LMFDB - Embedded newform 5.17.c.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,17,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.11622719283$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 354217 x^{12} + 47647865256 x^{10} + \cdots + 84\!\cdots\!36 $ x^14 + 354217x^12 + 47647865256x^10 + 3062948254140560x^8 + 97982926395671183360x^6 + 1450505914836224854327296x^4 + 7749363027207208037244731392x^2 + 8484029084015876402584471207936
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{34}\cdot 3^{10}\cdot 5^{18} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.4
Root			$-38.1160i$ of defining polynomial
Character	$\chi$	$=$	5.3
Dual form			5.17.c.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(38.1160 - 38.1160i) q^{2} +(7207.82 + 7207.82i) q^{3} +62630.3i q^{4} +(-287350. - 264609. i) q^{5} +549467. q^{6} +(-3.21528e6 + 3.21528e6i) q^{7} +(4.88519e6 + 4.88519e6i) q^{8} +6.08585e7i q^{9} +O(q^{10})$	\(q+(38.1160 - 38.1160i) q^{2} +(7207.82 + 7207.82i) q^{3} +62630.3i q^{4} +(-287350. - 264609. i) q^{5} +549467. q^{6} +(-3.21528e6 + 3.21528e6i) q^{7} +(4.88519e6 + 4.88519e6i) q^{8} +6.08585e7i q^{9} +(-2.10385e7 + 866777. i) q^{10} -7.10939e7 q^{11} +(-4.51428e8 + 4.51428e8i) q^{12} +(9.03933e8 + 9.03933e8i) q^{13} +2.45107e8i q^{14} +(-1.63909e8 - 3.97842e9i) q^{15} -3.73213e9 q^{16} +(6.85191e9 - 6.85191e9i) q^{17} +(2.31968e9 + 2.31968e9i) q^{18} +5.19796e9i q^{19} +(1.65726e10 - 1.79968e10i) q^{20} -4.63503e10 q^{21} +(-2.70982e9 + 2.70982e9i) q^{22} +(2.09756e10 + 2.09756e10i) q^{23} +7.04231e10i q^{24} +(1.25518e10 + 1.52071e11i) q^{25} +6.89087e10 q^{26} +(-1.28384e11 + 1.28384e11i) q^{27} +(-2.01374e11 - 2.01374e11i) q^{28} -6.38865e11i q^{29} +(-1.57889e11 - 1.45394e11i) q^{30} +1.54566e12 q^{31} +(-4.62410e11 + 4.62410e11i) q^{32} +(-5.12432e11 - 5.12432e11i) q^{33} -5.22335e11i q^{34} +(1.77470e12 - 7.31171e10i) q^{35} -3.81159e12 q^{36} +(7.62814e11 - 7.62814e11i) q^{37} +(1.98125e11 + 1.98125e11i) q^{38} +1.30308e13i q^{39} +(-1.11092e11 - 2.69642e12i) q^{40} +1.05863e12 q^{41} +(-1.76669e12 + 1.76669e12i) q^{42} +(-3.56832e12 - 3.56832e12i) q^{43} -4.45263e12i q^{44} +(1.61037e13 - 1.74877e13i) q^{45} +1.59901e12 q^{46} +(-3.13366e12 + 3.13366e12i) q^{47} +(-2.69005e13 - 2.69005e13i) q^{48} +1.25569e13i q^{49} +(6.27476e12 + 5.31791e12i) q^{50} +9.87746e13 q^{51} +(-5.66137e13 + 5.66137e13i) q^{52} +(-5.32069e13 - 5.32069e13i) q^{53} +9.78700e12i q^{54} +(2.04288e13 + 1.88121e13i) q^{55} -3.14145e13 q^{56} +(-3.74659e13 + 3.74659e13i) q^{57} +(-2.43510e13 - 2.43510e13i) q^{58} +2.46986e14i q^{59} +(2.49170e14 - 1.02657e13i) q^{60} -8.92145e13 q^{61} +(5.89145e13 - 5.89145e13i) q^{62} +(-1.95677e14 - 1.95677e14i) q^{63} -2.09339e14i q^{64} +(-2.05559e13 - 4.98934e14i) q^{65} -3.90637e13 q^{66} +(-1.19814e13 + 1.19814e13i) q^{67} +(4.29138e14 + 4.29138e14i) q^{68} +3.02376e14i q^{69} +(6.48576e13 - 7.04315e13i) q^{70} +3.71660e14 q^{71} +(-2.97306e14 + 2.97306e14i) q^{72} +(-4.65269e14 - 4.65269e14i) q^{73} -5.81509e13i q^{74} +(-1.00563e15 + 1.18657e15i) q^{75} -3.25550e14 q^{76} +(2.28587e14 - 2.28587e14i) q^{77} +(4.96681e14 + 4.96681e14i) q^{78} -5.63270e14i q^{79} +(1.07243e15 + 9.87557e14i) q^{80} +7.69019e14 q^{81} +(4.03507e13 - 4.03507e13i) q^{82} +(2.31937e14 + 2.31937e14i) q^{83} -2.90293e15i q^{84} +(-3.78197e15 + 1.55816e14i) q^{85} -2.72020e14 q^{86} +(4.60482e15 - 4.60482e15i) q^{87} +(-3.47307e14 - 3.47307e14i) q^{88} +3.86663e14i q^{89} +(-5.27508e13 - 1.28037e15i) q^{90} -5.81280e15 q^{91} +(-1.31371e15 + 1.31371e15i) q^{92} +(1.11409e16 + 1.11409e16i) q^{93} +2.38885e14i q^{94} +(1.37543e15 - 1.49363e15i) q^{95} -6.66593e15 q^{96} +(-4.82207e15 + 4.82207e15i) q^{97} +(4.78618e14 + 4.78618e14i) q^{98} -4.32667e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8} + 398727830 q^{10} - 539141632 q^{11} + 1973309928 q^{12} - 681358582 q^{13} + 3514452060 q^{15} - 22953579016 q^{16} + 13124182498 q^{17} - 11293583022 q^{18} - 20186820060 q^{20} + 133652286048 q^{21} - 244784660624 q^{22} + 236373052228 q^{23} + 13144083650 q^{25} + 223473840788 q^{26} + 608106053880 q^{27} - 1494176423768 q^{28} + 2252131613760 q^{30} - 1105223074952 q^{31} - 2024535639992 q^{32} - 6385551058704 q^{33} + 6956678093980 q^{35} + 12514339524924 q^{36} - 9027827087002 q^{37} - 7824802789560 q^{38} + 31912538913900 q^{40} + 39543901484288 q^{41} - 70814500818384 q^{42} - 63017457929452 q^{43} + 126481294123110 q^{45} + 44357914058008 q^{46} - 2826187575452 q^{47} - 405160526368272 q^{48} + 461109216233650 q^{50} + 208649050954008 q^{51} - 389623094881012 q^{52} - 275142037498442 q^{53} + 330504874256560 q^{55} + 865011118900080 q^{56} - 644237427525840 q^{57} - 991296507673440 q^{58} + 16\!\cdots\!80 q^{60}+ \cdots + 48\!\cdots\!02 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8 + 398727830 * q^10 - 539141632 * q^11 + 1973309928 * q^12 - 681358582 * q^13 + 3514452060 * q^15 - 22953579016 * q^16 + 13124182498 * q^17 - 11293583022 * q^18 - 20186820060 * q^20 + 133652286048 * q^21 - 244784660624 * q^22 + 236373052228 * q^23 + 13144083650 * q^25 + 223473840788 * q^26 + 608106053880 * q^27 - 1494176423768 * q^28 + 2252131613760 * q^30 - 1105223074952 * q^31 - 2024535639992 * q^32 - 6385551058704 * q^33 + 6956678093980 * q^35 + 12514339524924 * q^36 - 9027827087002 * q^37 - 7824802789560 * q^38 + 31912538913900 * q^40 + 39543901484288 * q^41 - 70814500818384 * q^42 - 63017457929452 * q^43 + 126481294123110 * q^45 + 44357914058008 * q^46 - 2826187575452 * q^47 - 405160526368272 * q^48 + 461109216233650 * q^50 + 208649050954008 * q^51 - 389623094881012 * q^52 - 275142037498442 * q^53 + 330504874256560 * q^55 + 865011118900080 * q^56 - 644237427525840 * q^57 - 991296507673440 * q^58 + 1631207111049480 * q^60 + 683634528395968 * q^61 - 938995013191864 * q^62 - 1361911146729372 * q^63 + 517066464980110 * q^65 - 196778043917184 * q^66 - 181547742064252 * q^67 - 917821658187868 * q^68 + 1066699466039880 * q^70 - 1337544011098792 * q^71 + 2573199832214340 * q^72 + 778038215296478 * q^73 - 1442550824447700 * q^75 - 233750796900240 * q^76 + 1099376123524976 * q^77 + 8472064951325256 * q^78 - 14934736099860320 * q^80 + 809940307363794 * q^81 - 303814693723184 * q^82 + 13357181209550188 * q^83 - 16045734952112470 * q^85 - 20034048539985352 * q^86 + 17327533268211840 * q^87 + 22952328705949920 * q^88 - 21878453293909290 * q^90 - 24534035720748632 * q^91 + 40652972845631848 * q^92 + 15958372062212256 * q^93 - 22489885958711400 * q^95 - 27488119051061472 * q^96 - 3303551663290402 * q^97 + 48233459501789102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	38.1160	−	38.1160i	0.148891	−	0.148891i	−0.628732	−	0.777622i	$-0.716426\pi$
$2$	38.1160	−	38.1160i	0.148891	−	0.148891i	0.777622	+	0.628732i	$0.216426\pi$
$3$	7207.82	+	7207.82i	1.09859	+	1.09859i	0.994576	+	0.104009i	$0.0331670\pi$
$3$	7207.82	+	7207.82i	1.09859	+	1.09859i	0.104009	+	0.994576i	$0.466833\pi$
$4$			62630.3i			0.955663i
$5$	−287350.	−	264609.i	−0.735615	−	0.677400i
$5$	−287350.	−	264609.i	−0.735615	−	0.677400i
$6$	549467.			0.327138
$7$	−3.21528e6	+	3.21528e6i	−0.557743	+	0.557743i	−0.928664	−	0.370921i	$-0.879042\pi$
$7$	−3.21528e6	+	3.21528e6i	−0.557743	+	0.557743i	0.370921	+	0.928664i	$0.379042\pi$
$8$	4.88519e6	+	4.88519e6i	0.291180	+	0.291180i
$9$			6.08585e7i			1.41378i
$10$	−2.10385e7	+	866777.i	−0.210385	+	0.00866777i
$11$	−7.10939e7			−0.331658			−0.165829	−	0.986155i	$-0.553030\pi$
$11$	−7.10939e7			−0.331658			−0.165829	+	0.986155i	$0.553030\pi$
$12$	−4.51428e8	+	4.51428e8i	−1.04988	+	1.04988i
$13$	9.03933e8	+	9.03933e8i	1.10813	+	1.10813i	0.993397	+	0.114730i	$0.0366004\pi$
$13$	9.03933e8	+	9.03933e8i	1.10813	+	1.10813i	0.114730	+	0.993397i	$0.463400\pi$
$14$			2.45107e8i			0.166086i
$15$	−1.63909e8	−	3.97842e9i	−0.0639549	−	1.55232i
$16$	−3.73213e9			−0.868955
$17$	6.85191e9	−	6.85191e9i	0.982246	−	0.982246i	−0.0175989	−	0.999845i	$-0.505602\pi$
$17$	6.85191e9	−	6.85191e9i	0.982246	−	0.982246i	0.999845	+	0.0175989i	$0.00560221\pi$
$18$	2.31968e9	+	2.31968e9i	0.210498	+	0.210498i
$19$			5.19796e9i			0.306058i	0.988222	+	0.153029i	$0.0489028\pi$
$19$			5.19796e9i			0.306058i	−0.988222	+	0.153029i	$0.951097\pi$
$20$	1.65726e10	−	1.79968e10i	0.647366	−	0.703000i
$21$	−4.63503e10			−1.22546
$22$	−2.70982e9	+	2.70982e9i	−0.0493808	+	0.0493808i
$23$	2.09756e10	+	2.09756e10i	0.267850	+	0.267850i	0.828233	−	0.560384i	$-0.189346\pi$
$23$	2.09756e10	+	2.09756e10i	0.267850	+	0.267850i	−0.560384	+	0.828233i	$0.689346\pi$
$24$			7.04231e10i			0.639772i
$25$	1.25518e10	+	1.52071e11i	0.0822596	+	0.996611i
$26$	6.89087e10			0.329980
$27$	−1.28384e11	+	1.28384e11i	−0.454571	+	0.454571i
$28$	−2.01374e11	−	2.01374e11i	−0.533015	−	0.533015i
$29$		−	6.38865e11i		−	1.27710i	−0.769580	−	0.638550i	$-0.779534\pi$
$29$		−	6.38865e11i		−	1.27710i	0.769580	−	0.638550i	$-0.220466\pi$
$30$	−1.57889e11	−	1.45394e11i	−0.240648	−	0.221603i
$31$	1.54566e12			1.81226			0.906132	−	0.422996i	$-0.139022\pi$
$31$	1.54566e12			1.81226			0.906132	+	0.422996i	$0.139022\pi$
$32$	−4.62410e11	+	4.62410e11i	−0.420559	+	0.420559i
$33$	−5.12432e11	−	5.12432e11i	−0.364355	−	0.364355i
$34$		−	5.22335e11i		−	0.292495i
$35$	1.77470e12	−	7.31171e10i	0.788100	−	0.0324694i
$36$	−3.81159e12			−1.35110
$37$	7.62814e11	−	7.62814e11i	0.217173	−	0.217173i	−0.590133	−	0.807306i	$-0.700925\pi$
$37$	7.62814e11	−	7.62814e11i	0.217173	−	0.217173i	0.807306	+	0.590133i	$0.200925\pi$
$38$	1.98125e11	+	1.98125e11i	0.0455692	+	0.0455692i
$39$			1.30308e13i			2.43474i
$40$	−1.11092e11	−	2.69642e12i	−0.0169512	−	0.411442i
$41$	1.05863e12			0.132578			0.0662892	−	0.997800i	$-0.478884\pi$
