	−1.45904e7			−1.93775
$197$	9.94059e6			1.30021			0.650105	−	0.759844i	$-0.274725\pi$
$197$	9.94059e6			1.30021			0.650105	+	0.759844i	$0.274725\pi$
$198$	−4.48868e6	−	5.28510e6i	−0.578260	−	0.680859i
$199$	8.27123e6			1.04957			0.524785	−	0.851235i	$-0.324146\pi$
$199$	8.27123e6			1.04957			0.524785	+	0.851235i	$0.324146\pi$
$200$	−839244.	−	2.35977e6i	−0.104905	−	0.294971i
$201$	4.14097e6	−	1.52118e6i	0.509934	−	0.187324i
$202$			1.14364e6i			0.138751i
$203$	−1.40580e7			−1.68049
$204$	−1.86162e6	−	5.06772e6i	−0.219281	−	0.596928i
$205$	−4.00903e6	+	5.68082e6i	−0.465348	+	0.659401i
$206$		−	4.33332e6i		−	0.495700i
$207$	2.80640e6	−	2.38350e6i	0.316402	−	0.268723i
$208$			3.41680e6i			0.379691i
$209$			2.79609e6i			0.306276i
$210$	2.14445e7	+	5.76223e6i	2.31557	+	0.622204i
$211$	6.31824e6			0.672587			0.336294	−	0.941757i	$-0.390827\pi$
$211$	6.31824e6			0.672587			0.336294	+	0.941757i	$0.390827\pi$
$212$	−1.11452e7			−1.16972
$213$	3.84170e6	−	1.41125e6i	0.397544	−	0.146037i
$214$	−520349.			−0.0530950
$215$	−2.77505e6	+	3.93227e6i	−0.279226	+	0.395665i
$216$	2.74633e6	+	1.55302e6i	0.272515	+	0.154105i
$217$			6.59963e6i			0.645863i
$218$	1.87649e6			0.181124
$219$	−1.77848e6	+	653325.i	−0.169324	+	0.0622009i
$220$	−4.46541e6	+	6.32752e6i	−0.419366	+	0.594245i
$221$			2.88945e6i			0.267694i
$222$	8.67361e6	−	3.18624e6i	0.792758	−	0.291219i
$223$		−	1.15621e7i		−	1.04261i	−0.853369	−	0.521307i	$-0.825445\pi$
$223$		−	1.15621e7i		−	1.04261i	0.853369	−	0.521307i	$-0.174555\pi$
$224$		−	2.57540e7i		−	2.29140i
$225$	−9.85654e6	−	5.70920e6i	−0.865320	−	0.501219i
$226$	9.65619e6			0.836528
$227$	−1.37437e7			−1.17497			−0.587484	−	0.809236i	$-0.699882\pi$
$227$	−1.37437e7			−1.17497			−0.587484	+	0.809236i	$0.699882\pi$
$228$	−2.52209e6	−	6.86565e6i	−0.212792	−	0.579265i
$229$	−4.67634e6			−0.389404			−0.194702	−	0.980862i	$-0.562374\pi$
$229$	−4.67634e6			−0.389404			−0.194702	+	0.980862i	$0.562374\pi$
$230$	−6.13543e6	−	4.32985e6i	−0.504268	−	0.355869i
$231$	−4.11822e6	−	1.12106e7i	−0.334098	−	0.909482i
$232$			4.07376e6i			0.326236i
$233$	1.90985e7			1.50984			0.754920	−	0.655817i	$-0.227676\pi$
$233$	1.90985e7			1.50984			0.754920	+	0.655817i	$0.227676\pi$
$234$	−6.28423e6	−	7.39923e6i	−0.490461	−	0.577483i
$235$	−1.54978e7	−	1.09370e7i	−1.19417	−	0.842742i
$236$			3.10777e7i			2.36436i
$237$	4.06919e6	+	1.10772e7i	0.305677	+	0.832115i
$238$		−	1.69804e7i		−	1.25955i
$239$			7.64223e6i			0.559792i	0.960030	+	0.279896i	$0.0902999\pi$
$239$			7.64223e6i			0.559792i	−0.960030	+	0.279896i	$0.909700\pi$
$240$	−2.67289e6	+	9.94734e6i	−0.193351	+	0.719570i
$241$	2.44181e6			0.174446			0.0872229	−	0.996189i	$-0.472201\pi$
$241$	2.44181e6			0.174446			0.0872229	+	0.996189i	$0.472201\pi$
$242$	−1.34653e7			−0.950105
$243$	1.40922e7	−	2.70196e6i	0.982111	−	0.188304i
$244$	2.39860e7			1.65116
$245$	1.92330e7	+	1.35730e7i	1.30782	+	0.922947i
$246$	−1.67679e7	+	6.15969e6i	−1.12635	+	0.413764i
$247$			3.91458e6i			0.259773i
$248$	1.91246e6			0.125383
$249$	−3.19277e6	−	8.69138e6i	−0.206809	−	0.562977i
$250$	−6.26035e6	+	2.23718e7i	−0.400662	+	1.43179i
$251$		−	2.52632e6i		−	0.159760i	−0.996805	−	0.0798798i	$-0.974546\pi$
$251$		−	2.52632e6i		−	0.159760i	0.996805	−	0.0798798i	$-0.0254536\pi$
$252$	2.02241e7	+	2.38124e7i	1.26377	+	1.48800i
$253$			4.03895e6i			0.249406i
$254$		−	8.39244e6i		−	0.512138i
$255$	−2.26036e6	+	8.41207e6i	−0.136319	+	0.507320i
$256$	7.66976e6			0.457153
$257$	−9.70704e6			−0.571857			−0.285928	−	0.958251i	$-0.592302\pi$
$257$	−9.70704e6			−0.571857			−0.285928	+	0.958251i	$0.592302\pi$
$258$	−1.16068e7	+	4.26374e6i	−0.675853	+	0.248274i
$259$	1.59155e7			0.916055
$260$	−6.25166e6	+	8.85864e6i	−0.355693	+	0.504019i
$261$	1.19935e7	+	1.41215e7i	0.674565	+	0.794252i
$262$		−	2.80615e7i		−	1.56029i
$263$	−2.50512e7			−1.37709			−0.688544	−	0.725195i	$-0.741750\pi$
$263$	−2.50512e7			−1.37709			−0.688544	+	0.725195i	$0.741750\pi$
$264$	−3.24865e6	+	1.19339e6i	−0.176560	+	0.0648590i
$265$	1.46916e7	+	1.03681e7i	0.789465	+	0.557136i
$266$		−	2.30047e7i		−	1.22228i
$267$	1.59971e7	−	5.87651e6i	0.840439	−	0.308735i
$268$		−	1.26589e7i		−	0.657643i
$269$			1.84000e7i			0.945282i	0.881255	+	0.472641i	$0.156699\pi$
$269$			1.84000e7i			0.945282i	−0.881255	+	0.472641i	$0.843301\pi$
$270$	−1.25070e7	−	2.64574e7i	−0.635423	−	1.34417i
$271$	−3.59204e7			−1.80482			−0.902408	−	0.430883i	$-0.858202\pi$
$271$	−3.59204e7			−1.80482			−0.902408	+	0.430883i	$0.858202\pi$
$272$	7.87660e6			0.391410
$273$	−5.76558e6	−	1.56951e7i	−0.283371	−	0.771393i
$274$	−3.25084e7			−1.58032
$275$	1.17726e7	−	4.18689e6i	0.566075	−	0.201323i
$276$	−3.64316e6	−	9.91742e6i	−0.173281	−	0.471706i
$277$			9.87614e6i			0.464673i	0.972635	+	0.232337i	$0.0746371\pi$
$277$			9.87614e6i			0.464673i	−0.972635	+	0.232337i	$0.925363\pi$
$278$	3.41120e7			1.58772
$279$	6.62944e6	−	5.63044e6i	0.305256	−	0.259257i
$280$	6.39040e6	−	9.05525e6i	0.291108	−	0.412502i
$281$		−	2.31654e7i		−	1.04405i	−0.852930	−	0.522025i	$-0.825177\pi$
$281$		−	2.31654e7i		−	1.04405i	0.852930	−	0.522025i	$-0.174823\pi$
$282$	−1.68042e7	−	4.57445e7i	−0.749326	−	2.03982i
$283$			3.21328e7i			1.41772i	0.705351	+	0.708859i	$0.250790\pi$
$283$			3.21328e7i			1.41772i	−0.705351	+	0.708859i	$0.749210\pi$
$284$		−	1.17440e7i		−	0.512697i
$285$	−3.06229e6	+	1.13965e7i	−0.132285	+	0.492309i
$286$	1.06489e7			0.455205
$287$	−3.07681e7			−1.30153
$288$	−2.58703e7	+	2.19719e7i	−1.08299	+	0.919793i
$289$	−1.74766e7			−0.724043
$290$	2.17873e7	−	3.08727e7i	0.893325	−	1.26585i
$291$	3.95115e7	−	1.45145e7i	1.60341	−	0.589012i
$292$			5.43679e6i			0.218370i
$293$	1.23376e7			0.490487			0.245244	−	0.969462i	$-0.421132\pi$
$293$	1.23376e7			0.490487			0.245244	+	0.969462i	$0.421132\pi$
$294$	2.08542e7	+	5.67695e7i	0.820640	+	2.23395i
$295$	2.89107e7	−	4.09666e7i	1.12614	−	1.59575i
$296$		−	4.61204e6i		−	0.177835i
$297$	−7.74783e6	+	1.37011e7i	−0.295741	+	0.522982i
$298$			4.42448e7i			1.67191i
$299$			5.65461e6i			0.211538i
$300$	−2.51304e7	+	2.08996e7i	−0.930754	+	0.774060i
$301$	−2.12977e7			−0.780967
$302$	5.06981e7			1.84065
$303$	2.43682e6	−	895164.i	0.0875983	−	0.0321792i
$304$	1.06711e7			0.379828
$305$	−3.16184e7	−	2.23135e7i	−1.11440	−	0.786444i
