LMFDB - Embedded newform 170.2.k.b.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(111,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("170.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.k (of order $8$, degree $4$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 $ x^16 + 28x^14 + 286x^12 + 1412x^10 + 3709x^8 + 5264x^6 + 3780x^4 + 1072*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			121.4
Root			$-1.09612i$ of defining polynomial
Character	$\chi$	$=$	170.121
Dual form			170.2.k.b.111.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.93656 - 0.802151i) q^{3} +1.00000i q^{4} +(-0.382683 - 0.923880i) q^{5} +(1.93656 + 0.802151i) q^{6} +(-0.434936 + 1.05003i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.985516 - 0.985516i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.93656 - 0.802151i) q^{3} +1.00000i q^{4} +(-0.382683 - 0.923880i) q^{5} +(1.93656 + 0.802151i) q^{6} +(-0.434936 + 1.05003i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.985516 - 0.985516i) q^{9} +(0.382683 - 0.923880i) q^{10} +(-0.233094 - 0.0965508i) q^{11} +(0.802151 + 1.93656i) q^{12} -3.10869i q^{13} +(-1.05003 + 0.434936i) q^{14} +(-1.48218 - 1.48218i) q^{15} -1.00000 q^{16} +(-3.02187 + 2.80505i) q^{17} +1.39373 q^{18} +(-0.972524 - 0.972524i) q^{19} +(0.923880 - 0.382683i) q^{20} +2.38233i q^{21} +(-0.0965508 - 0.233094i) q^{22} +(-0.694615 - 0.287719i) q^{23} +(-0.802151 + 1.93656i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(2.19817 - 2.19817i) q^{26} +(-1.28847 + 3.11065i) q^{27} +(-1.05003 - 0.434936i) q^{28} +(-0.432553 - 1.04428i) q^{29} -2.09612i q^{30} +(-0.863307 + 0.357593i) q^{31} +(-0.707107 - 0.707107i) q^{32} -0.528851 q^{33} +(-4.12025 - 0.153319i) q^{34} +1.13654 q^{35} +(0.985516 + 0.985516i) q^{36} +(4.54149 - 1.88115i) q^{37} -1.37536i q^{38} +(-2.49364 - 6.02017i) q^{39} +(0.923880 + 0.382683i) q^{40} +(-3.67824 + 8.88006i) q^{41} +(-1.68456 + 1.68456i) q^{42} +(5.13048 - 5.13048i) q^{43} +(0.0965508 - 0.233094i) q^{44} +(-1.28764 - 0.533357i) q^{45} +(-0.287719 - 0.694615i) q^{46} -9.71535i q^{47} +(-1.93656 + 0.802151i) q^{48} +(4.03636 + 4.03636i) q^{49} -1.00000 q^{50} +(-3.60198 + 7.85615i) q^{51} +3.10869 q^{52} +(-9.25847 - 9.25847i) q^{53} +(-3.11065 + 1.28847i) q^{54} +0.252299i q^{55} +(-0.434936 - 1.05003i) q^{56} +(-2.66347 - 1.10324i) q^{57} +(0.432553 - 1.04428i) q^{58} +(1.67839 - 1.67839i) q^{59} +(1.48218 - 1.48218i) q^{60} +(-2.81251 + 6.79001i) q^{61} +(-0.863307 - 0.357593i) q^{62} +(0.606184 + 1.46346i) q^{63} -1.00000i q^{64} +(-2.87205 + 1.18964i) q^{65} +(-0.373954 - 0.373954i) q^{66} +15.8174 q^{67} +(-2.80505 - 3.02187i) q^{68} -1.57596 q^{69} +(0.803658 + 0.803658i) q^{70} +(2.35153 - 0.974036i) q^{71} +1.39373i q^{72} +(-3.80933 - 9.19654i) q^{73} +(4.54149 + 1.88115i) q^{74} +(-0.802151 + 1.93656i) q^{75} +(0.972524 - 