$41$	1.05863e12			0.132578			0.0662892	+	0.997800i	$0.478884\pi$
$42$	−1.76669e12	+	1.76669e12i	−0.182459	+	0.182459i
$43$	−3.56832e12	−	3.56832e12i	−0.305292	−	0.305292i	0.537788	−	0.843080i	$-0.319260\pi$
$43$	−3.56832e12	−	3.56832e12i	−0.305292	−	0.305292i	−0.843080	+	0.537788i	$0.819260\pi$
$44$		−	4.45263e12i		−	0.316954i
$45$	1.61037e13	−	1.74877e13i	0.957693	−	1.04000i
$46$	1.59901e12			0.0797606
$47$	−3.13366e12	+	3.13366e12i	−0.131604	+	0.131604i	−0.769840	−	0.638236i	$-0.779664\pi$
$47$	−3.13366e12	+	3.13366e12i	−0.131604	+	0.131604i	0.638236	+	0.769840i	$0.279664\pi$
$48$	−2.69005e13	−	2.69005e13i	−0.954621	−	0.954621i
$49$			1.25569e13i			0.377845i
$50$	6.27476e12	+	5.31791e12i	0.160634	+	0.136138i
$51$	9.87746e13			2.15816
$52$	−5.66137e13	+	5.66137e13i	−1.05900	+	1.05900i
$53$	−5.32069e13	−	5.32069e13i	−0.854597	−	0.854597i	0.136099	−	0.990695i	$-0.456544\pi$
$53$	−5.32069e13	−	5.32069e13i	−0.854597	−	0.854597i	−0.990695	+	0.136099i	$0.956544\pi$
$54$			9.78700e12i			0.135363i
$55$	2.04288e13	+	1.88121e13i	0.243973	+	0.224665i
$56$	−3.14145e13			−0.324807
$57$	−3.74659e13	+	3.74659e13i	−0.336231	+	0.336231i
$58$	−2.43510e13	−	2.43510e13i	−0.190148	−	0.190148i
$59$			2.46986e14i			1.68212i	0.540944	+	0.841059i	$0.318067\pi$
$59$			2.46986e14i			1.68212i	−0.540944	+	0.841059i	$0.681933\pi$
$60$	2.49170e14	−	1.02657e13i	1.48349	−	0.0611193i
$61$	−8.92145e13			−0.465368			−0.232684	−	0.972552i	$-0.574751\pi$
$61$	−8.92145e13			−0.465368			−0.232684	+	0.972552i	$0.574751\pi$
$62$	5.89145e13	−	5.89145e13i	0.269829	−	0.269829i
$63$	−1.95677e14	−	1.95677e14i	−0.788526	−	0.788526i
$64$		−	2.09339e14i		−	0.743720i
$65$	−2.05559e13	−	4.98934e14i	−0.0645104	−	1.56580i
$66$	−3.90637e13			−0.108498
$67$	−1.19814e13	+	1.19814e13i	−0.0295059	+	0.0295059i	−0.721706	−	0.692200i	$-0.756642\pi$
$67$	−1.19814e13	+	1.19814e13i	−0.0295059	+	0.0295059i	0.692200	+	0.721706i	$0.256642\pi$
$68$	4.29138e14	+	4.29138e14i	0.938696	+	0.938696i
$69$			3.02376e14i			0.588511i
$70$	6.48576e13	−	7.04315e13i	0.112506	−	0.122175i
$71$	3.71660e14			0.575545			0.287772	−	0.957699i	$-0.407085\pi$
$71$	3.71660e14			0.575545			0.287772	+	0.957699i	$0.407085\pi$
$72$	−2.97306e14	+	2.97306e14i	−0.411664	+	0.411664i
$73$	−4.65269e14	−	4.65269e14i	−0.576927	−	0.576927i	0.357128	−	0.934055i	$-0.383756\pi$
$73$	−4.65269e14	−	4.65269e14i	−0.576927	−	0.576927i	−0.934055	+	0.357128i	$0.883756\pi$
$74$		−	5.81509e13i		−	0.0646699i
$75$	−1.00563e15	+	1.18657e15i	−1.00449	+	1.18523i
$76$	−3.25550e14			−0.292488
$77$	2.28587e14	−	2.28587e14i	0.184980	−	0.184980i
$78$	4.96681e14	+	4.96681e14i	0.362511	+	0.362511i
$79$		−	5.63270e14i		−	0.371278i	−0.982618	−	0.185639i	$-0.940564\pi$
$79$		−	5.63270e14i		−	0.371278i	0.982618	−	0.185639i	$-0.0594356\pi$
$80$	1.07243e15	+	9.87557e14i	0.639217	+	0.588630i
$81$	7.69019e14			0.415008
$82$	4.03507e13	−	4.03507e13i	0.0197397	−	0.0197397i
$83$	2.31937e14	+	2.31937e14i	0.102978	+	0.102978i	0.756719	−	0.653741i	$-0.226801\pi$
$83$	2.31937e14	+	2.31937e14i	0.102978	+	0.102978i	−0.653741	+	0.756719i	$0.726801\pi$
$84$		−	2.90293e15i		−	1.17112i
$85$	−3.78197e15	+	1.55816e14i	−1.38793	+	0.0571821i
$86$	−2.72020e14			−0.0909104
$87$	4.60482e15	−	4.60482e15i	1.40300	−	1.40300i
$88$	−3.47307e14	−	3.47307e14i	−0.0965722	−	0.0965722i
$89$			3.86663e14i			0.0982228i	0.998793	+	0.0491114i	$0.0156389\pi$
$89$			3.86663e14i			0.0982228i	−0.998793	+	0.0491114i	$0.984361\pi$
$90$	−5.27508e13	−	1.28037e15i	−0.0122543	−	0.297437i
$91$	−5.81280e15			−1.23610
$92$	−1.31371e15	+	1.31371e15i	−0.255974	+	0.255974i
$93$	1.11409e16	+	1.11409e16i	1.99093	+	1.99093i
$94$			2.38885e14i			0.0391892i
$95$	1.37543e15	−	1.49363e15i	0.207324	−	0.225141i
$96$	−6.66593e15			−0.924040
$97$	−4.82207e15	+	4.82207e15i	−0.615261	+	0.615261i	−0.944312	−	0.329051i	$-0.893271\pi$
$97$	−4.82207e15	+	4.82207e15i	−0.615261	+	0.615261i	0.329051	+	0.944312i	$0.393271\pi$
$98$	4.78618e14	+	4.78618e14i	0.0562575	+	0.0562575i
$99$		−	4.32667e15i		−	0.468891i
$100$	−9.52424e15	+	7.86125e14i	−0.952424	+	0.0786125i
$101$	1.26292e16			1.16628			0.583142	−	0.812370i	$-0.301823\pi$
$101$	1.26292e16			1.16628			0.583142	+	0.812370i	$0.301823\pi$
$102$	3.76490e15	−	3.76490e15i	0.321330	−	0.321330i
$103$	−9.21504e15	−	9.21504e15i	−0.727444	−	0.727444i	0.242666	−	0.970110i	$-0.421978\pi$
$103$	−9.21504e15	−	9.21504e15i	−0.727444	−	0.727444i	−0.970110	+	0.242666i	$0.921978\pi$
$104$			8.83177e15i			0.645329i
$105$	1.33187e16	+	1.22647e16i	0.901465	+	0.830124i
$106$	−4.05607e15			−0.254483
$107$	2.94389e15	−	2.94389e15i	0.171337	−	0.171337i	−0.616229	−	0.787567i	$-0.711341\pi$
$107$	2.94389e15	−	2.94389e15i	0.171337	−	0.171337i	0.787567	+	0.616229i	$0.211341\pi$
$108$	−8.04076e15	−	8.04076e15i	−0.434417	−	0.434417i
$109$		−	1.90989e16i		−	0.958512i	−0.877675	−	0.479256i	$-0.840907\pi$
$109$		−	1.90989e16i		−	0.958512i	0.877675	−	0.479256i	$-0.159093\pi$
$110$	1.49571e15	−	6.16226e13i	0.0697758	−	0.00287474i
$111$	1.09964e16			0.477165
$112$	1.19999e16	−	1.19999e16i	0.484654	−	0.484654i
$113$	−2.09182e16	−	2.09182e16i	−0.786859	−	0.786859i	0.194119	−	0.980978i	$-0.437815\pi$
$113$	−2.09182e16	−	2.09182e16i	−0.786859	−	0.786859i	−0.980978	+	0.194119i	$0.937815\pi$
$114$			2.85610e15i			0.100123i
$115$	−4.76995e14	−	1.15776e16i	−0.0155930	−	0.378475i
$116$	4.00123e16			1.22048
$117$	−5.50121e16	+	5.50121e16i	−1.56665	+	1.56665i
$118$	9.41412e15	+	9.41412e15i	0.250452	+	0.250452i
$119$			4.40616e16i			1.09568i
$120$	1.86346e16	−	2.02361e16i	0.433381	−	0.470626i
$121$	−4.08954e16			−0.890003
$122$	−3.40050e15	+	3.40050e15i	−0.0692890	+	0.0692890i
$123$	7.63041e15	+	7.63041e15i	0.145649	+	0.145649i
$124$			9.68054e16i			1.73191i
$125$	3.66326e16	−	4.70188e16i	0.614592	−	0.788845i
$126$	−1.49169e16			−0.234808
$127$	1.70522e16	−	1.70522e16i	0.251971	−	0.251971i	−0.569808	−	0.821778i	$-0.692982\pi$
$127$	1.70522e16	−	1.70522e16i	0.251971	−	0.251971i	0.821778	+	0.569808i	$0.192982\pi$
$128$	−3.82836e16	−	3.82836e16i	−0.531292	−	0.531292i
$129$		−	5.14396e16i		−	0.670780i
$130$	−1.98009e16	−	1.82339e16i	−0.242738	−	0.223528i
$131$	1.07082e14			0.00123466			0.000617330	−	1.00000i	$-0.499803\pi$
$131$	1.07082e14			0.00123466			0.000617330		1.00000i	$0.499803\pi$
$132$	3.20938e16	−	3.20938e16i	0.348200	−	0.348200i
$133$	−1.67129e16	−	1.67129e16i	−0.170702	−	0.170702i
$134$			9.13366e14i			0.00878631i
$135$	7.08629e16	−	2.91952e15i	0.642316	−	0.0264632i
$136$	6.69458e16			0.572021
$137$	−2.32468e16	+	2.32468e16i	−0.187327	+	0.187327i	−0.794539	−	0.607213i	$-0.792288\pi$
$137$	−2.32468e16	+	2.32468e16i	−0.187327	+	0.187327i	0.607213	+	0.794539i	$0.292288\pi$
$138$	1.15254e16	+	1.15254e16i	0.0876238	+	0.0876238i
$139$		−	8.69111e16i		−	0.623673i	−0.950136	−	0.311837i	$-0.899056\pi$
$139$		−	8.69111e16i		−	0.623673i	0.950136	−	0.311837i	$-0.100944\pi$
$140$	4.57935e15	+	1.11150e17i	0.0310298	+	0.753158i
$141$	−4.51737e16			−0.289156
$142$	1.41662e16	−	1.41662e16i	0.0856932	−	0.0856932i
$143$	−6.42641e16	−	6.42641e16i	−0.367519	−	0.367519i
$144$		−	2.27132e17i		−	1.22851i
$145$	−1.69050e17	+	1.83578e17i	−0.865108	+	0.939455i
$146$	−3.54684e16			−0.171798
$147$	−9.05077e16	+	9.05077e16i	−0.415094	+	0.415094i
$148$	4.77753e16	+	4.77753e16i	0.207544	+	0.207544i
$149$			3.20196e17i			1.31803i	0.752129	+	0.659016i	$0.229027\pi$
$149$			3.20196e17i			1.31803i	−0.752129	+	0.659016i	$0.770973\pi$
$150$	6.89681e15	+	8.35578e16i	0.0269103	+	0.326029i
$151$	4.67311e17			1.72898			0.864491	−	0.502649i	$-0.167641\pi$
$151$	4.67311e17			1.72898			0.864491	+	0.502649i	$0.167641\pi$
$152$	−2.53930e16	+	2.53930e16i	−0.0891180	+	0.0891180i
$153$	4.16997e17	+	4.16997e17i	1.38868	+	1.38868i
$154$		−	1.74256e16i		−	0.0550836i
$155$	−4.44146e17	−	4.08997e17i	−1.33313	−	1.22763i
$156$	−8.16122e17			−2.32680
$157$	3.01313e17	−	3.01313e17i	0.816244	−	0.816244i	−0.169317	−	0.985562i	$-0.554156\pi$
$157$	3.01313e17	−	3.01313e17i	0.816244	−	0.816244i	0.985562	+	0.169317i	$0.0541562\pi$
$158$	−2.14696e16	−	2.14696e16i	−0.0552799	−	0.0552799i
$159$		−	7.67011e17i		−	1.87769i
$160$	2.55231e17	−	1.05154e16i	0.594257	−	0.0244831i
$161$	−1.34885e17			−0.298783
$162$	2.93119e16	−	2.93119e16i	0.0617909	−	0.0617909i
$163$	2.83765e17	+	2.83765e17i	0.569452	+	0.569452i	0.931975	−	0.362523i	$-0.118084\pi$
$163$	2.83765e17	+	2.83765e17i	0.569452	+	0.569452i	−0.362523	+	0.931975i	$0.618084\pi$
$164$			6.63023e16i			0.126700i
$165$	1.16530e16	+	2.82841e17i	0.0212112	+	0.514839i
$166$	1.76810e16			0.0306650
$167$	7.17811e17	−	7.17811e17i	1.18653	−	1.18653i	0.208509	−	0.978021i	$-0.433139\pi$
$167$	7.17811e17	−	7.17811e17i	1.18653	−	1.18653i	0.978021	−	0.208509i	$-0.0668609\pi$
$168$	−2.26430e17	−	2.26430e17i	−0.356829	−	0.356829i
$169$			9.68774e17i			1.45589i
$170$	−1.38215e17	+	1.50093e17i	−0.198136	+	0.215163i
$171$	−3.16340e17			−0.432698
$172$	2.23485e17	−	2.23485e17i	0.291757	−	0.291757i
$173$	−2.70244e16	−	2.70244e16i	−0.0336811	−	0.0336811i	0.690066	−	0.723747i	$-0.257582\pi$
$173$	−2.70244e16	−	2.70244e16i	−0.0336811	−	0.0336811i	−0.723747	+	0.690066i	$0.757582\pi$
$174$		−	3.51035e17i		−	0.417788i
$175$	−5.29308e17	−	4.48592e17i	−0.601733	−	0.509973i
$176$	2.65332e17			0.288196
$177$	−1.78023e18	+	1.78023e18i	−1.84795	+	1.84795i
$178$	1.47380e16	+	1.47380e16i	0.0146245	+	0.0146245i
$179$		−	2.32900e17i		−	0.220976i	−0.993877	−	0.110488i	$-0.964759\pi$
$179$		−	2.32900e17i		−	0.220976i	0.993877	−	0.110488i	$-0.0352414\pi$
$180$	1.09526e18	+	1.00858e18i	0.993887	+	0.915232i
$181$	1.47693e18			1.28212			0.641062	−	0.767489i	$-0.278494\pi$
$181$	1.47693e18			1.28212			0.641062	+	0.767489i	$0.278494\pi$