$306$	−1.70571e7	+	1.44867e7i	−0.595307	+	0.505599i
$307$			3.27655e7i			1.13241i	0.824266	+	0.566203i	$0.191588\pi$
$307$			3.27655e7i			1.13241i	−0.824266	+	0.566203i	$0.808412\pi$
$308$	−3.42707e7			−1.17293
$309$	−9.23326e6	+	3.39183e6i	−0.312953	+	0.114963i
$310$	−1.44935e7	−	1.02282e7i	−0.486505	−	0.343333i
$311$			5.29003e7i			1.75864i	0.476230	+	0.879321i	$0.342003\pi$
$311$			5.29003e7i			1.75864i	−0.476230	+	0.879321i	$0.657997\pi$
$312$	−4.54817e6	+	1.67077e6i	−0.149752	+	0.0550113i
$313$		−	4.25349e7i		−	1.38712i	−0.720401	−	0.693558i	$-0.756042\pi$
$313$		−	4.25349e7i		−	1.38712i	0.720401	−	0.693558i	$-0.243958\pi$
$314$			6.21783e7i			2.00840i
$315$	−4.50741e6	−	5.02034e7i	−0.144210	−	1.60621i
$316$	3.38627e7			1.07315
$317$	1.94179e7			0.609571			0.304786	−	0.952421i	$-0.401415\pi$
$317$	1.94179e7			0.609571			0.304786	+	0.952421i	$0.401415\pi$
$318$	1.59301e7	+	4.33650e7i	0.495378	+	1.34852i
$319$	−2.03235e7			−0.626076
$320$	3.66104e7	+	2.58364e7i	1.11726	+	0.788464i
$321$	407294.	+	1.10874e6i	0.0123138	+	0.0335208i
$322$		−	3.32303e7i		−	0.995330i
$323$	9.02410e6			0.267791
$324$	6.66589e6	−	4.06309e7i	0.195985	−	1.19460i
$325$	1.64819e7	−	5.86172e6i	0.480127	−	0.170756i
$326$		−	2.21925e7i		−	0.640550i
$327$	−1.46879e6	−	3.99835e6i	−0.0420065	−	0.114350i
$328$			8.91606e6i			0.252669i
$329$		−	8.39382e7i		−	2.35707i
$330$	3.10022e7	+	8.33041e6i	0.862681	+	0.231806i
$331$	2.37685e7			0.655417			0.327709	−	0.944779i	$-0.393724\pi$
$331$	2.37685e7			0.655417			0.327709	+	0.944779i	$0.393724\pi$
$332$	−2.65694e7			−0.726050
$333$	−1.35782e7	−	1.59874e7i	−0.367714	−	0.432957i
$334$	−4.55494e7			−1.22249
$335$	−1.17762e7	+	1.66869e7i	−0.313234	+	0.443855i
$336$	−4.27845e7	+	1.57169e7i	−1.12790	+	0.414332i
$337$		−	2.12188e7i		−	0.554411i	−0.960811	−	0.277205i	$-0.910592\pi$
$337$		−	2.12188e7i		−	0.554411i	0.960811	−	0.277205i	$-0.0894082\pi$
$338$	−4.25032e7			−1.10071
$339$	−7.55822e6	−	2.05750e7i	−0.194008	−	0.528130i
$340$	2.04214e7	+	1.44116e7i	0.519576	+	0.366671i
$341$			9.54104e6i			0.240621i
$342$	−2.31086e7	+	1.96264e7i	−0.577692	+	0.490639i
$343$			3.90915e7i			0.968724i
$344$			6.17170e6i			0.151611i
$345$	−4.42347e6	+	1.64623e7i	−0.107722	+	0.400896i
$346$	3.61334e7			0.872330
$347$	4.05537e7			0.970604			0.485302	−	0.874347i	$-0.338710\pi$
$347$	4.05537e7			0.970604			0.485302	+	0.874347i	$0.338710\pi$
$348$	4.99032e7	−	1.83319e7i	1.18411	−	0.434981i
$349$	5.02250e7			1.18153			0.590763	−	0.806845i	$-0.298827\pi$
$349$	5.02250e7			1.18153			0.590763	+	0.806845i	$0.298827\pi$
$350$	−9.68586e7	+	3.44475e7i	−2.25909	+	0.803439i
$351$	−1.08471e7	+	1.91818e7i	−0.250838	+	0.443576i
$352$		−	3.72324e7i		−	0.853676i
$353$	−3.52598e7			−0.801596			−0.400798	−	0.916166i	$-0.631267\pi$
$353$	−3.52598e7			−0.801596			−0.400798	+	0.916166i	$0.631267\pi$
$354$	1.20920e8	−	4.44199e7i	2.72577	−	1.00131i
$355$	−1.09251e7	+	1.54809e7i	−0.244197	+	0.346028i
$356$		−	4.89027e7i		−	1.08388i
$357$	−3.61812e7	+	1.32911e7i	−0.795203	+	0.292117i
$358$			2.45970e7i			0.536084i
$359$		−	1.68991e7i		−	0.365241i	−0.983184	−	0.182620i	$-0.941542\pi$
$359$		−	1.68991e7i		−	0.365241i	0.983184	−	0.182620i	$-0.0584579\pi$
$360$	−1.45481e7	+	1.30617e6i	−0.311816	+	0.0279957i
$361$	−3.48202e7			−0.740133
$362$	3.42967e7			0.722980
$363$	1.05398e7	+	2.86914e7i	0.220349	+	0.599836i
$364$	−4.79796e7			−0.994838
$365$	5.05768e6	−	7.16677e6i	0.104009	−	0.147382i
$366$	−3.42836e7	−	9.33271e7i	−0.699268	−	1.90355i
$367$		−	3.38754e7i		−	0.685308i	−0.939462	−	0.342654i	$-0.888674\pi$
$367$		−	3.38754e7i		−	0.685308i	0.939462	−	0.342654i	$-0.111326\pi$
$368$	1.54144e7			0.309301
$369$	2.62496e7	+	3.09070e7i	0.522449	+	0.615146i
$370$	−2.46661e7	+	3.49521e7i	−0.486963	+	0.690030i
$371$			7.95719e7i			1.55825i
$372$	−8.60607e6	−	2.34275e7i	−0.167177	−	0.455090i
$373$		−	4.90621e7i		−	0.945409i	−0.881221	−	0.472704i	$-0.843278\pi$
$373$		−	4.90621e7i		−	0.945409i	0.881221	−	0.472704i	$-0.156722\pi$
$374$		−	2.45484e7i		−	0.469255i
$375$	5.25691e7	−	4.17184e6i	0.996866	−	0.0791104i
$376$	−2.43239e7			−0.457582
$377$	−2.84533e7			−0.531017
$378$	6.37450e7	−	1.12725e8i	1.18024	−	2.08711i
$379$	−4.36223e7			−0.801293			−0.400646	−	0.916233i	$-0.631214\pi$
$379$	−4.36223e7			−0.801293			−0.400646	+	0.916233i	$0.631214\pi$
$380$	2.76665e7	+	1.95246e7i	0.504201	+	0.355821i
$381$	−1.78823e7	+	6.56904e6i	−0.323331	+	0.118775i
$382$			1.37248e8i			2.46215i
$383$	4.69624e7			0.835900			0.417950	−	0.908470i	$-0.362749\pi$
$383$	4.69624e7			0.835900			0.417950	+	0.908470i	$0.362749\pi$
$384$	1.19542e7	+	3.25418e7i	0.211119	+	0.574709i
$385$	4.51756e7	+	3.18810e7i	0.791629	+	0.558662i
$386$			6.56679e7i			1.14180i
$387$	1.81700e7	+	2.13939e7i	0.313489	+	0.369110i
$388$		−	1.20786e8i		−	2.06786i
$389$			8.46600e7i			1.43823i	0.694889	+	0.719117i	$0.255453\pi$
$389$			8.46600e7i			1.43823i	−0.694889	+	0.719117i	$0.744547\pi$
$390$	4.34036e7	+	1.16627e7i	0.731698	+	0.196610i
$391$	1.30353e7			0.218067
$392$	3.01862e7			0.501130
$393$	−5.97922e7	+	2.19646e7i	−0.985070	+	0.361865i
$394$	−1.18237e8			−1.93315
$395$	−4.46377e7	−	3.15014e7i	−0.724287	−	0.511139i
$396$	2.92378e7	+	3.44255e7i	0.470825	+	0.554363i
$397$			6.77384e7i			1.08259i	0.840833	+	0.541294i	$0.182065\pi$
$397$			6.77384e7i			1.08259i	−0.840833	+	0.541294i	$0.817935\pi$
$398$	−9.83812e7			−1.56050
$399$	−4.90176e7	+	1.80066e7i	−0.771673	+	0.283473i
$400$	−1.59789e7	−	4.49292e7i	−0.249671	−	0.702019i
$401$		−	1.25256e8i		−	1.94252i	−0.238015	−	0.971262i	$-0.576497\pi$
$401$		−	1.25256e8i		−	1.94252i	0.238015	−	0.971262i	$-0.423503\pi$
$402$	−4.92543e7	+	1.80935e7i	−0.758169	+	0.278513i
$403$			1.33576e7i			0.204087i
$404$		−	7.44931e6i		−	0.112972i
$405$	−4.65847e7	+	4.73585e7i	−0.701258	+	0.712907i
$406$	1.67211e8			2.49854
$407$	2.30089e7			0.341282
$408$	3.85154e6	+	1.04847e7i	0.0567092	+	0.154374i
$409$	1.16966e8			1.70958			0.854791	−	0.518972i	$-0.173685\pi$
$409$	1.16966e8			1.70958			0.854791	+	0.518972i	$0.173685\pi$
$410$	4.76849e7	−	6.75698e7i	0.691878	−	0.980395i
$411$	2.54454e7	+	6.92676e7i	0.366509	+	0.997711i
$412$			2.82259e7i			0.403604i
$413$	2.21881e8			3.14970
$414$	−3.33804e7	+	2.83503e7i	−0.470425	+	0.399536i