0.972524i) q^{76} +(0.202762 - 0.202762i) q^{77} +(2.49364 - 6.02017i) q^{78} +(12.9573 + 5.36708i) q^{79} +(0.382683 + 0.923880i) q^{80} +11.2387i q^{81} +(-8.88006 + 3.67824i) q^{82} +(11.0125 + 11.0125i) q^{83} -2.38233 q^{84} +(3.74795 + 1.71840i) q^{85} +7.25559 q^{86} +(-1.67534 - 1.67534i) q^{87} +(0.233094 - 0.0965508i) q^{88} +11.9252i q^{89} +(-0.533357 - 1.28764i) q^{90} +(3.26421 + 1.35208i) q^{91} +(0.287719 - 0.694615i) q^{92} +(-1.38501 + 1.38501i) q^{93} +(6.86979 - 6.86979i) q^{94} +(-0.526326 + 1.27066i) q^{95} +(-1.93656 - 0.802151i) q^{96} +(6.02292 + 14.5406i) q^{97} +5.70827i q^{98} +(-0.324871 + 0.134566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.93656	−	0.802151i	1.11808	−	0.463122i	0.254364	−	0.967108i	$-0.418134\pi$
$3$	1.93656	−	0.802151i	1.11808	−	0.463122i	0.863712	+	0.503986i	$0.168134\pi$
$4$			1.00000i			0.500000i
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$6$	1.93656	+	0.802151i	0.790599	+	0.327477i
$7$	−0.434936	+	1.05003i	−0.164390	+	0.396874i	−0.984512	−	0.175315i	$-0.943906\pi$
$7$	−0.434936	+	1.05003i	−0.164390	+	0.396874i	0.820122	+	0.572189i	$0.193906\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.985516	−	0.985516i	0.328505	−	0.328505i
$10$	0.382683	−	0.923880i	0.121015	−	0.292156i
$11$	−0.233094	−	0.0965508i	−0.0702806	−	0.0291112i	0.347266	−	0.937767i	$-0.387110\pi$
$11$	−0.233094	−	0.0965508i	−0.0702806	−	0.0291112i	−0.417547	+	0.908655i	$0.637110\pi$
$12$	0.802151	+	1.93656i	0.231561	+	0.559038i
$13$		−	3.10869i		−	0.862194i	−0.902305	−	0.431097i	$-0.858127\pi$
$13$		−	3.10869i		−	0.862194i	0.902305	−	0.431097i	$-0.141873\pi$
$14$	−1.05003	+	0.434936i	−0.280632	+	0.116242i
$15$	−1.48218	−	1.48218i	−0.382698	−	0.382698i
$16$	−1.00000			−0.250000
$17$	−3.02187	+	2.80505i	−0.732912	+	0.680324i
$17$	−3.02187	+	2.80505i	−0.732912	+	0.680324i
$18$	1.39373			0.328505
$19$	−0.972524	−	0.972524i	−0.223112	−	0.223112i	0.586695	−	0.809808i	$-0.300429\pi$
$19$	−0.972524	−	0.972524i	−0.223112	−	0.223112i	−0.809808	+	0.586695i	$0.800429\pi$
$20$	0.923880	−	0.382683i	0.206586	−	0.0855706i
$21$			2.38233i			0.519868i
$22$	−0.0965508	−	0.233094i	−0.0205847	−	0.0496959i
$23$	−0.694615	−	0.287719i	−0.144837	−	0.0599935i	0.309087	−	0.951034i	$-0.399976\pi$
$23$	−0.694615	−	0.287719i	−0.144837	−	0.0599935i	−0.453925	+	0.891040i	$0.649976\pi$
$24$	−0.802151	+	1.93656i	−0.163738	+	0.395300i
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$	2.19817	−	2.19817i	0.431097	−	0.431097i
$27$	−1.28847	+	3.11065i	−0.247966	+	0.598644i
$28$	−1.05003	−	0.434936i	−0.198437	−	0.0821952i
$29$	−0.432553	−	1.04428i	−0.0803231	−	0.193917i	0.878616	−	0.477529i	$-0.158467\pi$
$29$	−0.432553	−	1.04428i	−0.0803231	−	0.193917i	−0.958939	+	0.283612i	$0.908467\pi$
$30$		−	2.09612i		−	0.382698i
$31$	−0.863307	+	0.357593i	−0.155054	+	0.0642257i	−0.458861	−	0.888508i	$-0.651742\pi$