$182$	−2.21561e17	+	2.21561e17i	−0.184044	+	0.184044i
$183$	−6.43042e17	−	6.43042e17i	−0.511247	−	0.511247i
$184$			2.04939e17i			0.155985i
$185$	−4.21042e17	+	1.73468e16i	−0.306868	+	0.0126428i
$186$	8.49290e17			0.592860
$187$	−4.87129e17	+	4.87129e17i	−0.325770	+	0.325770i
$188$	−1.96262e17	−	1.96262e17i	−0.125769	−	0.125769i
$189$		−	8.25583e17i		−	0.507068i
$190$	−4.50547e15	−	1.09357e17i	−0.00265284	−	0.0643899i
$191$	−5.10005e17			−0.287944			−0.143972	−	0.989582i	$-0.545987\pi$
$191$	−5.10005e17			−0.287944			−0.143972	+	0.989582i	$0.545987\pi$
$192$	1.50888e18	−	1.50888e18i	0.817040	−	0.817040i
$193$	−1.56746e18	−	1.56746e18i	−0.814211	−	0.814211i	0.171052	−	0.985262i	$-0.445284\pi$
$193$	−1.56746e18	−	1.56746e18i	−0.814211	−	0.814211i	−0.985262	+	0.171052i	$0.945284\pi$
$194$			3.67596e17i			0.183213i
$195$	3.44806e18	−	3.74439e18i	1.64929	−	1.79103i
$196$	−7.86442e17			−0.361092
$197$	−1.13851e18	+	1.13851e18i	−0.501888	+	0.501888i	−0.912024	−	0.410136i	$-0.865481\pi$
$197$	−1.13851e18	+	1.13851e18i	−0.501888	+	0.501888i	0.410136	+	0.912024i	$0.365481\pi$
$198$	−1.64915e17	−	1.64915e17i	−0.0698135	−	0.0698135i
$199$			1.01122e18i			0.411171i	0.978639	+	0.205586i	$0.0659099\pi$
$199$			1.01122e18i			0.411171i	−0.978639	+	0.205586i	$0.934090\pi$
$200$	−6.81576e17	+	8.04213e17i	−0.266241	+	0.314146i
$201$	−1.72719e17			−0.0648295
$202$	4.81374e17	−	4.81374e17i	0.173649	−	0.173649i
$203$	2.05413e18	+	2.05413e18i	0.712295	+	0.712295i
$204$			6.18629e18i			2.06248i
$205$	−3.04197e17	−	2.80123e17i	−0.0975267	−	0.0898086i
$206$	−7.02481e17			−0.216619
$207$	−1.27654e18	+	1.27654e18i	−0.378680	+	0.378680i
$208$	−3.37360e18	−	3.37360e18i	−0.962913	−	0.962913i
$209$		−	3.69543e17i		−	0.101507i
$210$	9.75139e17	−	4.01754e16i	0.257817	−	0.0106220i
$211$	−2.22306e18			−0.565837			−0.282919	−	0.959144i	$-0.591303\pi$
$211$	−2.22306e18			−0.565837			−0.282919	+	0.959144i	$0.591303\pi$
$212$	3.33237e18	−	3.33237e18i	0.816706	−	0.816706i
$213$	2.67886e18	+	2.67886e18i	0.632285	+	0.632285i
$214$		−	2.24419e17i		−	0.0510211i
$215$	8.11454e16	+	1.96957e18i	0.0177728	+	0.431383i
$216$	−1.25436e18			−0.264724
$217$	−4.96974e18	+	4.96974e18i	−1.01078	+	1.01078i
$218$	−7.27976e17	−	7.27976e17i	−0.142713	−	0.142713i
$219$		−	6.70714e18i		−	1.26761i
$220$	−1.17821e18	+	1.27946e18i	−0.214704	+	0.233156i
$221$	1.23873e19			2.17691
$222$	4.19141e17	−	4.19141e17i	0.0710454	−	0.0710454i
$223$	2.15119e18	+	2.15119e18i	0.351754	+	0.351754i	0.860762	−	0.509008i	$-0.169987\pi$
$223$	2.15119e18	+	2.15119e18i	0.351754	+	0.351754i	−0.509008	+	0.860762i	$0.669987\pi$
$224$		−	2.97355e18i		−	0.469128i
$225$	−9.25480e18	+	7.63886e17i	−1.40899	+	0.116297i
$226$	−1.59464e18			−0.234312
$227$	3.24742e18	−	3.24742e18i	0.460609	−	0.460609i	−0.438246	−	0.898855i	$-0.644400\pi$
$227$	3.24742e18	−	3.24742e18i	0.460609	−	0.460609i	0.898855	+	0.438246i	$0.144400\pi$
$228$	−2.34650e18	−	2.34650e18i	−0.321323	−	0.321323i
$229$		−	9.89106e18i		−	1.30785i	−0.756558	−	0.653927i	$-0.773120\pi$
$229$		−	9.89106e18i		−	1.30785i	0.756558	−	0.653927i	$-0.226880\pi$
$230$	−4.59475e17	−	4.23113e17i	−0.0586731	−	0.0540298i
$231$	3.29522e18			0.406433
$232$	3.12098e18	−	3.12098e18i	0.371866	−	0.371866i
$233$	2.97393e18	+	2.97393e18i	0.342360	+	0.342360i	0.857254	−	0.514894i	$-0.172169\pi$
$233$	2.97393e18	+	2.97393e18i	0.342360	+	0.342360i	−0.514894	+	0.857254i	$0.672169\pi$
$234$			4.19368e18i			0.466518i
$235$	1.72965e18	−	7.12610e16i	0.185958	−	0.00766142i
$236$	−1.54688e19			−1.60754
$237$	4.05994e18	−	4.05994e18i	0.407881	−	0.407881i
$238$	1.67945e18	+	1.67945e18i	0.163137	+	0.163137i
$239$			7.60192e18i			0.714069i	0.934091	+	0.357034i	$0.116212\pi$
$239$			7.60192e18i			0.714069i	−0.934091	+	0.357034i	$0.883788\pi$
$240$	6.11732e17	+	1.48480e19i	0.0555739	+	1.34889i
$241$	−8.05907e18			−0.708188			−0.354094	−	0.935210i	$-0.615211\pi$
$241$	−8.05907e18			−0.708188			−0.354094	+	0.935210i	$0.615211\pi$
$242$	−1.55877e18	+	1.55877e18i	−0.132513	+	0.132513i
$243$	1.10695e19	+	1.10695e19i	0.910493	+	0.910493i
$244$		−	5.58754e18i		−	0.444735i
$245$	3.32267e18	−	3.60822e18i	0.255952	−	0.277948i
$246$	5.81681e17			0.0433715
$247$	−4.69861e18	+	4.69861e18i	−0.339151	+	0.339151i
$248$	7.55086e18	+	7.55086e18i	0.527695	+	0.527695i
$249$			3.34352e18i			0.226261i
$250$	−3.95883e17	−	3.18846e18i	−0.0259446	−	0.208959i
$251$	−2.35256e19			−1.49332			−0.746658	−	0.665208i	$-0.768343\pi$
$251$	−2.35256e19			−1.49332			−0.746658	+	0.665208i	$0.768343\pi$
$252$	1.22553e19	−	1.22553e19i	0.753565	−	0.753565i
$253$	−1.49123e18	−	1.49123e18i	−0.0888345	−	0.0888345i
$254$		−	1.29992e18i		−	0.0750321i
$255$	−2.83829e19	−	2.61367e19i	−1.58758	−	1.46194i
$256$	1.08008e19			0.585511
$257$	−5.03017e18	+	5.03017e18i	−0.264312	+	0.264312i	−0.826803	−	0.562491i	$-0.809843\pi$
$257$	−5.03017e18	+	5.03017e18i	−0.264312	+	0.264312i	0.562491	+	0.826803i	$0.309843\pi$
$258$	−1.96067e18	−	1.96067e18i	−0.0998728	−	0.0998728i
$259$			4.90532e18i			0.242253i
$260$	3.12484e19	−	1.28742e18i	1.49638	−	0.0616502i
$261$	3.88804e19			1.80554
$262$	4.08155e15	−	4.08155e15i	0.000183829	−	0.000183829i
$263$	−1.84025e19	−	1.84025e19i	−0.803954	−	0.803954i	0.179757	−	0.983711i	$-0.442469\pi$
$263$	−1.84025e19	−	1.84025e19i	−0.803954	−	0.803954i	−0.983711	+	0.179757i	$0.942469\pi$
$264$		−	5.00665e18i		−	0.212186i
$265$	1.20995e18	+	2.93680e19i	0.0497509	+	1.20756i
$266$	−1.27406e18			−0.0508318
$267$	−2.78699e18	+	2.78699e18i	−0.107906	+	0.107906i
$268$	−7.50399e17	−	7.50399e17i	−0.0281977	−	0.0281977i
$269$		−	2.90668e19i		−	1.06018i	−0.847942	−	0.530088i	$-0.822159\pi$
$269$		−	2.90668e19i		−	1.06018i	0.847942	−	0.530088i	$-0.177841\pi$
$270$	2.58973e18	−	2.81229e18i	0.0916947	−	0.0995750i
$271$	2.71591e19			0.933599			0.466799	−	0.884363i	$-0.345407\pi$
$271$	2.71591e19			0.933599			0.466799	+	0.884363i	$0.345407\pi$
$272$	−2.55723e19	+	2.55723e19i	−0.853528	+	0.853528i
$273$	−4.18976e19	−	4.18976e19i	−1.35796	−	1.35796i
$274$			1.77215e18i			0.0557824i
$275$	−8.92358e17	−	1.08113e19i	−0.0272821	−	0.330534i
$276$	−1.89379e19			−0.562418
$277$	−7.09107e18	+	7.09107e18i	−0.204585	+	0.204585i	−0.801961	−	0.597376i	$-0.796210\pi$
$277$	−7.09107e18	+	7.09107e18i	−0.204585	+	0.204585i	0.597376	+	0.801961i	$0.296210\pi$
$278$	−3.31271e18	−	3.31271e18i	−0.0928591	−	0.0928591i
$279$			9.40668e19i			2.56214i
$280$	9.02695e18	+	8.31257e18i	0.238933	+	0.220024i
$281$	2.50353e19			0.644023			0.322012	−	0.946736i	$-0.395641\pi$
$281$	2.50353e19			0.644023			0.322012	+	0.946736i	$0.395641\pi$
$282$	−1.72184e18	+	1.72184e18i	−0.0430527	+	0.0430527i
$283$	4.53336e19	+	4.53336e19i	1.10187	+	1.10187i	0.994186	+	0.107680i	$0.0343421\pi$
$283$	4.53336e19	+	4.53336e19i	1.10187	+	1.10187i	0.107680	+	0.994186i	$0.465658\pi$
$284$			2.32772e19i			0.550027i
$285$	2.06796e19	−	8.51994e17i	0.475099	−	0.0195739i
$286$	−4.89898e18			−0.109440
$287$	−3.40379e18	+	3.40379e18i	−0.0739448	+	0.0739448i
$288$	−2.81416e19	−	2.81416e19i	−0.594578	−	0.594578i
$289$		−	4.52362e19i		−	0.929615i
$290$	5.53754e17	+	1.34407e19i	0.0110696	+	0.268683i
$291$	−6.95131e19			−1.35183
$292$	2.91399e19	−	2.91399e19i	0.551348	−	0.551348i
$293$	−5.17567e19	−	5.17567e19i	−0.952852	−	0.952852i	0.0460856	−	0.998937i	$-0.485325\pi$
$293$	−5.17567e19	−	5.17567e19i	−0.952852	−	0.952852i	−0.998937	+	0.0460856i	$0.985325\pi$
$294$			6.89959e18i			0.123607i
$295$	6.53548e19	−	7.09714e19i	1.13947	−	1.23739i
$296$	7.45298e18			0.126473
$297$	9.12734e18	−	9.12734e18i	0.150762	−	0.150762i
$298$	1.22046e19	+	1.22046e19i	0.196243	+	0.196243i
$299$			3.79210e19i			0.593623i
$300$	−7.43153e19	−	6.29828e19i	−1.13268	−	0.959957i
$301$	2.29463e19			0.340550
$302$	1.78120e19	−	1.78120e19i	0.257429	−	0.257429i
$303$	9.10288e19	+	9.10288e19i	1.28126	+	1.28126i
$304$		−	1.93995e19i		−	0.265951i
$305$	2.56358e19	+	2.36070e19i	0.342332	+	0.315240i
$306$	3.17885e19			0.413523
$307$	−4.78169e19	+	4.78169e19i	−0.606002	+	0.606002i	−0.941899	−	0.335896i	$-0.890961\pi$
$307$	−4.78169e19	+	4.78169e19i	−0.606002	+	0.606002i	0.335896	+	0.941899i	$0.390961\pi$
$308$	1.43165e19	+	1.43165e19i	0.176779	+	0.176779i
$309$		−	1.32841e20i		−	1.59832i
$310$	−3.25184e19	+	1.33975e18i	−0.381273	+	0.0157083i
$311$	−7.95480e19			−0.908963			−0.454482	−	0.890756i	$-0.650175\pi$
$311$	−7.95480e19			−0.908963			−0.454482	+	0.890756i	$0.650175\pi$
$312$	−6.36578e19	+	6.36578e19i	−0.708949	+	0.708949i
$313$	−8.35028e18	−	8.35028e18i	−0.0906455	−	0.0906455i	0.660330	−	0.750976i	$-0.270416\pi$
$313$	−8.35028e18	−	8.35028e18i	−0.0906455	−	0.0906455i	−0.750976	+	0.660330i	$0.770416\pi$
$314$		−	2.29697e19i		−	0.243062i
$315$	4.44980e18	+	1.08006e20i	0.0459046	+	1.11420i
$316$	3.52778e19			0.354817
$317$	7.24761e19	−	7.24761e19i	0.710757	−	0.710757i	−0.255937	−	0.966693i	$-0.582384\pi$
$317$	7.24761e19	−	7.24761e19i	0.710757	−	0.710757i	0.966693	+	0.255937i	$0.0823840\pi$
$318$	−2.92354e19	−	2.92354e19i	−0.279571	−	0.279571i
$319$			4.54194e19i			0.423561i
$320$	−5.53929e19	+	6.01534e19i	−0.503796	+	0.547092i
$321$	4.24381e19			0.376457
$322$	−5.14126e18	+	5.14126e18i	−0.0444859	+	0.0444859i
$323$	3.56159e19	+	3.56159e19i	0.300624	+	0.300624i
$324$			4.81639e19i			0.396608i
$325$	−1.26116e20	+	1.48808e20i	−1.01322	+	1.19553i
$326$	2.16320e19			0.169572
$327$	1.37662e20	−	1.37662e20i	1.05301	−	1.05301i
$328$	5.17160e18	+	5.17160e18i	0.0386042	+	0.0386042i
$329$		−	2.01512e19i		−	0.146802i
$330$	1.12249e19	+	1.03366e19i	0.0798128	+	0.0734965i
$331$	−1.73346e20			−1.20307			−0.601535	−	0.798847i	$-0.705444\pi$
$331$	−1.73346e20			−1.20307			−0.601535	+	0.798847i	$0.705444\pi$