$415$	3.50237e7	+	2.47167e7i	0.490024	+	0.345816i
$416$		−	5.21260e7i		−	0.724060i
$417$	−2.67006e7	−	7.26846e7i	−0.368225	−	1.00238i
$418$		−	3.32578e7i		−	0.455370i
$419$			8.41723e7i			1.14427i	0.820161	+	0.572133i	$0.193884\pi$
$419$			8.41723e7i			1.14427i	−0.820161	+	0.572133i	$0.806116\pi$
$420$	−1.39683e8	−	3.75334e7i	−1.88536	−	0.506605i
$421$	−1.05982e8			−1.42032			−0.710161	−	0.704039i	$-0.751378\pi$
$421$	−1.05982e8			−1.42032			−0.710161	+	0.704039i	$0.751378\pi$
$422$	−7.51515e7			−1.00000
$423$	−8.43173e7	+	7.16114e7i	−1.11403	+	0.946153i
$424$	2.30586e7			0.302507
$425$	−1.35127e7	−	3.79948e7i	−0.176026	−	0.494946i
$426$	−4.56946e7	+	1.67859e7i	−0.591067	+	0.217128i
$427$		−	1.71249e8i		−	2.19961i
$428$	3.38939e6			0.0432305
$429$	−8.33526e6	−	2.26903e7i	−0.105572	−	0.287388i
$430$	3.30075e7	−	4.67719e7i	0.415152	−	0.588273i
$431$		−	6.83902e7i		−	0.854205i	−0.904203	−	0.427103i	$-0.859534\pi$
$431$		−	6.83902e7i		−	0.854205i	0.904203	−	0.427103i	$-0.140466\pi$
$432$	5.22892e7	+	2.95690e7i	0.648576	+	0.366763i
$433$		−	1.01612e8i		−	1.25165i	−0.779964	−	0.625825i	$-0.784762\pi$
$433$		−	1.01612e8i		−	1.25165i	0.779964	−	0.625825i	$-0.215238\pi$
$434$		−	7.84986e7i		−	0.960268i
$435$	−8.28360e7	−	2.22584e7i	−1.00636	−	0.270412i
$436$	−1.22229e7			−0.147473
$437$	1.76600e7			0.211615
$438$	2.11540e7	−	7.77089e6i	0.251750	−	0.0924801i
$439$	−3.82362e7			−0.451940			−0.225970	−	0.974134i	$-0.572555\pi$
$439$	−3.82362e7			−0.451940			−0.225970	+	0.974134i	$0.572555\pi$
$440$	9.23856e6	−	1.30911e7i	0.108454	−	0.153680i
$441$	1.04639e8	−	8.88708e7i	1.22005	−	1.03620i
$442$		−	3.43683e7i		−	0.398007i
$443$	−1.20185e8			−1.38242			−0.691210	−	0.722654i	$-0.742922\pi$
$443$	−1.20185e8			−1.38242			−0.691210	+	0.722654i	$0.742922\pi$
$444$	−5.64972e7	+	2.07542e7i	−0.645473	+	0.237114i
$445$	−4.54927e7	+	6.44635e7i	−0.516252	+	0.731532i
$446$			1.37524e8i			1.55015i
$447$	9.42750e7	−	3.46318e7i	1.05554	−	0.387751i
$448$			1.98287e8i			2.20526i
$449$		−	6.41137e7i		−	0.708292i	−0.935190	−	0.354146i	$-0.884772\pi$
$449$		−	6.41137e7i		−	0.708292i	0.935190	−	0.354146i	$-0.115228\pi$
$450$	1.17237e8	+	6.79074e7i	1.28656	+	0.745211i
$451$	−4.44812e7			−0.484894
$452$	−6.28974e7			−0.681110
$453$	−3.96831e7	−	1.08026e8i	−0.426885	−	1.16207i
$454$	1.63473e8			1.74694
$455$	6.32466e7	+	4.46340e7i	0.671434	+	0.473839i
$456$	5.21799e6	+	1.42044e7i	0.0550312	+	0.149806i
$457$			1.07536e8i			1.12670i	0.826219	+	0.563348i	$0.190487\pi$
$457$			1.07536e8i			1.12670i	−0.826219	+	0.563348i	$0.809513\pi$
$458$	5.56222e7			0.578964
$459$	4.42189e7	+	2.50053e7i	0.457267	+	0.258580i
$460$	3.99643e7	+	2.82033e7i	0.410581	+	0.289752i
$461$			2.74690e7i			0.280376i	0.990125	+	0.140188i	$0.0447707\pi$
$461$			2.74690e7i			0.280376i	−0.990125	+	0.140188i	$0.955229\pi$
$462$	4.89837e7	+	1.33344e8i	0.496736	+	1.35222i
$463$			1.62428e8i			1.63650i	0.574860	+	0.818252i	$0.305057\pi$
$463$			1.62428e8i			1.63650i	−0.574860	+	0.818252i	$0.694943\pi$
$464$			7.75631e7i			0.776428i
$465$	−1.04494e7	+	3.88881e7i	−0.103928	+	0.386774i
$466$	−2.27165e8			−2.24483
$467$	−6.70106e7			−0.657950			−0.328975	−	0.944339i	$-0.606703\pi$
$467$	−6.70106e7			−0.657950			−0.328975	+	0.944339i	$0.606703\pi$
$468$	4.09335e7	+	4.81963e7i	0.399339	+	0.470193i
$469$	−9.03785e7			−0.876085
$470$	1.84337e8	+	1.30089e8i	1.77549	+	1.25299i
$471$	1.32487e8	−	4.86690e7i	1.26797	−	0.465789i
$472$		−	6.42972e7i		−	0.611457i
$473$	−3.07899e7			−0.290954
$474$	−4.84005e7	−	1.31756e8i	−0.454480	−	1.23719i
$475$	−1.83068e7	−	5.14747e7i	−0.170817	−	0.480300i
$476$			1.10605e8i			1.02554i
$477$	7.99313e7	−	6.78864e7i	0.736481	−	0.625500i
$478$		−	9.08996e7i		−	0.832297i
$479$		−	1.39226e8i		−	1.26681i	−0.773819	−	0.633407i	$-0.781656\pi$
$479$		−	1.39226e8i		−	1.26681i	0.773819	−	0.633407i	$-0.218344\pi$
$480$	4.07770e7	−	1.51754e8i	0.368716	−	1.37220i
$481$	3.22129e7			0.289464
$482$	−2.90438e7			−0.259366
$483$	−7.08058e7	+	2.60105e7i	−0.628388	+	0.230838i
$484$	8.77091e7			0.773586
$485$	−1.12364e8	+	1.59220e8i	−0.984918	+	1.39564i
$486$	−1.67618e8	+	3.21382e7i	−1.46020	+	0.279970i
$487$		−	3.73851e7i		−	0.323677i	−0.986817	−	0.161838i	$-0.948258\pi$
$487$		−	3.73851e7i		−	0.323677i	0.986817	−	0.161838i	$-0.0517423\pi$
$488$	−4.96251e7			−0.427014
$489$	−4.72868e7	+	1.73708e7i	−0.404402	+	0.148557i
$490$	−2.28765e8	−	1.61442e8i	−1.94447	−	1.37224i
$491$		−	1.38323e8i		−	1.16856i	−0.811553	−	0.584278i	$-0.801378\pi$
$491$		−	1.38323e8i		−	1.16856i	0.811553	−	0.584278i	$-0.198622\pi$
$492$	1.09221e8	−	4.01223e7i	0.917088	−	0.336892i
$493$			6.55920e7i			0.547407i
$494$		−	4.65615e7i		−	0.386230i
$495$	−6.51633e6	−	7.25787e7i	−0.0537263	−	0.598403i
$496$	3.64127e7			0.298406
$497$	−8.38467e7			−0.682994
$498$	3.79760e7	+	1.03379e8i	0.307483	+	0.837032i
$499$	1.75601e8			1.41327			0.706634	−	0.707580i	$-0.250213\pi$
$499$	1.75601e8			1.41327			0.706634	+	0.707580i	$0.250213\pi$
$500$	4.07780e7	−	1.45723e8i	0.326224	−	1.16578i
$501$	3.56530e7	+	9.70549e7i	0.283520	+	0.771799i
$502$			3.00490e7i			0.237530i
$503$	9.11890e7			0.716537			0.358268	−	0.933619i	$-0.383367\pi$
$503$	9.11890e7			0.716537			0.358268	+	0.933619i	$0.383367\pi$
$504$	−4.18420e7	−	4.92659e7i	−0.326829	−	0.384818i
$505$	−6.92987e6	+	9.81967e6i	−0.0538085	+	0.0762470i
$506$		−	4.80408e7i		−	0.370817i
$507$	3.32687e7	+	9.05642e7i	0.255277	+	0.694916i
$508$			5.46657e7i			0.416988i
$509$			1.82953e7i			0.138735i	0.997591	+	0.0693675i	$0.0220981\pi$
$509$			1.82953e7i			0.138735i	−0.997591	+	0.0693675i	$0.977902\pi$
$510$	2.68855e7	−	1.00056e8i	0.202679	−	0.754282i
$511$	3.88162e7			0.290904
$512$	−1.73403e8			−1.29195
$513$	5.99070e7	+	3.38767e7i	0.443737	+	0.250928i
$514$	1.15459e8			0.850235
$515$	2.62577e7	−	3.72073e7i	0.192236	−	0.272400i
$516$	7.56028e7	−	2.77726e7i	0.550287	−	0.202147i
$517$		−	1.21349e8i		−	0.878141i
$518$	−1.89305e8			−1.36199
$519$	−2.82828e7	−	7.69916e7i	−0.202311	−	0.550733i
$520$	1.29342e7	−	1.83278e7i	0.0919873	−	0.130347i
$521$			1.08670e8i			0.768416i	0.923247	+	0.384208i	$0.125525\pi$
$521$			1.08670e8i			0.768416i	−0.923247	+	0.384208i	$0.874475\pi$
$522$	−1.42655e8	−	1.67966e8i	−1.00294	−	1.18089i