$31$	−0.863307	+	0.357593i	−0.155054	+	0.0642257i	0.303806	+	0.952734i	$0.401742\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.528851			−0.0920611
$34$	−4.12025	−	0.153319i	−0.706618	−	0.0262940i
$35$	1.13654			0.192111
$36$	0.985516	+	0.985516i	0.164253	+	0.164253i
$37$	4.54149	−	1.88115i	0.746617	−	0.309259i	0.0232565	−	0.999730i	$-0.492597\pi$
$37$	4.54149	−	1.88115i	0.746617	−	0.309259i	0.723360	+	0.690471i	$0.242597\pi$
$38$		−	1.37536i		−	0.223112i
$39$	−2.49364	−	6.02017i	−0.399302	−	0.963999i
$40$	0.923880	+	0.382683i	0.146078	+	0.0605076i
$41$	−3.67824	+	8.88006i	−0.574445	+	1.38683i	0.323292	+	0.946299i	$0.395210\pi$
$41$	−3.67824	+	8.88006i	−0.574445	+	1.38683i	−0.897737	+	0.440533i	$0.854790\pi$
$42$	−1.68456	+	1.68456i	−0.259934	+	0.259934i
$43$	5.13048	−	5.13048i	0.782391	−	0.782391i	−0.197843	−	0.980234i	$-0.563394\pi$
$43$	5.13048	−	5.13048i	0.782391	−	0.782391i	0.980234	+	0.197843i	$0.0633936\pi$
$44$	0.0965508	−	0.233094i	0.0145556	−	0.0351403i
$45$	−1.28764	−	0.533357i	−0.191950	−	0.0795082i
$46$	−0.287719	−	0.694615i	−0.0424218	−	0.102415i
$47$		−	9.71535i		−	1.41713i	−0.705646	−	0.708565i	$-0.749343\pi$
$47$		−	9.71535i		−	1.41713i	0.705646	−	0.708565i	$-0.250657\pi$
$48$	−1.93656	+	0.802151i	−0.279519	+	0.115781i
$49$	4.03636	+	4.03636i	0.576622	+	0.576622i
$50$	−1.00000			−0.141421
$51$	−3.60198	+	7.85615i	−0.504378	+	1.10008i
$52$	3.10869			0.431097
$53$	−9.25847	−	9.25847i	−1.27175	−	1.27175i	−0.945170	−	0.326579i	$-0.894104\pi$
$53$	−9.25847	−	9.25847i	−1.27175	−	1.27175i	−0.326579	−	0.945170i	$-0.605896\pi$
$54$	−3.11065	+	1.28847i	−0.423305	+	0.175339i
$55$			0.252299i			0.0340201i
$56$	−0.434936	−	1.05003i	−0.0581208	−	0.140316i
$57$	−2.66347	−	1.10324i	−0.352785	−	0.146128i
$58$	0.432553	−	1.04428i	0.0567970	−	0.137120i
$59$	1.67839	−	1.67839i	0.218508	−	0.218508i	−0.589361	−	0.807870i	$-0.700621\pi$
$59$	1.67839	−	1.67839i	0.218508	−	0.218508i	0.807870	+	0.589361i	$0.200621\pi$
$60$	1.48218	−	1.48218i	0.191349	−	0.191349i
$61$	−2.81251	+	6.79001i	−0.360105	+	0.869371i	0.635178	+	0.772365i	$0.280927\pi$
$61$	−2.81251	+	6.79001i	−0.360105	+	0.869371i	−0.995284	+	0.0970059i	$0.969073\pi$
$62$	−0.863307	−	0.357593i	−0.109640	−	0.0454144i
$63$	0.606184	+	1.46346i	0.0763720	+	0.184378i
$64$		−	1.00000i		−	0.125000i
$65$	−2.87205	+	1.18964i	−0.356234	+	0.147557i
$66$	−0.373954	−	0.373954i	−0.0460305	−	0.0460305i
$67$	15.8174			1.93240			0.966201	−	0.257788i	$-0.0829936\pi$
$67$	15.8174			1.93240			0.966201	+	0.257788i	$0.0829936\pi$
$68$	−2.80505	−	3.02187i	−0.340162	−	0.366456i
$69$	−1.57596			−0.189723
$70$	0.803658	+	0.803658i	0.0960555	+	0.0960555i
$71$	2.35153	−	0.974036i	0.279075	−	0.115597i	−0.238756	−	0.971080i	$-0.576740\pi$
$71$	2.35153	−	0.974036i	0.279075	−	0.115597i	0.517831	+	0.855483i	$0.326740\pi$
$72$			1.39373i			0.164253i
$73$	−3.80933	−	9.19654i	−0.445849	−	1.07637i	−0.973863	−	0.227138i	$-0.927063\pi$