$332$	−1.45263e19	+	1.45263e19i	−0.0984126	+	0.0984126i
$333$	4.64238e19	+	4.64238e19i	0.307034	+	0.307034i
$334$		−	5.47202e19i		−	0.353326i
$335$	6.61324e18	−	2.72463e17i	0.0416923	−	0.00171771i
$336$	1.72986e20			1.06487
$337$	−4.24083e19	+	4.24083e19i	−0.254925	+	0.254925i	−0.822986	−	0.568062i	$-0.807694\pi$
$337$	−4.24083e19	+	4.24083e19i	−0.254925	+	0.254925i	0.568062	+	0.822986i	$0.307694\pi$
$338$	3.69258e19	+	3.69258e19i	0.216769	+	0.216769i
$339$		−	3.01549e20i		−	1.72886i
$340$	−9.75880e18	−	2.36866e20i	−0.0546469	−	1.32639i
$341$	−1.09887e20			−0.601052
$342$	−1.20576e19	+	1.20576e19i	−0.0644247	+	0.0644247i
$343$	−1.47227e20	−	1.47227e20i	−0.768484	−	0.768484i
$344$		−	3.48638e19i		−	0.177790i
$345$	8.00115e19	−	8.68877e19i	0.398657	−	0.432918i
$346$	−2.06012e18			−0.0100296
$347$	1.91600e20	−	1.91600e20i	0.911507	−	0.911507i	−0.0848839	−	0.996391i	$-0.527052\pi$
$347$	1.91600e20	−	1.91600e20i	0.911507	−	0.911507i	0.996391	+	0.0848839i	$0.0270519\pi$
$348$	2.88402e20	+	2.88402e20i	1.34080	+	1.34080i
$349$			3.65464e20i			1.66051i	0.557386	+	0.830254i	$0.311805\pi$
$349$			3.65464e20i			1.66051i	−0.557386	+	0.830254i	$0.688195\pi$
$350$	−3.72737e19	+	3.07654e18i	−0.165523	+	0.0136621i
$351$	−2.32102e20			−1.00745
$352$	3.28745e19	−	3.28745e19i	0.139482	−	0.139482i
$353$	5.12969e19	+	5.12969e19i	0.212762	+	0.212762i	0.805440	−	0.592678i	$-0.201929\pi$
$353$	5.12969e19	+	5.12969e19i	0.212762	+	0.212762i	−0.592678	+	0.805440i	$0.701929\pi$
$354$			1.35711e20i			0.550285i
$355$	−1.06796e20	−	9.83447e19i	−0.423379	−	0.389874i
$356$	−2.42168e19			−0.0938679
$357$	−3.17588e20	+	3.17588e20i	−1.20370	+	1.20370i
$358$	−8.87723e18	−	8.87723e18i	−0.0329013	−	0.0329013i
$359$			3.01556e20i			1.09298i	0.837466	+	0.546490i	$0.184036\pi$
$359$			3.01556e20i			1.09298i	−0.837466	+	0.546490i	$0.815964\pi$
$360$	1.64100e20	−	6.76088e18i	0.581688	−	0.0239653i
$361$	2.61423e20			0.906329
$362$	5.62945e19	−	5.62945e19i	0.190896	−	0.190896i
$363$	−2.94767e20	−	2.94767e20i	−0.977744	−	0.977744i
$364$		−	3.64057e20i		−	1.18130i
$365$	1.05804e19	+	2.56809e20i	0.0335862	+	0.815206i
$366$	−4.90204e19			−0.152240
$367$	−1.09886e19	+	1.09886e19i	−0.0333899	+	0.0333899i	−0.723605	−	0.690215i	$-0.757516\pi$
$367$	−1.09886e19	+	1.09886e19i	−0.0333899	+	0.0333899i	0.690215	+	0.723605i	$0.257516\pi$
$368$	−7.82836e19	−	7.82836e19i	−0.232749	−	0.232749i
$369$			6.44266e19i			0.187437i
$370$	−1.53873e19	+	1.67096e19i	−0.0438074	+	0.0475722i
$371$	3.42150e20			0.953291
$372$	−6.97756e20	+	6.97756e20i	−1.90265	+	1.90265i
$373$	−2.18448e20	−	2.18448e20i	−0.583013	−	0.583013i	0.352717	−	0.935730i	$-0.385258\pi$
$373$	−2.18448e20	−	2.18448e20i	−0.583013	−	0.583013i	−0.935730	+	0.352717i	$0.885258\pi$
$374$			3.71348e19i			0.0970082i
$375$	6.02944e20	−	7.48622e19i	1.54180	−	0.191431i
$376$	−3.06170e19			−0.0766409
$377$	5.77491e20	−	5.77491e20i	1.41519	−	1.41519i
$378$	−3.14679e19	−	3.14679e19i	−0.0754977	−	0.0754977i
$379$			1.91486e20i			0.449803i	0.974381	+	0.224902i	$0.0722061\pi$
$379$			1.91486e20i			0.449803i	−0.974381	+	0.224902i	$0.927794\pi$
$380$	9.35466e19	+	8.61434e19i	0.215159	+	0.198131i
$381$	2.45818e20			0.553622
$382$	−1.94394e19	+	1.94394e19i	−0.0428721	+	0.0428721i
$383$	−3.21274e20	−	3.21274e20i	−0.693881	−	0.693881i	0.269202	−	0.963084i	$-0.413240\pi$
$383$	−3.21274e20	−	3.21274e20i	−0.693881	−	0.693881i	−0.963084	+	0.269202i	$0.913240\pi$
$384$		−	5.51883e20i		−	1.16734i
$385$	−1.26170e20	+	5.19818e18i	−0.261380	+	0.0107687i
$386$	−1.19490e20			−0.242457
$387$	2.17163e20	−	2.17163e20i	0.431616	−	0.431616i
$388$	−3.02008e20	−	3.02008e20i	−0.587982	−	0.587982i
$389$			3.74739e20i			0.714714i	0.933968	+	0.357357i	$0.116322\pi$
$389$			3.74739e20i			0.714714i	−0.933968	+	0.357357i	$0.883678\pi$
$390$	−1.12948e19	−	2.74148e20i	−0.0211038	−	0.512233i
$391$	2.87445e20			0.526188
$392$	−6.13428e19	+	6.13428e19i	−0.110021	+	0.110021i
$393$	7.71830e17	+	7.71830e17i	0.00135638	+	0.00135638i
$394$			8.67909e19i			0.149453i
$395$	−1.49046e20	+	1.61855e20i	−0.251504	+	0.273118i
$396$	2.70981e20			0.448102
$397$	−6.26994e20	+	6.26994e20i	−1.01611	+	1.01611i	−0.0162393	+	0.999868i	$0.505169\pi$
$397$	−6.26994e20	+	6.26994e20i	−1.01611	+	1.01611i	−0.999868	+	0.0162393i	$0.994831\pi$
$398$	3.85438e19	+	3.85438e19i	0.0612195	+	0.0612195i
$399$		−	2.40927e20i		−	0.375061i
$400$	−4.68451e19	−	5.67548e20i	−0.0714799	−	0.866010i
$401$	−8.70385e20			−1.30184			−0.650918	−	0.759148i	$-0.725616\pi$
$401$	−8.70385e20			−1.30184			−0.650918	+	0.759148i	$0.725616\pi$
$402$	−6.58337e18	+	6.58337e18i	−0.00965251	+	0.00965251i
$403$	1.39718e21	+	1.39718e21i	2.00822	+	2.00822i
$404$			7.90970e20i			1.11457i
$405$	−2.20977e20	−	2.03489e20i	−0.305286	−	0.281126i
$406$	1.56590e20			0.212108
$407$	−5.42314e19	+	5.42314e19i	−0.0720271	+	0.0720271i
$408$	4.82533e20	+	4.82533e20i	0.628414	+	0.628414i
$409$			6.49167e20i			0.829030i	0.910043	+	0.414515i	$0.136049\pi$
$409$			6.49167e20i			0.829030i	−0.910043	+	0.414515i	$0.863951\pi$
$410$	−2.22719e19	+	9.17596e17i	−0.0278925	+	0.00114916i
$411$	−3.35118e20			−0.411588
$412$	5.77141e20	−	5.77141e20i	0.695191	−	0.695191i
$413$	−7.94129e20	−	7.94129e20i	−0.938190	−	0.938190i
$414$			9.73134e19i			0.112764i
$415$	−5.27437e18	−	1.28020e20i	−0.00599495	−	0.145510i
$416$	−8.35975e20			−0.932066
$417$	6.26440e20	−	6.26440e20i	0.685158	−	0.685158i
$418$	−1.40855e19	−	1.40855e19i	−0.0151134	−	0.0151134i
$419$		−	1.48035e21i		−	1.55830i	−0.626837	−	0.779150i	$-0.715651\pi$
$419$		−	1.48035e21i		−	1.55830i	0.626837	−	0.779150i	$-0.284349\pi$
$420$	−7.68143e20	+	8.34157e20i	−0.793319	+	0.861497i
$421$	−3.39298e20			−0.343815			−0.171908	−	0.985113i	$-0.554993\pi$
$421$	−3.39298e20			−0.343815			−0.171908	+	0.985113i	$0.554993\pi$
$422$	−8.47342e19	+	8.47342e19i	−0.0842479	+	0.0842479i
$423$	−1.90710e20	−	1.90710e20i	−0.186059	−	0.186059i
$424$		−	5.19852e20i		−	0.497683i
$425$	1.12798e21	+	9.55971e20i	1.05972	+	0.898118i
$426$	2.04215e20			0.188283
$427$	2.86850e20	−	2.86850e20i	0.259556	−	0.259556i
$428$	1.84377e20	+	1.84377e20i	0.163741	+	0.163741i
$429$		−	9.26408e20i		−	0.807503i
$430$	7.81649e19	+	7.19791e19i	0.0668751	+	0.0615827i
$431$	9.77693e20			0.821078			0.410539	−	0.911843i	$-0.365341\pi$
$431$	9.77693e20			0.821078			0.410539	+	0.911843i	$0.365341\pi$
$432$	4.79148e20	−	4.79148e20i	0.395002	−	0.395002i
$433$	1.09674e21	+	1.09674e21i	0.887564	+	0.887564i	0.994289	−	0.106725i	$-0.0340364\pi$
$433$	1.09674e21	+	1.09674e21i	0.887564	+	0.887564i	−0.106725	+	0.994289i	$0.534036\pi$
$434$			3.78853e20i			0.300991i
$435$	−2.54167e21	+	1.04716e20i	−1.98247	+	0.0816768i
$436$	1.19617e21			0.916014
$437$	−1.09030e20	+	1.09030e20i	−0.0819775	+	0.0819775i
$438$	−2.55649e20	−	2.55649e20i	−0.188735	−	0.188735i
$439$		−	1.84626e21i		−	1.33837i	−0.743097	−	0.669184i	$-0.766644\pi$
$439$		−	1.84626e21i		−	1.33837i	0.743097	−	0.669184i	$-0.233356\pi$
$440$	7.89794e18	+	1.91699e20i	0.00562202	+	0.136458i
$441$	−7.64194e20			−0.534189
$442$	4.72156e20	−	4.72156e20i	0.324121	−	0.324121i
$443$	−1.76600e21	−	1.76600e21i	−1.19059	−	1.19059i	−0.976903	−	0.213683i	$-0.931454\pi$
$443$	−1.76600e21	−	1.76600e21i	−1.19059	−	1.19059i	−0.213683	−	0.976903i	$-0.568546\pi$
$444$			6.88711e20i			0.456009i
$445$	1.02315e20	−	1.11107e20i	0.0665361	−	0.0722542i
$446$	1.63989e20			0.104746
$447$	−2.30792e21	+	2.30792e21i	−1.44797	+	1.44797i
$448$	6.73082e20	+	6.73082e20i	0.414805	+	0.414805i
$449$		−	2.40584e20i		−	0.145645i	−0.997345	−	0.0728226i	$-0.976799\pi$
$449$		−	2.40584e20i		−	0.145645i	0.997345	−	0.0728226i	$-0.0232007\pi$
$450$	−3.23640e20	+	3.81873e20i	−0.192470	+	0.227101i
$451$	−7.52621e19			−0.0439707
$452$	1.31011e21	−	1.31011e21i	0.751972	−	0.751972i
$453$	3.36829e21	+	3.36829e21i	1.89943	+	1.89943i
$454$		−	2.47558e20i		−	0.137161i
$455$	1.67031e21	+	1.53812e21i	0.909295	+	0.837334i
$456$	−3.66056e20			−0.195807
$457$	−2.00640e21	+	2.00640e21i	−1.05460	+	1.05460i	−0.0561813	+	0.998421i	$0.517892\pi$
$457$	−2.00640e21	+	2.00640e21i	−1.05460	+	1.05460i	−0.998421	+	0.0561813i	$0.982108\pi$
$458$	−3.77008e20	−	3.77008e20i	−0.194727	−	0.194727i
$459$			1.75936e21i			0.893002i
$460$	7.25112e20	−	2.98743e19i	0.361695	−	0.0149017i
$461$	−3.33613e21			−1.63544			−0.817721	−	0.575615i	$-0.804763\pi$
$461$	−3.33613e21			−1.63544			−0.817721	+	0.575615i	$0.804763\pi$
$462$	1.25601e20	−	1.25601e20i	0.0605141	−	0.0605141i
$463$	−1.85501e20	−	1.85501e20i	−0.0878414	−	0.0878414i	0.661821	−	0.749662i	$-0.269784\pi$
$463$	−1.85501e20	−	1.85501e20i	−0.0878414	−	0.0878414i	−0.749662	+	0.661821i	$0.769784\pi$
$464$			2.38433e21i			1.10974i
$465$	−2.53349e20	−	6.14930e21i	−0.115903	−	2.81321i
$466$	2.26709e20			0.101948
$467$	2.05840e21	−	2.05840e21i	0.909901	−	0.909901i	−0.0863624	−	0.996264i	$-0.527524\pi$
$467$	2.05840e21	−	2.05840e21i	0.909901	−	0.909901i	0.996264	+	0.0863624i	$0.0275243\pi$
$468$	−3.44542e21	−	3.44542e21i	−1.49719	−	1.49719i
$469$		−	7.70470e19i		−	0.0329134i
$470$	6.32112e19	−	6.86436e19i	0.0265468	−	0.0288282i
$471$	4.34361e21			1.79343
$472$	−1.20657e21	+	1.20657e21i	−0.489799	+	0.489799i
$473$	2.53686e20	+	2.53686e20i	0.101253	+	0.101253i
$474$		−	3.09498e20i		−	0.121459i
$475$	−7.90457e20	+	6.52438e19i	−0.305021	+	0.0251762i
$476$	−2.75959e21			−1.04710
$477$	3.23810e21	−	3.23810e21i	1.20821	−	1.20821i
$478$	2.89755e20	+	2.89755e20i	0.106318	+	0.106318i
$479$			1.09041e21i			0.393464i	0.980457	+	0.196732i	$0.0630329\pi$
$479$			1.09041e21i			0.393464i	−0.980457	+	0.196732i	$0.936967\pi$
$480$	1.91545e21	+	1.76387e21i	0.679738	+	0.625945i
$481$	1.37907e21			0.481310