$523$			1.47334e8i			1.02990i	0.857219	+	0.514952i	$0.172190\pi$
$523$			1.47334e8i			1.02990i	−0.857219	+	0.514952i	$0.827810\pi$
$524$			1.82784e8i			1.27041i
$525$	1.49214e8	+	1.79419e8i	1.03117	+	1.23991i
$526$	2.97969e8			2.04745
$527$	3.07927e7			0.210386
$528$	−6.18533e7	+	2.27218e7i	−0.420205	+	0.154362i
$529$	−1.22526e8			−0.827678
$530$	−1.74748e8	−	1.23322e8i	−1.17377	−	0.828348i
$531$	−1.89296e8	−	2.22883e8i	−1.26432	−	1.48865i
$532$			1.49846e8i			0.995197i
$533$	−6.22745e7			−0.411271
$534$	−1.90275e8	+	6.98974e7i	−1.24956	+	0.459026i
$535$	−4.46789e6	−	3.15305e6i	−0.0291770	−	0.0205906i
$536$			2.61901e7i			0.170076i
$537$	5.24103e7	−	1.92529e7i	0.338449	−	0.124329i
$538$		−	2.18857e8i		−	1.40544i
$539$			1.50596e8i			0.961714i
$540$	8.14668e7	+	1.72335e8i	0.517368	+	1.09444i
$541$	9.02632e7			0.570058			0.285029	−	0.958519i	$-0.407997\pi$
$541$	9.02632e7			0.570058			0.285029	+	0.958519i	$0.407997\pi$
$542$	4.27250e8			2.68340
$543$	−2.68451e7	−	7.30780e7i	−0.167674	−	0.456444i
$544$	−1.20164e8			−0.746408
$545$	1.61122e7	+	1.13706e7i	0.0995324	+	0.0702413i
$546$	6.85780e7	+	1.86683e8i	0.421315	+	1.14691i
$547$		−	1.91691e8i		−	1.17122i	−0.810592	−	0.585611i	$-0.800855\pi$
$547$		−	1.91691e8i		−	1.17122i	0.810592	−	0.585611i	$-0.199145\pi$
$548$	2.11750e8			1.28671
$549$	−1.72023e8	+	1.46100e8i	−1.03961	+	0.882946i
$550$	−1.40028e8	+	4.98004e7i	−0.841639	+	0.299327i
$551$			8.88629e7i			0.531209i
$552$	7.53739e6	+	2.05183e7i	0.0448130	+	0.121990i
$553$		−	2.41764e8i		−	1.42960i
$554$		−	1.17471e8i		−	0.690875i
$555$	9.37815e7	+	2.51995e7i	0.548578	+	0.147405i
$556$	−2.22195e8			−1.29274
$557$	1.22977e8			0.711634			0.355817	−	0.934556i	$-0.384203\pi$
$557$	1.22977e8			0.711634			0.355817	+	0.934556i	$0.384203\pi$
$558$	−7.88531e7	+	6.69706e7i	−0.453854	+	0.385462i
$559$	−4.31064e7			−0.246778
$560$	1.21671e8	−	1.72409e8i	0.692826	−	0.981739i
$561$	−5.23068e7	+	1.92149e7i	−0.296258	+	0.108830i
$562$			2.75538e8i			1.55229i
$563$	−1.42149e7			−0.0796559			−0.0398279	−	0.999207i	$-0.512681\pi$
$563$	−1.42149e7			−0.0796559			−0.0398279	+	0.999207i	$0.512681\pi$
$564$	1.09457e8	+	2.97965e8i	0.610109	+	1.66084i
$565$	8.29113e7	+	5.85115e7i	0.459693	+	0.324411i
$566$		−	3.82200e8i		−	2.10786i
$567$	−2.90086e8	−	4.75914e7i	−1.59139	−	0.261083i
$568$			2.42973e7i			0.132591i
$569$			1.16372e8i			0.631699i	0.948809	+	0.315849i	$0.102289\pi$
$569$			1.16372e8i			0.631699i	−0.948809	+	0.315849i	$0.897711\pi$
$570$	3.64240e7	−	1.35554e8i	0.196681	−	0.731963i
$571$	−2.29444e8			−1.23245			−0.616225	−	0.787570i	$-0.711339\pi$
$571$	−2.29444e8			−1.23245			−0.616225	+	0.787570i	$0.711339\pi$
$572$	−6.93637e7			−0.370633
$573$	2.92442e8	−	1.07428e8i	1.55445	−	0.571024i
$574$	3.65967e8			1.93511
$575$	−2.64442e7	−	7.43552e7i	−0.139100	−	0.391118i
$576$	1.99182e8	−	1.69167e8i	1.04228	−	0.885214i
$577$			1.79763e8i			0.935779i	0.883787	+	0.467890i	$0.154986\pi$
$577$			1.79763e8i			0.935779i	−0.883787	+	0.467890i	$0.845014\pi$
$578$	2.07874e8			1.07651
$579$	1.39922e8	−	5.14004e7i	0.720861	−	0.264808i
$580$	−1.41916e8	+	2.01095e8i	−0.727355	+	1.03067i
$581$			1.89693e8i			0.967214i
$582$	−4.69965e8	+	1.72641e8i	−2.38395	+	0.875741i
$583$			1.15037e8i			0.580537i
$584$		−	1.12483e7i		−	0.0564738i
$585$	−9.12297e6	−	1.01611e8i	−0.0455689	−	0.507546i
$586$	−1.46748e8			−0.729255
$587$	−2.09507e7			−0.103582			−0.0517911	−	0.998658i	$-0.516493\pi$
$587$	−2.09507e7			−0.103582			−0.0517911	+	0.998658i	$0.516493\pi$
$588$	−1.35838e8	−	3.69779e8i	−0.668174	−	1.81891i
$589$	4.17174e7			0.204160
$590$	−3.43874e8	+	4.87272e8i	−1.67434	+	2.37255i
$591$	9.25481e7	+	2.51935e8i	0.448338	+	1.22047i
$592$		−	8.78119e7i		−	0.423241i
$593$	−7.12863e6			−0.0341855			−0.0170928	−	0.999854i	$-0.505441\pi$
$593$	−7.12863e6			−0.0341855			−0.0170928	+	0.999854i	$0.505441\pi$
$594$	9.21557e7	−	1.62966e8i	0.439706	−	0.777568i
$595$	1.02893e8	−	1.45799e8i	0.488465	−	0.692158i
$596$		−	2.88197e8i		−	1.36129i
$597$	7.70062e7	+	2.09627e8i	0.361912	+	0.985198i
$598$		−	6.72580e7i		−	0.314515i
$599$		−	1.78170e8i		−	0.829001i	−0.910049	−	0.414500i	$-0.863956\pi$
$599$		−	1.78170e8i		−	0.829001i	0.910049	−	0.414500i	$-0.136044\pi$
$600$	5.19926e7	−	4.32396e7i	0.240707	−	0.200183i
$601$	−5.30074e7			−0.244182			−0.122091	−	0.992519i	$-0.538960\pi$
$601$	−5.30074e7			−0.244182			−0.122091	+	0.992519i	$0.538960\pi$
$602$	2.53323e8			1.16114
$603$	7.71059e7	+	9.07866e7i	0.351670	+	0.414066i
$604$	−3.30232e8			−1.49868
$605$	−1.15618e8	−	8.15931e7i	−0.522107	−	0.368457i
$606$	−2.89845e7	+	1.06474e7i	−0.130241	+	0.0478439i
$607$			1.06802e8i			0.477543i	0.971076	+	0.238772i	$0.0767447\pi$
$607$			1.06802e8i			0.477543i	−0.971076	+	0.238772i	$0.923255\pi$
$608$	−1.62795e8			−0.724322
$609$	−1.30881e8	−	3.56286e8i	−0.579464	−	1.57742i
$610$	3.76081e8	+	2.65405e8i	1.65688	+	1.16928i
$611$		−	1.69891e8i		−	0.744810i
$612$	1.11105e8	−	9.43621e7i	0.484705	−	0.411664i
$613$		−	2.08653e8i		−	0.905822i	−0.891556	−	0.452911i	$-0.850386\pi$
$613$		−	2.08653e8i		−	0.905822i	0.891556	−	0.452911i	$-0.149614\pi$
$614$		−	3.89725e8i		−	1.68366i
$615$	−1.81300e8	−	4.87159e7i	−0.779420	−	0.209433i
$616$	7.09032e7			0.303336
$617$	5.25824e6			0.0223864			0.0111932	−	0.999937i	$-0.496437\pi$
$617$	5.25824e6			0.0223864			0.0111932	+	0.999937i	$0.496437\pi$
$618$	1.09824e8	−	4.03437e7i	0.465298	−	0.170927i
$619$	2.96719e8			1.25105			0.625523	−	0.780205i	$-0.284886\pi$
$619$	2.96719e8			1.25105			0.625523	+	0.780205i	$0.284886\pi$
$620$	9.44059e7	+	6.66235e7i	0.396118	+	0.279545i
$621$	8.65356e7	+	4.89349e7i	0.361343	+	0.204336i
$622$		−	6.29217e8i		−	2.61474i
$623$	−3.49143e8			−1.44391
$624$	−8.65957e7	+	3.18109e7i	−0.356404	+	0.130925i
$625$	−1.89315e8	+	1.54157e8i	−0.775435	+	0.631428i
$626$			5.05927e8i			2.06236i
$627$	−7.08643e7	+	2.60320e7i	−0.287492	+	0.105610i
$628$		−	4.05010e8i		−	1.63526i
$629$		−	7.42590e7i		−	0.298399i
$630$	5.36128e7	+	5.97138e8i	0.214411	+	2.38810i
$631$	2.08250e8			0.828891			0.414446	−	0.910074i	$-0.363975\pi$
$631$	2.08250e8			0.828891			0.414446	+	0.910074i	$0.363975\pi$
$632$	−7.00590e7			−0.277532
$633$	5.88236e7	+	1.60130e8i	0.231921	+	0.631337i
$634$	−2.30964e8			−0.906309
$635$	5.08539e7	−	7.20603e7i	0.198611	−	0.281433i