$73$	−3.80933	−	9.19654i	−0.445849	−	1.07637i	0.528014	−	0.849236i	$-0.322937\pi$
$74$	4.54149	+	1.88115i	0.527938	+	0.218679i
$75$	−0.802151	+	1.93656i	−0.0926245	+	0.223615i
$76$	0.972524	−	0.972524i	0.111556	−	0.111556i
$77$	0.202762	−	0.202762i	0.0231069	−	0.0231069i
$78$	2.49364	−	6.02017i	0.282349	−	0.681650i
$79$	12.9573	+	5.36708i	1.45781	+	0.603844i	0.964042	−	0.265751i	$-0.0856200\pi$
$79$	12.9573	+	5.36708i	1.45781	+	0.603844i	0.493766	+	0.869595i	$0.335620\pi$
$80$	0.382683	+	0.923880i	0.0427853	+	0.103293i
$81$			11.2387i			1.24875i
$82$	−8.88006	+	3.67824i	−0.980638	+	0.406194i
$83$	11.0125	+	11.0125i	1.20877	+	1.20877i	0.971424	+	0.237349i	$0.0762786\pi$
$83$	11.0125	+	11.0125i	1.20877	+	1.20877i	0.237349	+	0.971424i	$0.423721\pi$
$84$	−2.38233			−0.259934
$85$	3.74795	+	1.71840i	0.406522	+	0.186387i
$86$	7.25559			0.782391
$87$	−1.67534	−	1.67534i	−0.179615	−	0.179615i
$88$	0.233094	−	0.0965508i	0.0248479	−	0.0102924i
$89$			11.9252i			1.26407i	0.774941	+	0.632034i	$0.217780\pi$
$89$			11.9252i			1.26407i	−0.774941	+	0.632034i	$0.782220\pi$
$90$	−0.533357	−	1.28764i	−0.0562208	−	0.135729i
$91$	3.26421	+	1.35208i	0.342182	+	0.141737i
$92$	0.287719	−	0.694615i	0.0299968	−	0.0724186i
$93$	−1.38501	+	1.38501i	−0.143618	+	0.143618i
$94$	6.86979	−	6.86979i	0.708565	−	0.708565i
$95$	−0.526326	+	1.27066i	−0.0539999	+	0.130367i
$96$	−1.93656	−	0.802151i	−0.197650	−	0.0818692i
$97$	6.02292	+	14.5406i	0.611535	+	1.47638i	0.861314	+	0.508073i	$0.169642\pi$
$97$	6.02292	+	14.5406i	0.611535	+	1.47638i	−0.249780	+	0.968303i	$0.580358\pi$
$98$			5.70827i			0.576622i
$99$	−0.324871	+	0.134566i	−0.0326507	+	0.0135244i
$100$	−0.707107	−	0.707107i	−0.0707107	−	0.0707107i
$101$	−1.90803			−0.189857			−0.0949283	−	0.995484i	$-0.530262\pi$
$101$	−1.90803			−0.189857			−0.0949283	+	0.995484i	$0.530262\pi$
$102$	−8.10212	+	3.00816i	−0.802230	+	0.297852i
$103$	1.64495			0.162082			0.0810408	−	0.996711i	$-0.474176\pi$
$103$	1.64495			0.162082			0.0810408	+	0.996711i	$0.474176\pi$
$104$	2.19817	+	2.19817i	0.215549	+	0.215549i
$105$	2.20099	−	0.911680i	0.214795	−	0.0889709i
$106$		−	13.0935i		−	1.27175i
$107$	−4.48481	−	10.8273i	−0.433563	−	1.04671i	−0.978130	−	0.207996i	$-0.933306\pi$
$107$	−4.48481	−	10.8273i	−0.433563	−	1.04671i	0.544566	−	0.838718i	$-0.316694\pi$
$108$	−3.11065	−	1.28847i	−0.299322	−	0.123983i
$109$	0.796977	−	1.92407i	0.0763366	−	0.184293i	−0.881104	−	0.472922i	$-0.843199\pi$
$109$	0.796977	−	1.92407i	0.0763366	−	0.184293i	0.957441	+	0.288629i	$0.0931994\pi$
$110$	−0.178403	+	0.178403i	−0.0170100	+	0.0170100i
$111$	7.28593	−	7.28593i	0.691550	−	0.691550i
$112$	0.434936	−	1.05003i	0.0410976	−	0.0992184i
$113$	−8.16143	−	3.38057i	−0.767763	−	0.318018i	−0.0357968	−	0.999359i	$-0.511397\pi$
$113$	−8.16143	−	3.38057i	−0.767763	−	0.318018i	−0.731966	+	0.681341i	$0.761397\pi$