$482$	−3.07180e20	+	3.07180e20i	−0.105443	+	0.105443i
$483$	−9.72223e20	−	9.72223e20i	−0.328238	−	0.328238i
$484$		−	2.56129e21i		−	0.850543i
$485$	2.66158e21	−	1.09656e20i	0.869373	−	0.0358178i
$486$	8.43848e20			0.271128
$487$	−2.48320e21	+	2.48320e21i	−0.784839	+	0.784839i	−0.980643	−	0.195804i	$-0.937268\pi$
$487$	−2.48320e21	+	2.48320e21i	−0.784839	+	0.784839i	0.195804	+	0.980643i	$0.437268\pi$
$488$	−4.35830e20	−	4.35830e20i	−0.135506	−	0.135506i
$489$			4.09065e21i			1.25118i
$490$	−1.08840e19	−	2.64178e20i	−0.00327507	−	0.0794927i
$491$	1.27845e21			0.378469			0.189235	−	0.981932i	$-0.439399\pi$
$491$	1.27845e21			0.378469			0.189235	+	0.981932i	$0.439399\pi$
$492$	−4.77895e20	+	4.77895e20i	−0.139191	+	0.139191i
$493$	−4.37745e21	−	4.37745e21i	−1.25443	−	1.25443i
$494$			3.58184e20i			0.100993i
$495$	−1.14488e21	+	1.24327e21i	−0.317627	+	0.344924i
$496$	−5.76862e21			−1.57478
$497$	−1.19499e21	+	1.19499e21i	−0.321006	+	0.321006i
$498$	1.27442e20	+	1.27442e20i	0.0336881	+	0.0336881i
$499$			1.06433e21i			0.276867i	0.990372	+	0.138433i	$0.0442067\pi$
$499$			1.06433e21i			0.276867i	−0.990372	+	0.138433i	$0.955793\pi$
$500$	2.94480e21	+	2.29431e21i	0.753870	+	0.587343i
$501$	1.03477e22			2.60701
$502$	−8.96703e20	+	8.96703e20i	−0.222341	+	0.222341i
$503$	1.60738e21	+	1.60738e21i	0.392260	+	0.392260i	0.875492	−	0.483232i	$-0.160537\pi$
$503$	1.60738e21	+	1.60738e21i	0.392260	+	0.392260i	−0.483232	+	0.875492i	$0.660537\pi$
$504$		−	1.91184e21i		−	0.459206i
$505$	−3.62899e21	−	3.34180e21i	−0.857936	−	0.790040i
$506$	−1.13680e20			−0.0264533
$507$	−6.98275e21	+	6.98275e21i	−1.59942	+	1.59942i
$508$	1.06798e21	+	1.06798e21i	0.240799	+	0.240799i
$509$		−	1.57224e21i		−	0.348961i	−0.984661	−	0.174480i	$-0.944175\pi$
$509$		−	1.57224e21i		−	0.348961i	0.984661	−	0.174480i	$-0.0558245\pi$
$510$	−2.07807e21	+	8.56156e19i	−0.454044	+	0.0187065i
$511$	2.99194e21			0.643554
$512$	2.92064e21	−	2.92064e21i	0.618470	−	0.618470i
$513$	−6.67336e20	−	6.67336e20i	−0.139125	−	0.139125i
$514$			3.83460e20i			0.0787073i
$515$	2.09555e20	+	5.08632e21i	0.0423486	+	1.02789i
$516$	3.22168e21			0.641039
$517$	2.22784e20	−	2.22784e20i	0.0436475	−	0.0436475i
$518$	1.86971e20	+	1.86971e20i	0.0360692	+	0.0360692i
$519$		−	3.89574e20i		−	0.0740032i
$520$	2.33697e21	−	2.53781e21i	0.437146	−	0.474714i
$521$	−9.53712e21			−1.75677			−0.878386	−	0.477952i	$-0.841379\pi$
$521$	−9.53712e21			−1.75677			−0.878386	+	0.477952i	$0.841379\pi$
$522$	1.48197e21	−	1.48197e21i	0.268828	−	0.268828i
$523$	2.07800e21	+	2.07800e21i	0.371221	+	0.371221i	0.867922	−	0.496701i	$-0.165455\pi$
$523$	2.07800e21	+	2.07800e21i	0.371221	+	0.371221i	−0.496701	+	0.867922i	$0.665455\pi$
$524$			6.70660e18i			0.00117992i
$525$	−5.81781e20	−	7.04852e21i	−0.100806	−	1.22130i
$526$	−1.40286e21			−0.239403
$527$	1.05907e22	−	1.05907e22i	1.78009	−	1.78009i
$528$	1.91246e21	+	1.91246e21i	0.316608	+	0.316608i
$529$		−	5.25266e21i		−	0.856513i
$530$	1.16551e21	+	1.07327e21i	0.187202	+	0.172387i
$531$	−1.50312e22			−2.37814
$532$	1.04673e21	−	1.04673e21i	0.163133	−	0.163133i
$533$	9.56930e20	+	9.56930e20i	0.146914	+	0.146914i
$534$			2.12458e20i			0.0321324i
$535$	−1.62491e21	+	6.69456e19i	−0.242102	+	0.00997452i
$536$	−1.17063e20			−0.0171831
$537$	1.67870e21	−	1.67870e21i	0.242761	−	0.242761i
$538$	−1.10791e21	−	1.10791e21i	−0.157850	−	0.157850i
$539$		−	8.92718e20i		−	0.125315i
$540$	1.82851e20	+	4.43817e21i	0.0252899	+	0.613838i
$541$	5.60262e21			0.763507			0.381753	−	0.924264i	$-0.375320\pi$
$541$	5.60262e21			0.763507			0.381753	+	0.924264i	$0.375320\pi$
$542$	1.03519e21	−	1.03519e21i	0.139004	−	0.139004i
$543$	1.06454e22	+	1.06454e22i	1.40852	+	1.40852i
$544$			6.33678e21i			0.826186i
$545$	−5.05376e21	+	5.48808e21i	−0.649296	+	0.705096i
$546$	−3.19394e21			−0.404376
$547$	−6.43235e21	+	6.43235e21i	−0.802547	+	0.802547i	−0.983493	−	0.180946i	$-0.942084\pi$
$547$	−6.43235e21	+	6.43235e21i	−0.802547	+	0.802547i	0.180946	+	0.983493i	$0.442084\pi$
$548$	−1.45596e21	−	1.45596e21i	−0.179021	−	0.179021i
$549$		−	5.42947e21i		−	0.657928i
$550$	−4.46097e20	−	3.78071e20i	−0.0532755	−	0.0451514i
$551$	3.32079e21			0.390867
$552$	−1.47716e21	+	1.47716e21i	−0.171363	+	0.171363i
$553$	1.81107e21	+	1.81107e21i	0.207078	+	0.207078i
$554$			5.40566e20i			0.0609216i
$555$	−3.15983e21	−	2.90976e21i	−0.351010	−	0.323231i
$556$	5.44327e21			0.596021
$557$	−3.00655e20	+	3.00655e20i	−0.0324509	+	0.0324509i	−0.723146	−	0.690695i	$-0.757305\pi$
$557$	−3.00655e20	+	3.00655e20i	−0.0324509	+	0.0324509i	0.690695	+	0.723146i	$0.257305\pi$
$558$	3.58545e21	+	3.58545e21i	0.381479	+	0.381479i
$559$		−	6.45105e21i		−	0.676606i
$560$	−6.62343e21	+	2.72883e20i	−0.684823	+	0.0282145i
$561$	−7.02227e21			−0.715772
$562$	9.54244e20	−	9.54244e20i	0.0958890	−	0.0958890i
$563$	−1.00921e22	−	1.00921e22i	−0.999799	−	0.999799i	0.000201395	−	1.00000i	$-0.499936\pi$
$563$	−1.00921e22	−	1.00921e22i	−0.999799	−	0.999799i	−1.00000		0.000201395i	$0.999936\pi$
$564$		−	2.82924e21i		−	0.276336i
$565$	4.75691e20	+	1.15460e22i	0.0458075	+	1.11184i
$566$	3.45587e21			0.328115
$567$	−2.47261e21	+	2.47261e21i	−0.231468	+	0.231468i
$568$	1.81563e21	+	1.81563e21i	0.167587	+	0.167587i
$569$			1.20187e22i			1.09385i	0.837181	+	0.546926i	$0.184202\pi$
$569$			1.20187e22i			1.09385i	−0.837181	+	0.546926i	$0.815798\pi$
$570$	7.55751e20	−	8.20700e20i	0.0678234	−	0.0736522i
$571$	1.23515e22			1.09303			0.546515	−	0.837449i	$-0.315954\pi$
$571$	1.23515e22			1.09303			0.546515	+	0.837449i	$0.315954\pi$
$572$	4.02488e21	−	4.02488e21i	0.351225	−	0.351225i
$573$	−3.67602e21	−	3.67602e21i	−0.316331	−	0.316331i
$574$			2.59478e20i			0.0220194i
$575$	−2.92649e21	+	3.45305e21i	−0.244909	+	0.288975i
$576$	1.27400e22			1.05146
$577$	1.40369e21	−	1.40369e21i	0.114252	−	0.114252i	−0.647669	−	0.761922i	$-0.724256\pi$
$577$	1.40369e21	−	1.40369e21i	0.114252	−	0.114252i	0.761922	+	0.647669i	$0.224256\pi$
$578$	−1.72422e21	−	1.72422e21i	−0.138411	−	0.138411i
$579$		−	2.25959e22i		−	1.78896i
$580$	−1.14975e22	−	1.05876e22i	−0.897802	−	0.826751i
$581$	−1.49149e21			−0.114871
$582$	−2.64956e21	+	2.64956e21i	−0.201275	+	0.201275i
$583$	3.78269e21	+	3.78269e21i	0.283434	+	0.283434i
$584$		−	4.54585e21i		−	0.335979i
$585$	3.03644e22	−	1.25100e21i	2.21369	−	0.0912034i
$586$	−3.94552e21			−0.283742
$587$	2.73739e21	−	2.73739e21i	0.194192	−	0.194192i	−0.603313	−	0.797505i	$-0.706153\pi$
$587$	2.73739e21	−	2.73739e21i	0.194192	−	0.194192i	0.797505	+	0.603313i	$0.206153\pi$
$588$	−5.66853e21	−	5.66853e21i	−0.396690	−	0.396690i
$589$			8.03429e21i			0.554658i
$590$	−2.14082e20	−	5.19621e21i	−0.0145802	−	0.353892i
$591$	−1.64123e22			−1.10273
$592$	−2.84692e21	+	2.84692e21i	−0.188713	+	0.188713i
$593$	−5.03168e21	−	5.03168e21i	−0.329060	−	0.329060i	0.523169	−	0.852229i	$-0.324750\pi$
$593$	−5.03168e21	−	5.03168e21i	−0.329060	−	0.329060i	−0.852229	+	0.523169i	$0.824750\pi$
$594$		−	6.95796e20i		−	0.0448942i
$595$	1.16591e22	−	1.26611e22i	0.742215	−	0.806001i
$596$	−2.00540e22			−1.25959
$597$	−7.28871e21	+	7.28871e21i	−0.451706	+	0.451706i
$598$	1.44540e21	+	1.44540e21i	0.0883849	+	0.0883849i
$599$			2.41530e22i			1.45732i	0.684873	+	0.728662i	$0.259858\pi$
$599$			2.41530e22i			1.45732i	−0.684873	+	0.728662i	$0.740142\pi$
$600$	−1.07093e22	+	8.83938e20i	−0.637604	+	0.0526274i
$601$	1.36202e22			0.800178			0.400089	−	0.916476i	$-0.368979\pi$
$601$	1.36202e22			0.800178			0.400089	+	0.916476i	$0.368979\pi$
$602$	8.74621e20	−	8.74621e20i	0.0507047	−	0.0507047i
$603$	−7.29170e20	−	7.29170e20i	−0.0417148	−	0.0417148i
$604$			2.92678e22i			1.65232i
$605$	1.17513e22	+	1.08213e22i	0.654700	+	0.602888i
$606$	6.93931e21			0.381536
$607$	2.37789e22	−	2.37789e22i	1.29027	−	1.29027i	0.355655	−	0.934617i	$-0.384258\pi$
$607$	2.37789e22	−	2.37789e22i	1.29027	−	1.29027i	0.934617	−	0.355655i	$-0.115742\pi$
$608$	−2.40359e21	−	2.40359e21i	−0.128716	−	0.128716i
$609$			2.96116e22i			1.56503i
$610$	1.87694e21	−	7.73291e19i	0.0979064	−	0.00403371i
$611$	−5.66524e21			−0.291668
$612$	−2.61167e22	+	2.61167e22i	−1.32711	+	1.32711i
$613$	−4.15852e21	−	4.15852e21i	−0.208571	−	0.208571i	0.595089	−	0.803660i	$-0.297117\pi$
$613$	−4.15852e21	−	4.15852e21i	−0.208571	−	0.208571i	−0.803660	+	0.595089i	$0.797117\pi$
$614$			3.64518e21i			0.180456i
$615$	−1.73519e20	−	4.21167e21i	−0.00847904	−	0.205804i
$616$	2.23338e21			0.107725
$617$	−1.41945e22	+	1.41945e22i	−0.675832	+	0.675832i	−0.959054	−	0.283222i	$-0.908597\pi$
$617$	−1.41945e22	+	1.41945e22i	−0.675832	+	0.675832i	0.283222	+	0.959054i	$0.408597\pi$
$618$	−5.06335e21	−	5.06335e21i	−0.237975	−	0.237975i
$619$		−	1.98460e22i		−	0.920761i	−0.887722	−	0.460381i	$-0.847713\pi$
$619$		−	1.98460e22i		−	0.920761i	0.887722	−	0.460381i	$-0.152287\pi$
$620$	2.56156e22	−	2.78170e22i	1.17320	−	1.27402i
$621$	−5.38587e21			−0.243513
$622$	−3.03205e21	+	3.03205e21i	−0.135336	+	0.135336i
$623$	−1.24323e21	−	1.24323e21i	−0.0547831	−	0.0547831i
$624$		−	4.86326e22i		−	2.11568i
$625$	−2.29680e22	+	3.81753e21i	−0.986467	+	0.163962i
$626$	−6.36559e20			−0.0269926
$627$	2.66360e21	−	2.66360e21i	0.111514	−	0.111514i
$628$	1.88713e22	+	1.88713e22i	0.780055	+	0.780055i
$629$		−	1.04535e22i		−	0.426634i
$630$	4.28636e21	+	3.94714e21i	0.172729	+	0.159059i
$631$	1.07541e22			0.427898			0.213949	−	0.976845i	$-0.431367\pi$
$631$	1.07541e22			0.427898			0.213949	+	0.976845i	$0.431367\pi$
$632$	2.75168e21	−	2.75168e21i	0.108109	−	0.108109i
$633$	−1.60234e22	−	1.60234e22i	−0.621620	−	0.621620i
$634$		−	5.52500e21i		−	0.211650i
$635$	−9.41210e21	+	3.87775e20i	−0.356038	+	0.0146686i
$636$	4.80382e22			1.79444
$637$	−1.13506e22	+	1.13506e22i	−0.418700	+	0.418700i