$636$	−1.03764e8	−	2.82466e8i	−0.403342	−	1.09798i
$637$			2.10837e8i			0.815695i
$638$	2.41736e8			0.930848
$639$	7.15334e7	+	8.42254e7i	0.274161	+	0.322805i
$640$	−1.31134e8	−	9.25429e7i	−0.500236	−	0.353023i
$641$			4.68502e8i			1.77884i	0.457088	+	0.889421i	$0.348892\pi$
$641$			4.68502e8i			1.77884i	−0.457088	+	0.889421i	$0.651108\pi$
$642$	−4.84451e6	−	1.31878e7i	−0.0183082	−	0.0498386i
$643$			6.77858e7i			0.254980i	0.991840	+	0.127490i	$0.0406921\pi$
$643$			6.77858e7i			0.254980i	−0.991840	+	0.127490i	$0.959308\pi$
$644$			2.16452e8i			0.810408i
$645$	−1.25496e8	−	3.37212e7i	−0.467681	−	0.125668i
$646$	−1.07336e8			−0.398151
$647$	3.49360e8			1.28991			0.644956	−	0.764220i	$-0.276876\pi$
$647$	3.49360e8			1.28991			0.644956	+	0.764220i	$0.276876\pi$
$648$	−1.37912e7	+	8.40619e7i	−0.0506846	+	0.308940i
$649$	3.20771e8			1.17344
$650$	−1.96041e8	+	6.97215e7i	−0.713851	+	0.253879i
$651$	−1.67262e8	+	6.14434e7i	−0.606252	+	0.222706i
$652$			1.44555e8i			0.521543i
$653$	−1.61388e8			−0.579604			−0.289802	−	0.957087i	$-0.593589\pi$
$653$	−1.61388e8			−0.579604			−0.289802	+	0.957087i	$0.593589\pi$
$654$	1.74704e7	+	4.75579e7i	0.0624552	+	0.170016i
$655$	1.70038e8	−	2.40945e8i	0.605093	−	0.857421i
$656$			1.69759e8i			0.601342i
$657$	−3.31158e7	−	3.89915e7i	−0.116772	−	0.137491i
$658$			9.98393e8i			3.50448i
$659$			9.59866e7i			0.335393i	0.985839	+	0.167697i	$0.0536329\pi$
$659$			9.59866e7i			0.335393i	−0.985839	+	0.167697i	$0.946367\pi$
$660$	−2.01939e8	−	5.42617e7i	−0.702405	−	0.188739i
$661$	1.66521e8			0.576586			0.288293	−	0.957542i	$-0.406912\pi$
$661$	1.66521e8			0.576586			0.288293	+	0.957542i	$0.406912\pi$
$662$	−2.82712e8			−0.974473
$663$	−7.32305e7	+	2.69012e7i	−0.251276	+	0.0923062i
$664$	5.49698e7			0.187767
$665$	1.39397e8	−	1.97526e8i	0.474011	−	0.671677i
$666$	1.61505e8	+	1.90160e8i	0.546717	+	0.643720i
$667$			1.28362e8i			0.432574i
$668$	2.96695e8			0.995361
$669$	2.93031e8	−	1.07645e8i	0.978669	−	0.359513i
$670$	1.40070e8	−	1.98480e8i	0.465716	−	0.659923i
$671$		−	2.47574e8i		−	0.819478i
$672$	6.52711e8	−	2.39773e8i	2.15087	−	0.790119i
$673$		−	3.63557e8i		−	1.19269i	−0.802728	−	0.596345i	$-0.796619\pi$
$673$		−	3.63557e8i		−	1.19269i	0.802728	−	0.596345i	$-0.203381\pi$
$674$			2.52385e8i			0.824296i
$675$	5.29287e7	−	3.02958e8i	0.172100	−	0.985080i
$676$	2.76853e8			0.896208
$677$	−4.99793e8			−1.61074			−0.805368	−	0.592775i	$-0.798032\pi$
$677$	−4.99793e8			−1.61074			−0.805368	+	0.592775i	$0.798032\pi$
$678$	8.99003e7	+	2.44727e8i	0.288451	+	0.785223i
$679$	−8.62356e8			−2.75472
$680$	−4.22502e7	−	2.98165e7i	−0.134370	−	0.0948265i
$681$	−1.27956e8	−	3.48321e8i	−0.405152	−	1.10291i
$682$		−	1.13485e8i		−	0.357754i
$683$	−262982.			−0.000825399			−0.000412700	−	1.00000i	$-0.500131\pi$
$683$	−262982.			−0.000825399			−0.000412700		1.00000i	$0.500131\pi$
$684$	1.50522e8	−	1.27840e8i	0.470363	−	0.399483i
$685$	−2.79128e8	−	1.96984e8i	−0.868425	−	0.612858i
$686$		−	4.64969e8i		−	1.44030i
$687$	−4.35373e7	−	1.18518e8i	−0.134274	−	0.365521i
$688$			1.17507e8i			0.360827i
$689$			1.61053e8i			0.492393i
$690$	5.26145e7	−	1.95808e8i	0.160161	−	0.596052i
$691$	−4.32873e8			−1.31198			−0.655989	−	0.754770i	$-0.727748\pi$
$691$	−4.32873e8			−1.31198			−0.655989	+	0.754770i	$0.727748\pi$
$692$	−2.35362e8			−0.710260
$693$	2.45782e8	−	2.08745e8i	0.738500	−	0.627214i
$694$	−4.82361e8			−1.44309
$695$	2.92897e8	+	2.06702e8i	0.872492	+	0.615729i
$696$	−1.03246e8	+	3.79272e7i	−0.306227	+	0.112492i
$697$			1.43558e8i			0.423965i
$698$	−5.97395e8			−1.75669
$699$	1.77809e8	+	4.84033e8i	0.520622	+	1.41724i
$700$	6.30907e8	−	2.24380e8i	1.83938	−	0.654169i
$701$		−	3.96250e8i		−	1.15031i	−0.818044	−	0.575155i	$-0.804942\pi$
$701$		−	3.96250e8i		−	1.15031i	0.818044	−	0.575155i	$-0.195058\pi$
$702$	1.29020e8	−	2.28156e8i	0.372945	−	0.659508i
$703$		−	1.00605e8i		−	0.289569i
$704$			2.86661e8i			0.821583i
$705$	1.32902e8	−	4.94602e8i	0.379283	−	1.41153i
$706$	4.19393e8			1.19181
$707$	−5.31846e7			−0.150497
$708$	−7.87635e8	+	2.89337e8i	−2.21935	+	0.815276i
$709$	−4.09941e7			−0.115022			−0.0575112	−	0.998345i	$-0.518316\pi$
$709$	−4.09941e7			−0.115022			−0.0575112	+	0.998345i	$0.518316\pi$
$710$	1.29947e8	−	1.84136e8i	0.363071	−	0.514474i
$711$	−2.42856e8	+	2.06260e8i	−0.675678	+	0.573859i
$712$			1.01176e8i			0.280308i
$713$	6.02608e7			0.166252
$714$	4.30352e8	−	1.58090e8i	1.18231	−	0.434319i
$715$	9.14352e7	+	6.45270e7i	0.250147	+	0.176532i
$716$		−	1.60217e8i		−	0.436486i
$717$	−1.93685e8	+	7.11501e7i	−0.525459	+	0.193027i
$718$			2.01004e8i			0.543039i
$719$		−	4.41110e8i		−	1.18675i	−0.804925	−	0.593377i	$-0.797794\pi$
$719$		−	4.41110e8i		−	1.18675i	0.804925	−	0.593377i	$-0.202206\pi$
$720$	−2.76991e8	+	2.48691e7i	−0.742110	+	0.0666288i
$721$	2.01520e8			0.537665
$722$	4.14165e8			1.10043
$723$	2.27335e7	+	6.18854e7i	0.0601523	+	0.163747i
$724$	−2.23398e8			−0.588658
$725$	3.74146e8	−	1.33064e8i	0.981809	−	0.349178i
$726$	−1.25364e8	−	3.41267e8i	−0.327615	−	0.891834i
$727$			2.20449e8i			0.573726i	0.957972	+	0.286863i	$0.0926124\pi$
$727$			2.20449e8i			0.573726i	−0.957972	+	0.286863i	$0.907388\pi$
$728$	9.92657e7			0.257279
$729$	1.99679e8	+	3.31998e8i	0.515406	+	0.856946i
$730$	−6.01580e7	+	8.52442e7i	−0.154641	+	0.219127i
$731$			9.93712e7i			0.254395i
$732$	2.23313e8	+	6.07903e8i	0.569352	+	1.54989i
$733$			5.85539e8i			1.48677i	0.668863	+	0.743385i	$0.266781\pi$
$733$			5.85539e8i			1.48677i	−0.668863	+	0.743385i	$0.733219\pi$
$734$			4.02927e8i			1.01891i
$735$	−1.64933e8	+	6.13808e8i	−0.415379	+	1.54586i
$736$	−2.35158e8			−0.589829
$737$	−1.30659e8			−0.326391
$738$	−3.12223e8	−	3.67620e8i	−0.776776	−	0.914598i
$739$	2.72485e6			0.00675164			0.00337582	−	0.999994i	$-0.498925\pi$
$739$	2.72485e6			0.00675164			0.00337582	+	0.999994i	$0.498925\pi$
$740$	1.60668e8	−	2.27667e8i	0.396491	−	0.561830i
$741$	−9.92114e7	+	3.64452e7i	−0.243841	+	0.0895748i
$742$		−	9.46459e8i		−	2.31681i
$743$	6.73301e8			1.64151			0.820753	−	0.571283i	$-0.193554\pi$
$743$	6.73301e8			1.64151			0.820753	+	0.571283i	$0.193554\pi$
$744$	1.78052e7	+	4.84695e7i	0.0432344	+	0.117693i
$745$	−2.68101e8	+	3.79900e8i	−0.648379	+	0.918758i
$746$			5.83563e8i			1.40563i