$114$	−1.10324	−	2.66347i	−0.103328	−	0.249457i
$115$			0.751846i			0.0701100i
$116$	1.04428	−	0.432553i	0.0969586	−	0.0401616i
$117$	−3.06366	−	3.06366i	−0.283235	−	0.283235i
$118$	2.37361			0.218508
$119$	−1.63106	−	4.39307i	−0.149519	−	0.402712i
$120$	2.09612			0.191349
$121$	−7.73316	−	7.73316i	−0.703015	−	0.703015i
$122$	−6.79001	+	2.81251i	−0.614738	+	0.254633i
$123$			20.1473i			1.81662i
$124$	−0.357593	−	0.863307i	−0.0321128	−	0.0775272i
$125$	0.923880	+	0.382683i	0.0826343	+	0.0342282i
$126$	−0.606184	+	1.46346i	−0.0540032	+	0.130375i
$127$	7.38362	−	7.38362i	0.655191	−	0.655191i	−0.299048	−	0.954238i	$-0.596669\pi$
$127$	7.38362	−	7.38362i	0.655191	−	0.655191i	0.954238	+	0.299048i	$0.0966689\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	5.82008	−	14.0509i	0.512430	−	1.23712i
$130$	−2.87205	−	1.18964i	−0.251896	−	0.104339i
$131$	−3.71255	−	8.96288i	−0.324367	−	0.783090i	−0.998990	−	0.0449283i	$-0.985694\pi$
$131$	−3.71255	−	8.96288i	−0.324367	−	0.783090i	0.674624	−	0.738162i	$-0.264306\pi$
$132$		−	0.528851i		−	0.0460305i
$133$	1.44417	−	0.598193i	0.125225	−	0.0518699i
$134$	11.1846	+	11.1846i	0.966201	+	0.966201i
$135$	3.36694			0.289780
$136$	0.153319	−	4.12025i	0.0131470	−	0.353309i
$137$	−4.55218			−0.388919			−0.194460	−	0.980911i	$-0.562295\pi$
$137$	−4.55218			−0.388919			−0.194460	+	0.980911i	$0.562295\pi$
$138$	−1.11437	−	1.11437i	−0.0948617	−	0.0948617i
$139$	−11.5541	+	4.78586i	−0.980004	+	0.405931i	−0.814427	−	0.580266i	$-0.802949\pi$
$139$	−11.5541	+	4.78586i	−0.980004	+	0.405931i	−0.165577	+	0.986197i	$0.552949\pi$
$140$			1.13654i			0.0960555i
$141$	−7.79318	−	18.8144i	−0.656304	−	1.58446i
$142$	2.35153	+	0.974036i	0.197336	+	0.0817393i
$143$	−0.300146	+	0.724617i	−0.0250995	+	0.0605955i
$144$	−0.985516	+	0.985516i	−0.0821263	+	0.0821263i
$145$	−0.799254	+	0.799254i	−0.0663745	+	0.0663745i
$146$	3.80933	−	9.19654i	0.315263	−	0.761111i
$147$	11.0544	+	4.57890i	0.911754	+	0.377661i
$148$	1.88115	+	4.54149i	0.154629	+	0.373308i
$149$			22.2607i			1.82367i	0.410556	+	0.911835i	$0.365334\pi$
$149$			22.2607i			1.82367i	−0.410556	+	0.911835i	$0.634666\pi$
$150$	−1.93656	+	0.802151i	−0.158120	+	0.0654954i
$151$	−7.13341	−	7.13341i	−0.580509	−	0.580509i	0.354534	−	0.935043i	$-0.384639\pi$
$151$	−7.13341	−	7.13341i	−0.580509	−	0.580509i	−0.935043	+	0.354534i	$0.884639\pi$
$152$	1.37536			0.111556
$153$	−0.213685	+	5.74252i	−0.0172754	+	0.464255i
$154$	0.286749			0.0231069
$155$	0.660746	+	0.660746i	0.0530724	+	0.0530724i
$156$	6.02017	−	2.49364i	0.482000	−	0.199651i
$157$		−	16.5315i		−	1.31936i	−0.751549	−	0.659678i	$-0.770693\pi$
$157$		−	16.5315i		−	1.31936i	0.751549	−	0.659678i	$-0.229307\pi$
$158$	5.36708	+	12.9573i	0.426982	+	1.03083i
$159$	−25.3563	−	10.5029i	−2.01089	−	0.832937i
$160$	−0.382683	+	0.923880i	−0.0302538	+	0.0730391i
$161$	0.604226	−	0.604226i	0.0476197	−	0.0476197i