$638$	1.73121e21	+	1.73121e21i	0.0630643	+	0.0630643i
$639$			2.26187e22i			0.813693i
$640$	8.70589e20	+	2.11310e22i	0.0309295	+	0.750724i
$641$	3.41733e22			1.19901			0.599504	−	0.800372i	$-0.295365\pi$
$641$	3.41733e22			1.19901			0.599504	+	0.800372i	$0.295365\pi$
$642$	1.61757e21	−	1.61757e21i	0.0560510	−	0.0560510i
$643$	−2.10321e22	−	2.10321e22i	−0.719770	−	0.719770i	0.248788	−	0.968558i	$-0.419968\pi$
$643$	−2.10321e22	−	2.10321e22i	−0.719770	−	0.719770i	−0.968558	+	0.248788i	$0.919968\pi$
$644$		−	8.44787e21i		−	0.285536i
$645$	−1.36114e22	+	1.47812e22i	−0.454386	+	0.493436i
$646$	2.71507e21			0.0895203
$647$	3.43962e22	−	3.43962e22i	1.12015	−	1.12015i	0.128431	−	0.991718i	$-0.459006\pi$
$647$	3.43962e22	−	3.43962e22i	1.12015	−	1.12015i	0.991718	−	0.128431i	$-0.0409940\pi$
$648$	3.75680e21	+	3.75680e21i	0.120842	+	0.120842i
$649$		−	1.75592e22i		−	0.557888i
$650$	8.64929e20	+	1.04790e22i	0.0271440	+	0.328861i
$651$	−7.16419e22			−2.22085
$652$	−1.77723e22	+	1.77723e22i	−0.544205	+	0.544205i
$653$	−2.95865e22	−	2.95865e22i	−0.894928	−	0.894928i	0.100054	−	0.994982i	$-0.468098\pi$
$653$	−2.95865e22	−	2.95865e22i	−0.894928	−	0.894928i	−0.994982	+	0.100054i	$0.968098\pi$
$654$		−	1.04942e22i		−	0.313566i
$655$	−3.07701e19	−	2.83350e19i	−0.000908235	−	0.000836358i
$656$	−3.95095e21			−0.115205
$657$	2.83156e22	−	2.83156e22i	0.815647	−	0.815647i
$658$	−7.68083e20	−	7.68083e20i	−0.0218575	−	0.0218575i
$659$			3.83787e22i			1.07896i	0.841997	+	0.539482i	$0.181380\pi$
$659$			3.83787e22i			1.07896i	−0.841997	+	0.539482i	$0.818620\pi$
$660$	−1.77144e22	+	7.29828e20i	−0.492012	+	0.0202707i
$661$	−3.55615e22			−0.975816			−0.487908	−	0.872895i	$-0.662240\pi$
$661$	−3.55615e22			−0.975816			−0.487908	+	0.872895i	$0.662240\pi$
$662$	−6.60727e21	+	6.60727e21i	−0.179126	+	0.179126i
$663$	8.92857e22	+	8.92857e22i	2.39152	+	2.39152i
$664$			2.26611e21i			0.0599704i
$665$	3.80059e20	+	9.22482e21i	0.00993752	+	0.241204i
$666$	3.53898e21			0.0914290
$667$	1.34006e22	−	1.34006e22i	0.342071	−	0.342071i
$668$	4.49568e22	+	4.49568e22i	1.13392	+	1.13392i
$669$			3.10107e22i			0.772864i
$670$	2.41685e20	−	2.62455e20i	0.00595184	−	0.00646334i
$671$	6.34261e21			0.154343
$672$	2.14328e22	−	2.14328e22i	0.515377	−	0.515377i
$673$	−1.69157e22	−	1.69157e22i	−0.401948	−	0.401948i	0.476971	−	0.878919i	$-0.341735\pi$
$673$	−1.69157e22	−	1.69157e22i	−0.401948	−	0.401948i	−0.878919	+	0.476971i	$0.841735\pi$
$674$			3.23287e21i			0.0759118i
$675$	−2.11350e22	−	1.79120e22i	−0.490424	−	0.415638i
$676$	−6.06747e22			−1.39134
$677$	−5.35206e22	+	5.35206e22i	−1.21286	+	1.21286i	−0.242781	+	0.970081i	$0.578060\pi$
$677$	−5.35206e22	+	5.35206e22i	−1.21286	+	1.21286i	−0.970081	+	0.242781i	$0.921940\pi$
$678$	−1.14939e22	−	1.14939e22i	−0.257412	−	0.257412i
$679$		−	3.10086e22i		−	0.686315i
$680$	−1.92368e22	−	1.77145e22i	−0.420787	−	0.387487i
$681$	4.68137e22			1.01204
$682$	−4.18846e21	+	4.18846e21i	−0.0894910	+	0.0894910i
$683$	4.30788e21	+	4.30788e21i	0.0909698	+	0.0909698i	0.751127	−	0.660157i	$-0.229510\pi$
$683$	4.30788e21	+	4.30788e21i	0.0909698	+	0.0909698i	−0.660157	+	0.751127i	$0.729510\pi$
$684$		−	1.98125e22i		−	0.413514i
$685$	1.28313e22	−	5.28645e20i	0.264695	−	0.0109053i
$686$	−1.12234e22			−0.228840
$687$	7.12930e22	−	7.12930e22i	1.43679	−	1.43679i
$688$	1.33174e22	+	1.33174e22i	0.265285	+	0.265285i
$689$		−	9.61910e22i		−	1.89400i
$690$	−2.62093e20	−	6.36153e21i	−0.00510108	−	0.123814i
$691$	−8.73479e22			−1.68046			−0.840230	−	0.542231i	$-0.817580\pi$
$691$	−8.73479e22			−1.68046			−0.840230	+	0.542231i	$0.817580\pi$
$692$	1.69255e21	−	1.69255e21i	0.0321878	−	0.0321878i
$693$	1.39115e22	+	1.39115e22i	0.261521	+	0.261521i
$694$		−	1.46061e22i		−	0.271430i
$695$	−2.29975e22	+	2.49739e22i	−0.422476	+	0.458783i
$696$	4.49909e22			0.817053
$697$	7.25363e21	−	7.25363e21i	0.130225	−	0.130225i
$698$	1.39300e22	+	1.39300e22i	0.247234	+	0.247234i
$699$			4.28711e22i			0.752223i
$700$	2.80955e22	−	3.31507e22i	0.487363	−	0.575054i
$701$	7.26398e22			1.24575			0.622874	−	0.782322i	$-0.285965\pi$
$701$	7.26398e22			1.24575			0.622874	+	0.782322i	$0.285965\pi$
$702$	−8.84679e21	+	8.84679e21i	−0.149999	+	0.149999i
$703$	3.96507e21	+	3.96507e21i	0.0664674	+	0.0664674i
$704$			1.48827e22i			0.246661i
$705$	1.29806e22	+	1.19534e22i	0.212708	+	0.195874i
$706$	3.91046e21			0.0633564
$707$	−4.06064e22	+	4.06064e22i	−0.650487	+	0.650487i
$708$	−1.11496e23	−	1.11496e23i	−1.76602	−	1.76602i
$709$			1.64799e22i			0.258098i	0.991638	+	0.129049i	$0.0411925\pi$
$709$			1.64799e22i			0.258098i	−0.991638	+	0.129049i	$0.958807\pi$
$710$	−7.81916e21	+	3.22146e20i	−0.121086	+	0.00498869i
$711$	3.42798e22			0.524905
$712$	−1.88892e21	+	1.88892e21i	−0.0286005	+	0.0286005i
$713$	3.24211e22	+	3.24211e22i	0.485414	+	0.485414i
$714$			2.42104e22i			0.358440i
$715$	1.46140e21	+	3.54712e22i	0.0213954	+	0.519310i
$716$	1.45866e22			0.211179
$717$	−5.47932e22	+	5.47932e22i	−0.784465	+	0.784465i
$718$	1.14941e22	+	1.14941e22i	0.162734	+	0.162734i
$719$		−	1.26598e23i		−	1.77254i	−0.463167	−	0.886271i	$-0.653287\pi$
$719$		−	1.26598e23i		−	1.77254i	0.463167	−	0.886271i	$-0.346713\pi$
$720$	−6.01013e22	+	6.52664e22i	−0.832192	+	0.903711i
$721$	5.92578e22			0.811454
$722$	9.96439e21	−	9.96439e21i	0.134944	−	0.134944i
$723$	−5.80883e22	−	5.80883e22i	−0.778005	−	0.778005i
$724$			9.25004e22i			1.22528i
$725$	9.71527e22	−	8.01892e21i	1.27277	−	0.105054i
$726$	−2.24706e22			−0.291154
$727$	−5.19538e22	+	5.19538e22i	−0.665798	+	0.665798i	−0.956740	−	0.290943i	$-0.906031\pi$
$727$	−5.19538e22	+	5.19538e22i	−0.665798	+	0.665798i	0.290943	+	0.956740i	$0.406031\pi$
$728$	−2.83966e22	−	2.83966e22i	−0.359928	−	0.359928i
$729$			1.26470e23i			1.58550i
$730$	1.01918e22	+	9.38525e21i	0.126377	+	0.116376i
$731$	−4.88996e22			−0.599745
$732$	4.02739e22	−	4.02739e22i	0.488580	−	0.488580i
$733$	−4.02984e22	−	4.02984e22i	−0.483567	−	0.483567i	0.422702	−	0.906269i	$-0.361082\pi$
$733$	−4.02984e22	−	4.02984e22i	−0.483567	−	0.483567i	−0.906269	+	0.422702i	$0.861082\pi$
$734$			8.37687e20i			0.00994290i
$735$	4.99565e22	−	2.05819e21i	0.586535	−	0.0241650i
$736$	−1.93986e22			−0.225293
$737$	8.51804e20	−	8.51804e20i	0.00978587	−	0.00978587i
$738$	2.45569e21	+	2.45569e21i	0.0279076	+	0.0279076i
$739$		−	4.99280e22i		−	0.561291i	−0.959811	−	0.280646i	$-0.909451\pi$
$739$		−	4.99280e22i		−	0.561291i	0.959811	−	0.280646i	$-0.0905486\pi$
$740$	−1.08643e21	−	2.63700e22i	−0.0120823	−	0.293262i
$741$	−6.77334e22			−0.745173
$742$	1.30414e22	−	1.30414e22i	0.141936	−	0.141936i
$743$	1.25219e23	+	1.25219e23i	1.34821	+	1.34821i	0.887604	+	0.460608i	$0.152369\pi$
$743$	1.25219e23	+	1.25219e23i	1.34821	+	1.34821i	0.460608	+	0.887604i	$0.347631\pi$
$744$			1.08850e23i			1.15944i
$745$	8.47269e22	−	9.20083e22i	0.892835	−	0.969565i
$746$	−1.66528e22			−0.173610
$747$	−1.41154e22	+	1.41154e22i	−0.145589	+	0.145589i
$748$	−3.05091e22	−	3.05091e22i	−0.311326	−	0.311326i
$749$			1.89309e22i			0.191124i
$750$	2.01284e22	−	2.58353e22i	0.201057	−	0.258061i
$751$	1.29330e23			1.27814			0.639071	−	0.769148i	$-0.279319\pi$
$751$	1.29330e23			1.27814			0.639071	+	0.769148i	$0.279319\pi$
$752$	1.16952e22	−	1.16952e22i	0.114358	−	0.114358i
$753$	−1.69568e23	−	1.69568e23i	−1.64053	−	1.64053i
$754$		−	4.40233e22i		−	0.421417i
$755$	−1.34282e23	−	1.23655e23i	−1.27187	−	1.17121i
$756$	5.17066e22			0.484586
$757$	9.06309e22	−	9.06309e22i	0.840445	−	0.840445i	−0.148472	−	0.988917i	$-0.547435\pi$
$757$	9.06309e22	−	9.06309e22i	0.840445	−	0.840445i	0.988917	+	0.148472i	$0.0474355\pi$
$758$	7.29867e21	+	7.29867e21i	0.0669715	+	0.0669715i
$759$		−	2.14971e22i		−	0.195185i
$760$	1.40159e22	−	5.77449e20i	0.125925	−	0.00518806i
$761$	1.76896e22			0.157268			0.0786339	−	0.996904i	$-0.474944\pi$
$761$	1.76896e22			0.157268			0.0786339	+	0.996904i	$0.474944\pi$
$762$	9.36960e21	−	9.36960e21i	0.0824292	−	0.0824292i
$763$	6.14085e22	+	6.14085e22i	0.534604	+	0.534604i
$764$		−	3.19418e22i		−	0.275177i
$765$	−9.48273e21	−	2.30165e23i	−0.0808429	−	1.96222i
$766$	−2.44914e22			−0.206625
$767$	−2.23259e23	+	2.23259e23i	−1.86400	+	1.86400i
$768$	7.78501e22	+	7.78501e22i	0.643234	+	0.643234i
$769$			1.60000e23i			1.30831i	0.756361	+	0.654154i	$0.226975\pi$
$769$			1.60000e23i			1.30831i	−0.756361	+	0.654154i	$0.773025\pi$
$770$	−4.61098e21	+	5.00725e21i	−0.0373136	+	0.0405204i
$771$	−7.25130e22			−0.580739
$772$	9.81703e22	−	9.81703e22i	0.778111	−	0.778111i
$773$	−2.75094e22	−	2.75094e22i	−0.215797	−	0.215797i	0.590928	−	0.806724i	$-0.298762\pi$
$773$	−2.75094e22	−	2.75094e22i	−0.215797	−	0.215797i	−0.806724	+	0.590928i	$0.798762\pi$
$774$		−	1.65548e22i		−	0.128527i
$775$	1.94009e22	+	2.35050e23i	0.149076	+	1.80612i
$776$	−4.71134e22			−0.358303
$777$	−3.53567e22	+	3.53567e22i	−0.266136	+	0.266136i
$778$	1.42836e22	+	1.42836e22i	0.106414	+	0.106414i
$779$			5.50271e21i			0.0405767i
$780$	2.34512e23	+	2.15953e23i	1.71163	+	1.57617i
$781$	−2.64228e22			−0.190884
$782$	1.09563e22	−	1.09563e22i	0.0783445	−	0.0783445i
$783$	8.20203e22	+	8.20203e22i	0.580533	+	0.580533i
$784$		−	4.68640e22i		−	0.328330i
$785$	−1.66312e23	+	6.85200e21i	−1.15337	+	0.0475182i
$786$	5.88381e19			0.000403904
$787$	−2.24408e22	+	2.24408e22i	−0.152490	+	0.152490i	−0.779229	−	0.626739i	$-0.784389\pi$
$787$	−2.24408e22	+	2.24408e22i	−0.152490	+	0.152490i	0.626739	+	0.779229i	$0.284389\pi$
$788$	−7.13053e22	−	7.13053e22i	−0.479636	−	0.479636i
$789$		−	2.65284e23i		−	1.76642i
$790$	4.88229e20	+	1.18503e22i	0.00321816	+	0.0781113i
$791$	1.34516e23			0.877731
$792$	2.11366e22	−	2.11366e22i	0.136532	−	0.136532i
$793$	−8.06440e22	−	8.06440e22i	−0.515687	−	0.515687i