$747$	1.90550e8	−	1.61836e8i	0.457137	−	0.388251i
$748$			1.59901e8i			0.382073i
$749$		−	2.41987e7i		−	0.0575899i
$750$	−6.25277e8	+	4.96214e7i	−1.48214	+	0.117621i
$751$	8.01454e8			1.89216			0.946082	−	0.323927i	$-0.105003\pi$
$751$	8.01454e8			1.89216			0.946082	+	0.323927i	$0.105003\pi$
$752$	−4.63119e8			−1.08903
$753$	6.40272e7	−	2.35203e7i	0.149961	−	0.0550882i
$754$	3.38434e8			0.789515
$755$	4.35311e8	+	3.07205e8i	1.01148	+	0.713817i
$756$	−4.15215e8	+	7.34258e8i	−0.960965	+	1.69935i
$757$		−	5.24719e8i		−	1.20959i	−0.796380	−	0.604797i	$-0.793254\pi$
$757$		−	5.24719e8i		−	1.20959i	0.796380	−	0.604797i	$-0.206746\pi$
$758$	5.18861e8			1.19136
$759$	−1.02363e8	+	3.76031e7i	−0.234110	+	0.0860001i
$760$	−5.72398e7	−	4.03948e7i	−0.130394	−	0.0920206i
$761$		−	1.32891e8i		−	0.301538i	−0.988569	−	0.150769i	$-0.951825\pi$
$761$		−	1.32891e8i		−	0.301538i	0.988569	−	0.150769i	$-0.0481750\pi$
$762$	2.12698e8	−	7.81346e7i	0.480728	−	0.176595i
$763$			8.72657e7i			0.196458i
$764$		−	8.93988e8i		−	2.00471i
$765$	−2.34240e8	+	2.10308e7i	−0.523211	+	0.0469754i
$766$	−5.58589e8			−1.24281
$767$	4.49085e8			0.995274
$768$	7.14064e7	+	1.94383e8i	0.157635	+	0.429116i
$769$	−2.57071e8			−0.565294			−0.282647	−	0.959224i	$-0.591212\pi$
$769$	−2.57071e8			−0.565294			−0.282647	+	0.959224i	$0.591212\pi$
$770$	−5.37335e8	−	3.79204e8i	−1.17699	−	0.830618i
$771$	−9.03737e7	−	2.46016e8i	−0.197187	−	0.536784i
$772$		−	4.27740e8i		−	0.929668i
$773$	−7.62255e8			−1.65029			−0.825147	−	0.564917i	$-0.808908\pi$
$773$	−7.62255e8			−1.65029			−0.825147	+	0.564917i	$0.808908\pi$
$774$	−2.16121e8	−	2.54467e8i	−0.466094	−	0.548792i
$775$	−6.24680e7	−	1.75646e8i	−0.134200	−	0.377340i
$776$			2.49896e8i			0.534779i
$777$	1.48175e8	+	4.03364e8i	0.315873	+	0.859872i
$778$		−	1.00698e9i		−	2.13836i
$779$			1.94490e8i			0.411420i
$780$	−2.82718e8	−	7.59674e7i	−0.595757	−	0.160082i
$781$	−1.21217e8			−0.254454
$782$	−1.55047e8			−0.324222
$783$	−2.46235e8	+	4.35436e8i	−0.512937	+	0.907067i
$784$	5.74737e8			1.19267
$785$	−3.76768e8	+	5.33883e8i	−0.778871	+	1.10367i
$786$	7.11192e8	−	2.61256e8i	1.46460	−	0.538020i
$787$			6.33980e8i			1.30062i	0.759667	+	0.650312i	$0.225362\pi$
$787$			6.33980e8i			1.30062i	−0.759667	+	0.650312i	$0.774638\pi$
$788$	7.70160e8			1.57399
$789$	−2.33230e8	−	6.34900e8i	−0.474847	−	1.29263i
$790$	5.30938e8	+	3.74690e8i	1.07687	+	0.759960i
$791$			4.49058e8i			0.907347i
$792$	−6.04907e7	−	7.12234e7i	−0.121762	−	0.143366i
$793$		−	3.46608e8i		−	0.695054i
$794$		−	8.05706e8i		−	1.60959i
$795$	−1.25988e8	+	4.68874e8i	−0.250743	+	0.933157i
$796$	6.40824e8			1.27057
$797$	−1.28919e8			−0.254649			−0.127325	−	0.991861i	$-0.540639\pi$
$797$	−1.28919e8			−0.254649			−0.127325	+	0.991861i	$0.540639\pi$
$798$	5.83034e8	−	2.14177e8i	1.14732	−	0.421467i
$799$	−3.91641e8			−0.767799
$800$	2.43771e8	+	6.85430e8i	0.476116	+	1.33873i
$801$	2.97869e8	+	3.50720e8i	0.579600	+	0.682437i
$802$			1.48985e9i			2.88814i
$803$	5.61162e7			0.108378
$804$	3.20827e8	−	1.17856e8i	0.617309	−	0.226768i
$805$	2.01359e8	−	2.85327e8i	0.385996	−	0.546959i
$806$		−	1.58881e8i		−	0.303435i
$807$	−4.66331e8	+	1.71307e8i	−0.887307	+	0.325952i
$808$			1.54120e7i			0.0292163i
$809$			1.31019e7i			0.0247451i	0.999923	+	0.0123726i	$0.00393841\pi$
$809$			1.31019e7i			0.0247451i	−0.999923	+	0.0123726i	$0.996062\pi$
$810$	5.54096e8	−	5.63300e8i	1.04263	−	1.05995i
$811$	6.44274e8			1.20784			0.603918	−	0.797047i	$-0.293605\pi$
$811$	6.44274e8			1.20784			0.603918	+	0.797047i	$0.293605\pi$
$812$	−1.08916e9			−2.03434
$813$	−3.34423e8	−	9.10368e8i	−0.622335	−	1.69412i
$814$	−2.73677e8			−0.507417
$815$	1.34475e8	−	1.90552e8i	0.248410	−	0.351998i
$816$	7.33321e7	+	1.99625e8i	0.134966	+	0.367405i
$817$			1.34626e8i			0.246867i
$818$	−1.39124e9			−2.54180
$819$	3.44099e8	−	2.92246e8i	0.626371	−	0.531983i
$820$	−3.10605e8	+	4.40129e8i	−0.563334	+	0.798249i
$821$		−	9.84742e8i		−	1.77948i	−0.456468	−	0.889740i	$-0.650886\pi$
$821$		−	9.84742e8i		−	1.77948i	0.456468	−	0.889740i	$-0.349114\pi$
$822$	−3.02657e8	−	8.23896e8i	−0.544924	−	1.48339i
$823$		−	4.83684e8i		−	0.867686i	−0.900989	−	0.433843i	$-0.857157\pi$
$823$		−	4.83684e8i		−	0.867686i	0.900989	−	0.433843i	$-0.142843\pi$
$824$		−	5.83970e7i		−	0.104378i
$825$	2.15717e8	+	2.59385e8i	0.384169	+	0.461937i
$826$	−2.63913e9			−4.68296
$827$	3.06240e8			0.541434			0.270717	−	0.962659i	$-0.412739\pi$
$827$	3.06240e8			0.541434			0.270717	+	0.962659i	$0.412739\pi$
$828$	2.17430e8	−	1.84665e8i	0.383025	−	0.325307i
$829$	5.74507e8			1.00840			0.504199	−	0.863588i	$-0.331788\pi$
$829$	5.74507e8			1.00840			0.504199	+	0.863588i	$0.331788\pi$
$830$	−4.16585e8	−	2.93989e8i	−0.728567	−	0.514159i
$831$	−2.50301e8	+	9.19480e7i	−0.436174	+	0.160228i
$832$			4.01331e8i			0.696840i
$833$	4.86032e8			0.840871
$834$	3.17587e8	+	8.64538e8i	0.547476	+	1.49034i
$835$	−3.91103e8	−	2.76006e8i	−0.671787	−	0.474089i
$836$			2.16631e8i			0.370767i
$837$	2.04419e8	+	1.15597e8i	0.348614	+	0.197138i
$838$		−	1.00118e9i		−	1.70129i
$839$			4.06052e8i			0.687537i	0.939054	+	0.343768i	$0.111704\pi$
$839$			4.06052e8i			0.687537i	−0.939054	+	0.343768i	$0.888296\pi$
$840$	2.88992e8	+	7.76534e7i	0.487583	+	0.131015i
$841$	−5.10802e7			−0.0858746
$842$	1.26059e9			2.11173
$843$	5.87105e8	−	2.15673e8i	0.980017	−	0.360008i
$844$	4.89514e8			0.814212
$845$	−3.64947e8	−	2.57548e8i	−0.604867	−	0.426862i
$846$	1.00290e9	−	8.51774e8i	1.65633	−	1.40674i
$847$		−	6.26202e8i		−	1.03054i
$848$	4.39028e8			0.719954
$849$	−8.14376e8	+	2.99161e8i	−1.33077	+	0.488856i
$850$	1.60726e8	+	4.51925e8i	0.261715	+	0.735884i
$851$		−	1.45323e8i		−	0.235802i
$852$	2.97641e8	−	1.09338e8i	0.481253	−	0.176788i
$853$			7.67399e8i			1.23644i	0.786004	+	0.618221i	$0.212146\pi$
$853$			7.67399e8i			1.23644i	−0.786004	+	0.618221i	$0.787854\pi$
$854$			2.03690e9i			3.27037i
$855$	−3.17344e8	+	2.84921e7i	−0.507729	+	0.0455854i
$856$	−7.01236e6			−0.0111800
$857$	2.99694e8			0.476141			0.238070	−	0.971248i	$-0.423485\pi$
$857$	2.99694e8			0.476141			0.238070	+	0.971248i	$0.423485\pi$
$858$	9.91427e7	+	2.69887e8i	0.156964	+	0.427287i
$859$	−2.47498e8			−0.390474			−0.195237	−	0.980756i	$-0.562548\pi$
$859$	−2.47498e8			−0.390474			−0.195237	+	0.980756i	$0.562548\pi$