$794$			4.77971e22i			0.302578i
$795$	−2.02958e23	+	2.20401e23i	−1.27195	+	1.38126i
$796$	−6.33333e22			−0.392941
$797$	7.06646e22	−	7.06646e22i	0.434046	−	0.434046i	−0.455957	−	0.890002i	$-0.650703\pi$
$797$	7.06646e22	−	7.06646e22i	0.434046	−	0.434046i	0.890002	+	0.455957i	$0.150703\pi$
$798$	−9.18317e21	−	9.18317e21i	−0.0558431	−	0.0558431i
$799$			4.29431e22i			0.258535i
$800$	−7.61231e22	−	6.45149e22i	−0.453729	−	0.384539i
$801$	−2.35317e22			−0.138865
$802$	−3.31756e22	+	3.31756e22i	−0.193831	+	0.193831i
$803$	3.30777e22	+	3.30777e22i	0.191343	+	0.191343i
$804$		−	1.08175e22i		−	0.0619551i
$805$	3.87590e22	+	3.56917e22i	0.219789	+	0.202395i
$806$	1.06510e23			0.598010
$807$	2.09508e23	−	2.09508e23i	1.16469	−	1.16469i
$808$	6.16960e22	+	6.16960e22i	0.339599	+	0.339599i
$809$		−	7.10099e22i		−	0.387018i	−0.981099	−	0.193509i	$-0.938013\pi$
$809$		−	7.10099e22i		−	0.387018i	0.981099	−	0.193509i	$-0.0619868\pi$
$810$	−1.61790e22	+	6.66568e20i	−0.0873114	+	0.00359720i
$811$	1.19142e23			0.636647			0.318324	−	0.947982i	$-0.396880\pi$
$811$	1.19142e23			0.636647			0.318324	+	0.947982i	$0.396880\pi$
$812$	−1.28651e23	+	1.28651e23i	−0.680714	+	0.680714i
$813$	1.95758e23	+	1.95758e23i	1.02564	+	1.02564i
$814$			4.13417e21i			0.0214483i
$815$	−6.45295e21	−	1.56626e23i	−0.0331511	−	0.804645i
$816$	−3.68640e23			−1.87535
$817$	1.85480e22	−	1.85480e22i	0.0934372	−	0.0934372i
$818$	2.47437e22	+	2.47437e22i	0.123435	+	0.123435i
$819$		−	3.53758e23i		−	1.74757i
$820$	1.75442e22	−	1.90519e22i	0.0858268	−	0.0932027i
$821$	1.09754e23			0.531712			0.265856	−	0.964013i	$-0.414345\pi$
$821$	1.09754e23			0.531712			0.265856	+	0.964013i	$0.414345\pi$
$822$	−1.27734e22	+	1.27734e22i	−0.0612817	+	0.0612817i
$823$	9.85869e21	+	9.85869e21i	0.0468404	+	0.0468404i	0.730139	−	0.683299i	$-0.239455\pi$
$823$	9.85869e21	+	9.85869e21i	0.0468404	+	0.0468404i	−0.683299	+	0.730139i	$0.739455\pi$
$824$		−	9.00344e22i		−	0.423634i
$825$	7.14939e22	−	8.43578e22i	0.333148	−	0.393092i
$826$	−6.05381e22			−0.279375
$827$	1.22782e23	−	1.22782e23i	0.561164	−	0.561164i	−0.368474	−	0.929638i	$-0.620120\pi$
$827$	1.22782e23	−	1.22782e23i	0.561164	−	0.561164i	0.929638	+	0.368474i	$0.120120\pi$
$828$	−7.99503e22	−	7.99503e22i	−0.361890	−	0.361890i
$829$			1.65238e23i			0.740752i	0.928882	+	0.370376i	$0.120771\pi$
$829$			1.65238e23i			0.740752i	−0.928882	+	0.370376i	$0.879229\pi$
$830$	−5.08064e21	−	4.67857e21i	−0.0225577	−	0.0207725i
$831$	−1.02222e23			−0.449508
$832$	1.89228e23	−	1.89228e23i	0.824137	−	0.824137i
$833$	8.60387e22	+	8.60387e22i	0.371136	+	0.371136i
$834$		−	4.77548e22i		−	0.204027i
$835$	−3.96202e23	+	1.63234e22i	−1.67658	+	0.0690746i
$836$	2.31446e22			0.0970062
$837$	−1.98439e23	+	1.98439e23i	−0.823803	+	0.823803i
$838$	−5.64249e22	−	5.64249e22i	−0.232016	−	0.232016i
$839$			2.26686e23i			0.923270i	0.887070	+	0.461635i	$0.152737\pi$
$839$			2.26686e23i			0.923270i	−0.887070	+	0.461635i	$0.847263\pi$
$840$	5.14913e21	+	1.24980e23i	0.0207730	+	0.504204i
$841$	−1.57902e23			−0.630987
$842$	−1.29327e22	+	1.29327e22i	−0.0511909	+	0.0511909i
$843$	1.80450e23	+	1.80450e23i	0.707514	+	0.707514i
$844$		−	1.39231e23i		−	0.540750i
$845$	2.56347e23	−	2.78377e23i	0.986220	−	1.07098i
$846$	−1.45382e22			−0.0554049
$847$	1.31490e23	−	1.31490e23i	0.496393	−	0.496393i
$848$	1.98575e23	+	1.98575e23i	0.742606	+	0.742606i
$849$			6.53512e23i			2.42099i
$850$	7.94319e22	−	6.55626e21i	0.291503	−	0.0240605i
$851$	3.20009e22			0.116339
$852$	−1.67778e23	+	1.67778e23i	−0.604251	+	0.604251i
$853$	6.65043e22	+	6.65043e22i	0.237278	+	0.237278i	0.815722	−	0.578444i	$-0.196340\pi$
$853$	6.65043e22	+	6.65043e22i	0.237278	+	0.237278i	−0.578444	+	0.815722i	$0.696340\pi$
$854$		−	2.18671e22i		−	0.0772910i
$855$	9.09002e22	+	8.37065e22i	0.318299	+	0.293110i
$856$	2.87630e22			0.0997800
$857$	−3.37105e23	+	3.37105e23i	−1.15856	+	1.15856i	−0.173773	+	0.984786i	$0.555596\pi$
$857$	−3.37105e23	+	3.37105e23i	−1.15856	+	1.15856i	−0.984786	+	0.173773i	$0.944404\pi$
$858$	−3.53110e22	−	3.53110e22i	−0.120230	−	0.120230i
$859$		−	3.99068e22i		−	0.134617i	−0.997732	−	0.0673087i	$-0.978559\pi$
$859$		−	3.99068e22i		−	0.134617i	0.997732	−	0.0673087i	$-0.0214412\pi$
$860$	−1.23355e23	+	5.08216e21i	−0.412257	+	0.0169848i
$861$	−4.90678e22			−0.162469
$862$	3.72658e22	−	3.72658e22i	0.122251	−	0.122251i
$863$	−3.19599e23	−	3.19599e23i	−1.03877	−	1.03877i	−0.999218	−	0.0395501i	$-0.987408\pi$
$863$	−3.19599e23	−	3.19599e23i	−1.03877	−	1.03877i	−0.0395501	−	0.999218i	$-0.512592\pi$
$864$		−	1.18732e23i		−	0.382348i
$865$	6.14548e20	+	1.49163e22i	0.00196077	+	0.0475920i
$866$	8.36065e22			0.264300
$867$	3.26054e23	−	3.26054e23i	1.02126	−	1.02126i
$868$	−3.11256e23	−	3.11256e23i	−0.965963	−	0.965963i
$869$			4.00450e22i			0.123138i
$870$	−9.28871e22	+	1.00870e23i	−0.283010	+	0.307332i
$871$	−2.16608e22			−0.0653926
$872$	9.33020e22	−	9.33020e22i	0.279099	−	0.279099i
$873$	−2.93464e23	−	2.93464e23i	−0.869843	−	0.869843i
$874$			8.31158e21i			0.0244114i
$875$	3.33947e22	+	2.68963e23i	0.0971882	+	0.782758i
$876$	4.20071e23			1.21140
$877$	−8.33936e22	+	8.33936e22i	−0.238307	+	0.238307i	−0.816149	−	0.577842i	$-0.803895\pi$
$877$	−8.33936e22	+	8.33936e22i	−0.238307	+	0.238307i	0.577842	+	0.816149i	$0.303895\pi$
$878$	−7.03719e22	−	7.03719e22i	−0.199271	−	0.199271i
$879$		−	7.46105e23i		−	2.09358i
$880$	−7.62430e22	−	7.02093e22i	−0.212001	−	0.195224i
$881$	6.58112e23			1.81340			0.906698	−	0.421780i	$-0.138594\pi$
$881$	6.58112e23			1.81340			0.906698	+	0.421780i	$0.138594\pi$
$882$	−2.91280e22	+	2.91280e22i	−0.0795357	+	0.0795357i
$883$	−2.63900e23	−	2.63900e23i	−0.714090	−	0.714090i	0.253298	−	0.967388i	$-0.418485\pi$
$883$	−2.63900e23	−	2.63900e23i	−0.714090	−	0.714090i	−0.967388	+	0.253298i	$0.918485\pi$
$884$			7.75823e23i			2.08039i
$885$	9.82614e23	−	4.04833e22i	2.61118	−	0.107580i
$886$	−1.34626e23			−0.354534
$887$	−8.84723e22	+	8.84723e22i	−0.230897	+	0.230897i	−0.813067	−	0.582170i	$-0.802204\pi$
$887$	−8.84723e22	+	8.84723e22i	−0.230897	+	0.230897i	0.582170	+	0.813067i	$0.302204\pi$
$888$	5.37197e22	+	5.37197e22i	0.138941	+	0.138941i
$889$			1.09655e23i			0.281070i
$890$	−3.35150e20	−	8.13479e21i	−0.000851373	−	0.0206646i
$891$	−5.46725e22			−0.137641
$892$	−1.34730e23	+	1.34730e23i	−0.336159	+	0.336159i
$893$	−1.62886e22	−	1.62886e22i	−0.0402784	−	0.0402784i
$894$			1.75937e23i			0.431179i
$895$	−6.16276e22	+	6.69238e22i	−0.149689	+	0.162554i
$896$	2.46185e23			0.592650
$897$	−2.73328e23	+	2.73328e23i	−0.652145	+	0.652145i
$898$	−9.17011e21	−	9.17011e21i	−0.0216852	−	0.0216852i
$899$		−	9.87470e23i		−	2.31444i
$900$	−4.78424e22	−	5.79632e23i	−0.111141	−	1.34652i
$901$	−7.29138e23			−1.67885
$902$	−2.86869e21	+	2.86869e21i	−0.00654683	+	0.00654683i
$903$	1.65393e23	+	1.65393e23i	0.374123	+	0.374123i
$904$		−	2.04379e23i		−	0.458235i
$905$	−4.24394e23	−	3.90808e23i	−0.943150	−	0.868511i
$906$	2.56772e23			0.565616
$907$	−3.86194e23	+	3.86194e23i	−0.843233	+	0.843233i	−0.989278	−	0.146045i	$-0.953346\pi$
$907$	−3.86194e23	+	3.86194e23i	−0.843233	+	0.843233i	0.146045	+	0.989278i	$0.453346\pi$
$908$	2.03387e23	+	2.03387e23i	0.440187	+	0.440187i
$909$			7.68594e23i			1.64887i
$910$	1.22292e23	−	5.03840e21i	0.260057	−	0.0107142i
$911$	−2.76711e23			−0.583283			−0.291641	−	0.956528i	$-0.594201\pi$
$911$	−2.76711e23			−0.583283			−0.291641	+	0.956528i	$0.594201\pi$
$912$	1.39828e23	−	1.39828e23i	0.292169	−	0.292169i
$913$	−1.64893e22	−	1.64893e22i	−0.0341536	−	0.0341536i
$914$			1.52952e23i			0.314041i
$915$	1.46231e22	+	3.54933e23i	0.0297626	+	0.722399i
$916$	6.19480e23			1.24987
$917$	−3.44300e20	+	3.44300e20i	−0.000688623	+	0.000688623i
$918$	6.70596e22	+	6.70596e22i	0.132960	+	0.132960i
$919$			7.25565e23i			1.42611i	0.701110	+	0.713053i	$0.252688\pi$
$919$			7.25565e23i			1.42611i	−0.701110	+	0.713053i	$0.747312\pi$
$920$	5.42288e22	−	5.88892e22i	0.105664	−	0.114745i
$921$	−6.89311e23			−1.33149
$922$	−1.27160e23	+	1.27160e23i	−0.243502	+	0.243502i
$923$	3.35956e23	+	3.35956e23i	0.637777	+	0.637777i
$924$			2.06381e23i			0.388413i
$925$	1.25576e23	+	1.06427e23i	0.234301	+	0.198572i
$926$	−1.41412e22			−0.0261575
$927$	5.60814e23	−	5.60814e23i	1.02844	−	1.02844i
$928$	2.95418e23	+	2.95418e23i	0.537097	+	0.537097i
$929$			3.00953e23i			0.542467i	0.962514	+	0.271233i	$0.0874315\pi$
$929$			3.00953e23i			0.542467i	−0.962514	+	0.271233i	$0.912568\pi$
$930$	−2.44043e23	−	2.24730e23i	−0.436117	−	0.401603i
$931$	−6.52701e22			−0.115642
$932$	−1.86258e23	+	1.86258e23i	−0.327181	+	0.327181i
$933$	−5.73368e23	−	5.73368e23i	−0.998574	−	0.998574i
$934$		−	1.56916e23i		−	0.270952i
$935$	2.68875e23	−	1.10776e22i	0.460318	−	0.0189649i
$936$	−5.37489e23			−0.912352
$937$	6.48097e23	−	6.48097e23i	1.09074	−	1.09074i	0.0952958	−	0.995449i	$-0.469620\pi$
$937$	6.48097e23	−	6.48097e23i	1.09074	−	1.09074i	0.995449	−	0.0952958i	$-0.0303797\pi$
$938$	−2.93673e21	−	2.93673e21i	−0.00490050	−	0.00490050i
$939$		−	1.20375e23i		−	0.199164i
$940$	4.46310e21	+	1.08329e23i	0.00732173	+	0.177714i
$941$	−6.79669e23			−1.10556			−0.552778	−	0.833329i	$-0.686432\pi$
$941$	−6.79669e23			−1.10556			−0.552778	+	0.833329i	$0.686432\pi$
$942$	1.65561e23	−	1.65561e23i	0.267025	−	0.267025i
$943$	2.22053e22	+	2.22053e22i	0.0355111	+	0.0355111i
$944$		−	9.21785e23i		−	1.46168i
$945$	−2.18457e23	+	2.37231e23i	−0.343488	+	0.373007i
$946$	1.93390e22			0.0301512
$947$	2.88497e23	−	2.88497e23i	0.446006	−	0.446006i	−0.448018	−	0.894024i	$-0.647870\pi$
$947$	2.88497e23	−	2.88497e23i	0.446006	−	0.446006i	0.894024	+	0.448018i	$0.147870\pi$
$948$	2.54276e23	+	2.54276e23i	0.389797	+	0.389797i
$949$		−	8.41143e23i		−	1.27862i