$860$	−2.15001e8	+	3.04657e8i	−0.338021	+	0.478979i
$861$	−2.86455e8	−	7.79788e8i	−0.448793	−	1.22171i
$862$			8.13459e8i			1.27003i
$863$	−5.04285e8			−0.784592			−0.392296	−	0.919839i	$-0.628319\pi$
$863$	−5.04285e8			−0.784592			−0.392296	+	0.919839i	$0.628319\pi$
$864$	−7.97713e8	−	4.51098e8i	−1.23682	−	0.699407i
$865$	3.10254e8	+	2.18950e8i	0.479367	+	0.338296i
$866$			1.20862e9i			1.86095i
$867$	−1.62710e8	−	4.42929e8i	−0.249664	−	0.679637i
$868$			5.11315e8i			0.781861i
$869$		−	3.49516e8i		−	0.532608i
$870$	9.85283e8	+	2.64750e8i	1.49625	+	0.402048i
$871$	−1.82926e8			−0.276834
$872$	2.52881e7			0.0381388
$873$	7.35715e8	+	8.66251e8i	1.10577	+	1.30197i
$874$	−2.10055e8			−0.314628
$875$	−1.04039e9	−	2.91136e8i	−1.55301	−	0.434582i
$876$	−1.37790e8	+	5.06172e7i	−0.204978	+	0.0752983i
$877$		−	1.25925e9i		−	1.86686i	−0.358755	−	0.933432i	$-0.616799\pi$
$877$		−	1.25925e9i		−	1.86686i	0.358755	−	0.933432i	$-0.383201\pi$
$878$	4.54795e8			0.671943
$879$	1.14864e8	+	3.12685e8i	0.169129	+	0.460405i
$880$	1.75899e8	−	2.49251e8i	0.258117	−	0.365753i
$881$			3.01970e7i			0.0441608i	0.999756	+	0.0220804i	$0.00702898\pi$
$881$			3.01970e7i			0.0441608i	−0.999756	+	0.0220804i	$0.992971\pi$
$882$	−1.24462e9	+	1.05706e9i	−1.81397	+	1.54062i
$883$		−	2.99514e8i		−	0.435045i	−0.976055	−	0.217523i	$-0.930202\pi$
$883$		−	2.99514e8i		−	0.435045i	0.976055	−	0.217523i	$-0.0697976\pi$
$884$			2.23864e8i			0.324062i
$885$	1.30742e9	+	3.51309e8i	1.88619	+	0.506827i
$886$	1.42953e9			2.05538
$887$	−5.62808e8			−0.806472			−0.403236	−	0.915096i	$-0.632115\pi$
$887$	−5.62808e8			−0.806472			−0.403236	+	0.915096i	$0.632115\pi$
$888$	1.16888e8	−	4.29387e7i	0.166929	−	0.0613211i
$889$	3.90288e8			0.555495
$890$	5.41107e8	−	7.66753e8i	0.767562	−	1.08764i
$891$	−4.19375e8	−	6.88025e7i	−0.592884	−	0.0972683i
$892$		−	8.95791e8i		−	1.26215i
$893$	−5.30588e8			−0.745080
$894$	−1.12134e9	+	4.11924e8i	−1.56937	+	0.576507i
$895$	−1.49045e8	+	2.11198e8i	−0.207897	+	0.294592i
$896$		−	7.10239e8i		−	0.987371i
$897$	−1.43311e8	+	5.26451e7i	−0.198564	+	0.0729425i
$898$			7.62593e8i			1.05309i
$899$			3.03225e8i			0.417336i
$900$	−7.63648e8	−	4.42327e8i	−1.04753	−	0.606759i
$901$	3.71268e8			0.507591
$902$	5.29076e8			0.720939
$903$	−1.98284e8	−	5.39770e8i	−0.269293	−	0.733069i
$904$	1.30129e8			0.176145
$905$	2.94483e8	+	2.07820e8i	0.397296	+	0.280377i
$906$	4.72006e8	+	1.28490e9i	0.634692	+	1.72776i
$907$			3.12764e8i			0.419175i	0.977790	+	0.209588i	$0.0672121\pi$
$907$			3.12764e8i			0.419175i	−0.977790	+	0.209588i	$0.932788\pi$
$908$	−1.06481e9			−1.42238
$909$	4.53742e7	+	5.34249e7i	0.0604112	+	0.0711298i
$910$	−7.52279e8	−	5.30893e8i	−0.998286	−	0.704503i
$911$		−	2.78730e8i		−	0.368663i	−0.982864	−	0.184331i	$-0.940988\pi$
$911$		−	2.78730e8i		−	0.368663i	0.982864	−	0.184331i	$-0.0590120\pi$
$912$	9.93490e7	+	2.70448e8i	0.130972	+	0.356533i
$913$			2.74238e8i			0.360342i
$914$		−	1.27908e9i		−	1.67517i
$915$	2.71144e8	−	1.00908e9i	0.353945	−	1.31723i
$916$	−3.62306e8			−0.471399
$917$	1.30499e9			1.69239
$918$	−5.25957e8	−	2.97423e8i	−0.679864	−	0.384456i
$919$	5.75417e8			0.741372			0.370686	−	0.928758i	$-0.379123\pi$
$919$	5.75417e8			0.741372			0.370686	+	0.928758i	$0.379123\pi$
$920$	−8.26828e7	−	5.83503e7i	−0.106182	−	0.0749341i
$921$	−8.30411e8	+	3.05051e8i	−1.06295	+	0.390475i
$922$		−	3.26727e8i		−	0.416862i
$923$	−1.69705e8			−0.215820
$924$	−3.19064e8	−	8.68558e8i	−0.404448	−	1.10099i
$925$	−4.23584e8	+	1.50646e8i	−0.535197	+	0.190341i
$926$		−	1.93198e9i		−	2.43315i
$927$	−1.71926e8	−	2.02430e8i	−0.215825	−	0.254118i
$928$		−	1.18329e9i		−	1.48063i
$929$			4.36852e8i			0.544863i	0.962175	+	0.272431i	$0.0878278\pi$
$929$			4.36852e8i			0.544863i	−0.962175	+	0.272431i	$0.912172\pi$
$930$	1.24289e8	−	4.62549e8i	0.154520	−	0.575055i
$931$	6.58467e8			0.815990
$932$	1.47968e9			1.82776
$933$	−1.34071e9	+	4.92509e8i	−1.65078	+	0.606414i
$934$	7.97049e8			0.978238
$935$	1.48751e8	−	2.10781e8i	0.181981	−	0.257868i
$936$	−8.46880e7	−	9.97140e7i	−0.103275	−	0.121599i
$937$			1.21122e8i			0.147233i	0.997287	+	0.0736165i	$0.0234541\pi$
$937$			1.21122e8i			0.147233i	−0.997287	+	0.0736165i	$0.976546\pi$
$938$	1.07500e9			1.30256
$939$	1.07801e9	−	3.96005e8i	1.30204	−	0.478304i
$940$	−1.20071e9	−	8.47358e8i	−1.44562	−	1.02020i
$941$			1.48647e9i			1.78396i	0.452071	+	0.891982i	$0.350686\pi$
$941$			1.48647e9i			1.78396i	−0.452071	+	0.891982i	$0.649314\pi$
$942$	−1.57585e9	+	5.78887e8i	−1.88522	+	0.692534i
$943$			2.80941e8i			0.335027i
$944$		−	1.22420e9i		−	1.45524i
$945$	1.23039e9	−	5.81636e8i	1.45797	−	0.689217i
$946$	3.66227e8			0.432590
$947$	−1.38450e9			−1.63021			−0.815105	−	0.579313i	$-0.803321\pi$
$947$	−1.38450e9			−1.63021			−0.815105	+	0.579313i	$0.803321\pi$
$948$	3.15266e8	+	8.58217e8i	0.370042	+	1.00733i
$949$	7.85638e7			0.0919229
$950$	2.17748e8	+	6.12260e8i	0.253971	+	0.714110i
$951$	1.80783e8	+	4.92129e8i	0.210192	+	0.572186i
$952$		−	2.28833e8i		−	0.265220i
$953$	5.27582e7			0.0609553			0.0304777	−	0.999535i	$-0.490297\pi$
$953$	5.27582e7			0.0609553			0.0304777	+	0.999535i	$0.490297\pi$
$954$	−9.50733e8	+	8.07466e8i	−1.09500	+	0.929992i
$955$	−8.31651e8	+	1.17845e9i	−0.954840	+	1.35302i
$956$			5.92091e8i			0.677665i
$957$	−1.89214e8	−	5.15080e8i	−0.215883	−	0.587678i
$958$			1.65600e9i			1.88349i
$959$		−	1.51180e9i		−	1.71410i
$960$	−3.13952e8	+	1.16840e9i	−0.354854	+	1.32061i
$961$	−7.45152e8			−0.839605
$962$	−3.83153e8			−0.430375
$963$	−2.43080e7	+	2.06450e7i	−0.0272189	+	0.0231172i
$964$	1.89182e8			0.211178
$965$	−3.97914e8	+	5.63846e8i	−0.442799	+	0.627450i
$966$	8.42191e8	−	3.09378e8i	0.934285	−	0.343209i
$967$			3.67686e8i			0.406628i	0.979114	+	0.203314i	$0.0651712\pi$
$967$			3.67686e8i			0.406628i	−0.979114	+	0.203314i	$0.934829\pi$
$968$	−1.81463e8			−0.200060
$969$	8.40154e7	+	2.28707e8i	0.0923396	+	0.251367i
$970$	1.33649e9	−	1.89382e9i	1.46437	−	2.07503i
$971$			1.31090e9i			1.43189i	0.698156	+	0.715946i	$0.254004\pi$
$971$			1.31090e9i			1.43189i	−0.698156	+	0.715946i	$0.745996\pi$
$972$	1.09181e9	−	2.09338e8i	1.18891	−	0.227955i
$973$			1.58637e9i			1.72213i
$974$			4.44672e8i			0.481241i
$975$	3.02008e8	+	3.63144e8i	0.325840	+	0.391800i