$950$	−2.76422e22	+	3.26159e22i	−0.0416662	+	0.0491632i
$951$	1.04479e24			1.56165
$952$	−2.15249e23	+	2.15249e23i	−0.319041	+	0.319041i
$953$	−1.23591e23	−	1.23591e23i	−0.181653	−	0.181653i	0.610423	−	0.792076i	$-0.291000\pi$
$953$	−1.23591e23	−	1.23591e23i	−0.181653	−	0.181653i	−0.792076	+	0.610423i	$0.791000\pi$
$954$		−	2.46847e23i		−	0.359783i
$955$	1.46550e23	+	1.34952e23i	0.211816	+	0.195053i
$956$	−4.76111e23			−0.682409
$957$	−3.27375e23	+	3.27375e23i	−0.465318	+	0.465318i
$958$	4.15620e22	+	4.15620e22i	0.0585831	+	0.0585831i
$959$		−	1.49490e23i		−	0.208960i
$960$	−8.32837e23	+	3.43126e22i	−1.15449	+	0.0475646i
$961$	1.66165e24			2.28430
$962$	5.25645e22	−	5.25645e22i	0.0716625	−	0.0716625i
$963$	1.79161e23	+	1.79161e23i	0.242233	+	0.242233i
$964$		−	5.04742e23i		−	0.676789i
$965$	3.56447e22	+	8.65171e23i	0.0473998	+	1.15049i
$966$	−7.41146e22			−0.0977432
$967$	3.27694e23	−	3.27694e23i	0.428605	−	0.428605i	−0.459548	−	0.888153i	$-0.651989\pi$
$967$	3.27694e23	−	3.27694e23i	0.428605	−	0.428605i	0.888153	+	0.459548i	$0.151989\pi$
$968$	−1.99782e23	−	1.99782e23i	−0.259151	−	0.259151i
$969$			5.13426e23i			0.660523i
$970$	9.72692e22	−	1.05629e23i	0.124109	−	0.134774i
$971$	−1.26366e24			−1.59910			−0.799549	−	0.600601i	$-0.794928\pi$
$971$	−1.26366e24			−1.59910			−0.799549	+	0.600601i	$0.794928\pi$
$972$	−6.93285e23	+	6.93285e23i	−0.870125	+	0.870125i
$973$	2.79444e23	+	2.79444e23i	0.347850	+	0.347850i
$974$			1.89300e23i			0.233710i
$975$	−1.98160e24	+	1.63560e23i	−2.42649	+	0.200281i
$976$	3.32961e23			0.404384
$977$	8.87844e23	−	8.87844e23i	1.06950	−	1.06950i	0.0721009	−	0.997397i	$-0.477030\pi$
$977$	8.87844e23	−	8.87844e23i	1.06950	−	1.06950i	0.997397	−	0.0721009i	$-0.0229704\pi$
$978$	1.55919e23	+	1.55919e23i	0.186290	+	0.186290i
$979$		−	2.74894e22i		−	0.0325764i
$980$	2.25984e23	+	2.08100e23i	0.265625	+	0.244604i
$981$	1.16233e24			1.35512
$982$	4.87293e22	−	4.87293e22i	0.0563506	−	0.0563506i
$983$	1.11074e24	+	1.11074e24i	1.27405	+	1.27405i	0.943944	+	0.330104i	$0.107084\pi$
$983$	1.11074e24	+	1.11074e24i	1.27405	+	1.27405i	0.330104	+	0.943944i	$0.392916\pi$
$984$			7.45520e22i			0.0848200i
$985$	6.28411e23	−	2.58903e22i	0.709176	−	0.0292178i
$986$	−3.33702e23			−0.373545
$987$	1.45246e23	−	1.45246e23i	0.161275	−	0.161275i
$988$	−2.94275e23	−	2.94275e23i	−0.324114	−	0.324114i
$989$		−	1.49695e23i		−	0.163545i
$990$	3.75026e21	+	9.10265e22i	0.00406424	+	0.0986476i
$991$	−1.32847e24			−1.42811			−0.714057	−	0.700088i	$-0.753144\pi$
$991$	−1.32847e24			−1.42811			−0.714057	+	0.700088i	$0.753144\pi$
$992$	−7.14730e23	+	7.14730e23i	−0.762164	+	0.762164i
$993$	−1.24945e24	−	1.24945e24i	−1.32167	−	1.32167i
$994$			9.10966e22i			0.0955897i
$995$	2.67579e23	−	2.90575e23i	0.278527	−	0.302464i
$996$	−2.09406e23			−0.216229
$997$	−1.25033e24	+	1.25033e24i	−1.28075	+	1.28075i	−0.340501	+	0.940244i	$0.610597\pi$
$997$	−1.25033e24	+	1.25033e24i	−1.28075	+	1.28075i	−0.940244	+	0.340501i	$0.889403\pi$
$998$	4.05679e22	+	4.05679e22i	0.0412229	+	0.0412229i
$999$			1.95867e23i			0.197441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.17.c.a.3.4	yes	14
3.2	odd	2		45.17.g.a.28.4		14
4.3	odd	2		80.17.p.c.33.1		14
5.2	odd	4	inner	5.17.c.a.2.4	✓	14
5.3	odd	4		25.17.c.b.7.4		14
5.4	even	2		25.17.c.b.18.4		14
15.2	even	4		45.17.g.a.37.4		14
20.7	even	4		80.17.p.c.17.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.17.c.a.2.4	✓	14	5.2	odd	4	inner
5.17.c.a.3.4	yes	14	1.1	even	1	trivial
25.17.c.b.7.4		14	5.3	odd	4
25.17.c.b.18.4		14	5.4	even	2
45.17.g.a.28.4		14	3.2	odd	2
45.17.g.a.37.4		14	15.2	even	4
80.17.p.c.17.1		14	20.7	even	4
80.17.p.c.33.1		14	4.3	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(38.1160 - 38.1160i) q^{2} +(7207.82 + 7207.82i) q^{3} +62630.3i q^{4} +(-287350. - 264609. i) q^{5} +549467. q^{6} +(-3.21528e6 + 3.21528e6i) q^{7} +(4.88519e6 + 4.88519e6i) q^{8} +6.08585e7i q^{9} +O(q^{10})\)	\(q+(38.1160 - 38.1160i) q^{2} +(7207.82 + 7207.82i) q^{3} +62630.3i q^{4} +(-287350. - 264609. i) q^{5} +549467. q^{6} +(-3.21528e6 + 3.21528e6i) q^{7} +(4.88519e6 + 4.88519e6i) q^{8} +6.08585e7i q^{9} +(-2.10385e7 + 866777. i) q^{10} -7.10939e7 q^{11} +(-4.51428e8 + 4.51428e8i) q^{12} +(9.03933e8 + 9.03933e8i) q^{13} +2.45107e8i q^{14} +(-1.63909e8 - 3.97842e9i) q^{15} -3.73213e9 q^{16} +(6.85191e9 - 6.85191e9i) q^{17} +(2.31968e9 + 2.31968e9i) q^{18} +5.19796e9i q^{19} +(1.65726e10 - 1.79968e10i) q^{20} -4.63503e10 q^{21} +(-2.70982e9 + 2.70982e9i) q^{22} +(2.09756e10 + 2.09756e10i) q^{23} +7.04231e10i q^{24} +(1.25518e10 + 1.52071e11i) q^{25} +6.89087e10 q^{26} +(-1.28384e11 + 1.28384e11i) q^{27} +(-2.01374e11 - 2.01374e11i) q^{28} -6.38865e11i q^{29} +(-1.57889e11 - 1.45394e11i) q^{30} +1.54566e12 q^{31} +(-4.62410e11 + 4.62410e11i) q^{32} +(-5.12432e11 - 5.12432e11i) q^{33} -5.22335e11i q^{34} +(1.77470e12 - 7.31171e10i) q^{35} -3.81159e12 q^{36} +(7.62814e11 - 7.62814e11i) q^{37} +(1.98125e11 + 1.98125e11i) q^{38} +1.30308e13i q^{39} +(-1.11092e11 - 2.69642e12i) q^{40} +1.05863e12 q^{41} +(-1.76669e12 + 1.76669e12i) q^{42} +(-3.56832e12 - 3.56832e12i) q^{43} -4.45263e12i q^{44} +(1.61037e13 - 1.74877e13i) q^{45} +1.59901e12 q^{46} +(-3.13366e12 + 3.13366e12i) q^{47} +(-2.69005e13 - 2.69005e13i) q^{48} +1.25569e13i q^{49} +(6.27476e12 + 5.31791e12i) q^{50} +9.87746e13 q^{51} +(-5.66137e13 + 5.66137e13i) q^{52} +(-5.32069e13 - 5.32069e13i) q^{53} +9.78700e12i q^{54} +(2.04288e13 + 1.88121e13i) q^{55} -3.14145e13 q^{56} +(-3.74659e13 + 3.74659e13i) q^{57} +(-2.43510e13 - 2.43510e13i) q^{58} +2.46986e14i q^{59} +(2.49170e14 - 1.02657e13i) q^{60} -8.92145e13 q^{61} +(5.89145e13 - 5.89145e13i) q^{62} +(-1.95677e14 - 1.95677e14i) q^{63} -2.09339e14i q^{64} +(-2.05559e13 - 4.98934e14i) q^{65} -3.90637e13 q^{66} +(-1.19814e13 + 1.19814e13i) q^{67} +(4.29138e14 + 4.29138e14i) q^{68} +3.02376e14i q^{69} +(6.48576e13 - 7.04315e13i) q^{70} +3.71660e14 q^{71} +(-2.97306e14 + 2.97306e14i) q^{72} +(-4.65269e14 - 4.65269e14i) q^{73} -5.81509e13i q^{74} +(-1.00563e15 + 1.18657e15i) q^{75} -3.25550e14 q^{76} +(2.28587e14 - 2.28587e14i) q^{77} +(4.96681e14 + 4.96681e14i) q^{78} -5.63270e14i q^{79} +(1.07243e15 + 9.87557e14i) q^{80} +7.69019e14 q^{81} +(4.03507e13 - 4.03507e13i) q^{82} +(2.31937e14 + 2.31937e14i) q^{83} -2.90293e15i q^{84} +(-3.78197e15 + 1.55816e14i) q^{85} -2.72020e14 q^{86} +(4.60482e15 - 4.60482e15i) q^{87} +(-3.47307e14 - 3.47307e14i) q^{88} +3.86663e14i q^{89} +(-5.27508e13 - 1.28037e15i) q^{90} -5.81280e15 q^{91} +(-1.31371e15 + 1.31371e15i) q^{92} +(1.11409e16 + 1.11409e16i) q^{93} +2.38885e14i q^{94} +(1.37543e15 - 1.49363e15i) q^{95} -6.66593e15 q^{96} +(-4.82207e15 + 4.82207e15i) q^{97} +(4.78618e14 + 4.78618e14i) q^{98} -4.32667e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8} + 398727830 q^{10} - 539141632 q^{11} + 1973309928 q^{12} - 681358582 q^{13} + 3514452060 q^{15} - 22953579016 q^{16} + 13124182498 q^{17} - 11293583022 q^{18} - 20186820060 q^{20} + 133652286048 q^{21} - 244784660624 q^{22} + 236373052228 q^{23} + 13144083650 q^{25} + 223473840788 q^{26} + 608106053880 q^{27} - 1494176423768 q^{28} + 2252131613760 q^{30} - 1105223074952 q^{31} - 2024535639992 q^{32} - 6385551058704 q^{33} + 6956678093980 q^{35} + 12514339524924 q^{36} - 9027827087002 q^{37} - 7824802789560 q^{38} + 31912538913900 q^{40} + 39543901484288 q^{41} - 70814500818384 q^{42} - 63017457929452 q^{43} + 126481294123110 q^{45} + 44357914058008 q^{46} - 2826187575452 q^{47} - 405160526368272 q^{48} + 461109216233650 q^{50} + 208649050954008 q^{51} - 389623094881012 q^{52} - 275142037498442 q^{53} + 330504874256560 q^{55} + 865011118900080 q^{56} - 644237427525840 q^{57} - 991296507673440 q^{58} + 16\!\cdots\!80 q^{60}+ \cdots + 48\!\cdots\!02 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8 + 398727830 * q^10 - 539141632 * q^11 + 1973309928 * q^12 - 681358582 * q^13 + 3514452060 * q^15 - 22953579016 * q^16 + 13124182498 * q^17 - 11293583022 * q^18 - 20186820060 * q^20 + 133652286048 * q^21 - 244784660624 * q^22 + 236373052228 * q^23 + 13144083650 * q^25 + 223473840788 * q^26 + 608106053880 * q^27 - 1494176423768 * q^28 + 2252131613760 * q^30 - 1105223074952 * q^31 - 2024535639992 * q^32 - 6385551058704 * q^33 + 6956678093980 * q^35 + 12514339524924 * q^36 - 9027827087002 * q^37 - 7824802789560 * q^38 + 31912538913900 * q^40 + 39543901484288 * q^41 - 70814500818384 * q^42 - 63017457929452 * q^43 + 126481294123110 * q^45 + 44357914058008 * q^46 - 2826187575452 * q^47 - 405160526368272 * q^48 + 461109216233650 * q^50 + 208649050954008 * q^51 - 389623094881012 * q^52 - 275142037498442 * q^53 + 330504874256560 * q^55 + 865011118900080 * q^56 - 644237427525840 * q^57 - 991296507673440 * q^58 + 1631207111049480 * q^60 + 683634528395968 * q^61 - 938995013191864 * q^62 - 1361911146729372 * q^63 + 517066464980110 * q^65 - 196778043917184 * q^66 - 181547742064252 * q^67 - 917821658187868 * q^68 + 1066699466039880 * q^70 - 1337544011098792 * q^71 + 2573199832214340 * q^72 + 778038215296478 * q^73 - 1442550824447700 * q^75 - 233750796900240 * q^76 + 1099376123524976 * q^77 + 8472064951325256 * q^78 - 14934736099860320 * q^80 + 809940307363794 * q^81 - 303814693723184 * q^82 + 13357181209550188 * q^83 - 16045734952112470 * q^85 - 20034048539985352 * q^86 + 17327533268211840 * q^87 + 22952328705949920 * q^88 - 21878453293909290 * q^90 - 24534035720748632 * q^91 + 40652972845631848 * q^92 + 15958372062212256 * q^93 - 22489885958711400 * q^95 - 27488119051061472 * q^96 - 3303551663290402 * q^97 + 48233459501789102 * q^98

Introduction

L-functions

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