$976$	−9.44846e8			−1.01628
$977$	−7.72338e7			−0.0828178			−0.0414089	−	0.999142i	$-0.513185\pi$
$977$	−7.72338e7			−0.0828178			−0.0414089	+	0.999142i	$0.513185\pi$
$978$	5.62447e8	−	2.06615e8i	0.601264	−	0.220874i
$979$	−5.04753e8			−0.537936
$980$	1.49010e9	+	1.05158e9i	1.58321	+	1.11729i
$981$	8.76598e7	−	7.44502e7i	0.0928525	−	0.0788604i
$982$			1.64527e9i			1.73741i
$983$	1.49397e9			1.57283			0.786417	−	0.617696i	$-0.211934\pi$
$983$	1.49397e9			1.57283			0.786417	+	0.617696i	$0.211934\pi$
$984$	−2.25969e8	+	8.30096e7i	−0.237172	+	0.0871251i
$985$	−1.01522e9	−	7.16457e8i	−1.06231	−	0.749689i
$986$		−	7.80177e8i		−	0.813883i
$987$	2.12734e9	−	7.81475e8i	2.21251	−	0.812762i
$988$			3.03287e8i			0.314473i
$989$			1.94467e8i			0.201029i
$990$	7.75077e7	+	8.63279e8i	0.0798802	+	0.889704i
$991$	−4.50465e8			−0.462849			−0.231425	−	0.972853i	$-0.574339\pi$
$991$	−4.50465e8			−0.462849			−0.231425	+	0.972853i	$0.574339\pi$
$992$	−5.55503e8			−0.569052
$993$	2.21288e8	+	6.02391e8i	0.226001	+	0.615220i
$994$	9.97305e8			1.01547
$995$	−8.44734e8	−	5.96140e8i	−0.857533	−	0.605172i
$996$	−2.47364e8	−	6.73375e8i	−0.250356	−	0.681521i
$997$		−	1.44711e9i		−	1.46021i	−0.683332	−	0.730107i	$-0.739470\pi$
$997$		−	1.44711e9i		−	1.46021i	0.683332	−	0.730107i	$-0.260530\pi$
$998$	−2.08866e9			−2.10124
$999$	2.78771e8	−	4.92972e8i	0.279609	−	0.494454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.7.d.c.14.2	yes	8
3.2	odd	2	inner	15.7.d.c.14.8	yes	8
4.3	odd	2		240.7.c.c.209.3		8
5.2	odd	4		75.7.c.e.26.2		8
5.3	odd	4		75.7.c.e.26.7		8
5.4	even	2	inner	15.7.d.c.14.7	yes	8
12.11	even	2		240.7.c.c.209.5		8
15.2	even	4		75.7.c.e.26.8		8
15.8	even	4		75.7.c.e.26.1		8
15.14	odd	2	inner	15.7.d.c.14.1	✓	8
20.19	odd	2		240.7.c.c.209.6		8
60.59	even	2		240.7.c.c.209.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.7.d.c.14.1	✓	8	15.14	odd	2	inner
15.7.d.c.14.2	yes	8	1.1	even	1	trivial
15.7.d.c.14.7	yes	8	5.4	even	2	inner
15.7.d.c.14.8	yes	8	3.2	odd	2	inner
75.7.c.e.26.1		8	15.8	even	4
75.7.c.e.26.2		8	5.2	odd	4
75.7.c.e.26.7		8	5.3	odd	4
75.7.c.e.26.8		8	15.2	even	4
240.7.c.c.209.3		8	4.3	odd	2
240.7.c.c.209.4		8	60.59	even	2
240.7.c.c.209.5		8	12.11	even	2
240.7.c.c.209.6		8	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.8944 q^{2} +(9.31012 + 25.3441i) q^{3} +77.4763 q^{4} +(-102.129 - 72.0738i) q^{5} +(-110.738 - 301.452i) q^{6} -553.145i q^{7} -160.292 q^{8} +(-555.643 + 471.913i) q^{9} +O(q^{10})\)	\(q-11.8944 q^{2} +(9.31012 + 25.3441i) q^{3} +77.4763 q^{4} +(-102.129 - 72.0738i) q^{5} +(-110.738 - 301.452i) q^{6} -553.145i q^{7} -160.292 q^{8} +(-555.643 + 471.913i) q^{9} +(1214.76 + 857.274i) q^{10} -799.678i q^{11} +(721.314 + 1963.56i) q^{12} -1119.56i q^{13} +6579.32i q^{14} +(875.810 - 3259.38i) q^{15} -3051.91 q^{16} -2580.88 q^{17} +(6609.03 - 5613.11i) q^{18} -3496.52 q^{19} +(-7912.58 - 5584.01i) q^{20} +(14018.9 - 5149.85i) q^{21} +9511.67i q^{22} -5050.73 q^{23} +(-1492.34 - 4062.45i) q^{24} +(5235.72 + 14721.7i) q^{25} +13316.5i q^{26} +(-17133.3 - 9688.69i) q^{27} -42855.6i q^{28} -25414.6i q^{29} +(-10417.2 + 38768.3i) q^{30} -11931.1 q^{31} +46559.2 q^{32} +(20267.1 - 7445.10i) q^{33} +30697.9 q^{34} +(-39867.3 + 56492.2i) q^{35} +(-43049.2 + 36562.0i) q^{36} +28772.8i q^{37} +41589.0 q^{38} +(28374.3 - 10423.3i) q^{39} +(16370.5 + 11552.9i) q^{40} -55623.9i q^{41} +(-166747. + 61254.2i) q^{42} -38502.9i q^{43} -61956.0i q^{44} +(90759.9 - 8148.69i) q^{45} +60075.3 q^{46} +151747. q^{47} +(-28413.6 - 77347.8i) q^{48} -188320. q^{49} +(-62275.6 - 175105. i) q^{50} +(-24028.3 - 65409.9i) q^{51} -86739.6i q^{52} -143854. q^{53} +(203790. + 115241. i) q^{54} +(-57635.9 + 81670.4i) q^{55} +88664.7i q^{56} +(-32553.1 - 88616.1i) q^{57} +302291. i q^{58} +401125. i q^{59} +(67854.5 - 252525. i) q^{60} +309592. q^{61} +141913. q^{62} +(261036. + 307351. i) q^{63} -358471. q^{64} +(-80691.2 + 114340. i) q^{65} +(-241064. + 88554.8i) q^{66} -163390. i q^{67} -199957. q^{68} +(-47022.9 - 128006. i) q^{69} +(474197. - 671940. i) q^{70} -151582. i q^{71} +(89065.1 - 75643.8i) q^{72} +70173.6i q^{73} -342234. i q^{74} +(-324362. + 269755. i) q^{75} -270898. q^{76} -442338. q^{77} +(-337495. + 123978. i) q^{78} +437071. q^{79} +(311689. + 219963. i) q^{80} +(86037.8 - 524430. i) q^{81} +661612. i q^{82} -342935. q^{83} +(1.08614e6 - 398991. i) q^{84} +(263583. + 186014. i) q^{85} +457968. i q^{86} +(644110. - 236613. i) q^{87} +128182. i q^{88} -631196. i q^{89} +(-1.07953e6 + 96923.6i) q^{90} -619281. q^{91} -391311. q^{92} +(-111080. - 302383. i) q^{93} -1.80494e6 q^{94} +(357097. + 252008. i) q^{95} +(433472. + 1.18000e6i) q^{96} -1.55901e6i q^{97} +2.23995e6 q^{98} +(377378. + 444336. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 72 q^{4} - 612 q^{6} - 1980 q^{9}+O(q^{10}) \) 8 * q + 72 * q^4 - 612 * q^6 - 1980 * q^9	\( 8 q + 72 q^{4} - 612 q^{6} - 1980 q^{9} + 4240 q^{10} + 1980 q^{15} + 784 q^{16} - 28520 q^{19} + 24228 q^{21} + 14904 q^{24} + 800 q^{25} - 71100 q^{30} + 5896 q^{31} + 105344 q^{34} - 186624 q^{36} + 233568 q^{39} + 141920 q^{40} - 159300 q^{45} + 59336 q^{46} - 1041472 q^{49} + 66888 q^{51} + 917892 q^{54} + 442800 q^{55} - 638640 q^{60} + 1493416 q^{61} - 2063584 q^{64} - 1221840 q^{66} + 1502532 q^{69} + 2273400 q^{70} - 2574000 q^{75} - 219168 q^{76} - 1286360 q^{79} - 1752192 q^{81} + 6238728 q^{84} + 1651240 q^{85} - 2737440 q^{90} + 383616 q^{91} - 7641736 q^{94} - 151056 q^{96} + 6322320 q^{99}+O(q^{100}) \) 8 * q + 72 * q^4 - 612 * q^6 - 1980 * q^9 + 4240 * q^10 + 1980 * q^15 + 784 * q^16 - 28520 * q^19 + 24228 * q^21 + 14904 * q^24 + 800 * q^25 - 71100 * q^30 + 5896 * q^31 + 105344 * q^34 - 186624 * q^36 + 233568 * q^39 + 141920 * q^40 - 159300 * q^45 + 59336 * q^46 - 1041472 * q^49 + 66888 * q^51 + 917892 * q^54 + 442800 * q^55 - 638640 * q^60 + 1493416 * q^61 - 2063584 * q^64 - 1221840 * q^66 + 1502532 * q^69 + 2273400 * q^70 - 2574000 * q^75 - 219168 * q^76 - 1286360 * q^79 - 1752192 * q^81 + 6238728 * q^84 + 1651240 * q^85 - 2737440 * q^90 + 383616 * q^91 - 7641736 * q^94 - 151056 * q^96 + 6322320 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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