$162$	−7.94697	+	7.94697i	−0.624373	+	0.624373i
$163$	0.715103	−	1.72641i	0.0560112	−	0.135223i	−0.893397	−	0.449269i	$-0.851685\pi$
$163$	0.715103	−	1.72641i	0.0560112	−	0.135223i	0.949408	+	0.314046i	$0.101685\pi$
$164$	−8.88006	−	3.67824i	−0.693416	−	0.287222i
$165$	0.202382	+	0.488594i	0.0157554	+	0.0380370i
$166$			15.5740i			1.20877i
$167$	−21.9273	+	9.08260i	−1.69679	+	0.702833i	−0.999897	−	0.0143440i	$-0.995434\pi$
$167$	−21.9273	+	9.08260i	−1.69679	+	0.702833i	−0.696891	+	0.717177i	$0.745434\pi$
$168$	−1.68456	−	1.68456i	−0.129967	−	0.129967i
$169$	3.33607			0.256621
$170$	1.43510	+	3.86529i	0.110068	+	0.296454i
$171$	−1.91688			−0.146587
$172$	5.13048	+	5.13048i	0.391195	+	0.391195i
$173$	−3.84503	+	1.59266i	−0.292332	+	0.121088i	−0.524030	−	0.851700i	$-0.675572\pi$
$173$	−3.84503	+	1.59266i	−0.292332	+	0.121088i	0.231698	+	0.972788i	$0.425572\pi$
$174$		−	2.36928i		−	0.179615i
$175$	−0.434936	−	1.05003i	−0.0328781	−	0.0793748i
$176$	0.233094	+	0.0965508i	0.0175701	+	0.00727779i
$177$	1.90399	−	4.59664i	0.143113	−	0.345505i
$178$	−8.43238	+	8.43238i	−0.632034	+	0.632034i
$179$	9.42514	−	9.42514i	0.704468	−	0.704468i	−0.260898	−	0.965366i	$-0.584019\pi$
$179$	9.42514	−	9.42514i	0.704468	−	0.704468i	0.965366	+	0.260898i	$0.0840186\pi$
$180$	0.533357	−	1.28764i	0.0397541	−	0.0959749i
$181$	−7.74313	−	3.20731i	−0.575543	−	0.238398i	0.0758745	−	0.997117i	$-0.475825\pi$
$181$	−7.74313	−	3.20731i	−0.575543	−	0.238398i	−0.651417	+	0.758720i	$0.725825\pi$
$182$	1.35208	+	3.26421i	0.100223	+	0.241959i
$183$			15.4054i			1.13880i
$184$	0.694615	−	0.287719i	0.0512077	−	0.0212109i
$185$	−3.47591	−	3.47591i	−0.255554	−	0.255554i
$186$	−1.95869			−0.143618
$187$	0.975211	−	0.362076i	0.0713145	−	0.0264776i
$188$	9.71535			0.708565
$189$	−2.70587	−	2.70587i	−0.196823	−	0.196823i
$190$	−1.27066	+	0.526326i	−0.0921837	+	0.0381837i
$191$		−	8.37154i		−	0.605743i	−0.953031	−	0.302872i	$-0.902055\pi$
$191$		−	8.37154i		−	0.605743i	0.953031	−	0.302872i	$-0.0979453\pi$
$192$	−0.802151	−	1.93656i	−0.0578903	−	0.139760i
$193$	−7.26832	−	3.01064i	−0.523185	−	0.216710i	0.105430	−	0.994427i	$-0.466378\pi$
$193$	−7.26832	−	3.01064i	−0.523185	−	0.216710i	−0.628615	+	0.777716i	$0.716378\pi$
$194$	−6.02292	+	14.5406i	−0.432420	+	1.04395i
$195$	−4.60764	+	4.60764i	−0.329960	+	0.329960i
$196$	−4.03636	+	4.03636i	−0.288311	+	0.288311i
$197$	−0.174372	+	0.420971i	−0.0124235	+	0.0299929i	−0.929970	−	0.367637i	$-0.880167\pi$
$197$	−0.174372	+	0.420971i	−0.0124235	+	0.0299929i	0.917546	+	0.397629i	$0.130167\pi$
$198$	−0.324871	−	0.134566i	−0.0230875	−	0.00956318i
$199$	−3.51474	−	8.48532i	−0.249153	−	0.601509i	0.748980	−	0.662593i	$-0.230544\pi$
$199$	−3.51474	−	8.48532i	−0.249153	−	0.601509i	−0.998133	+	0.0610845i	$0.980544\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	30.6314	−	12.6879i	2.16057	−	0.894939i
$202$	−1.34918	−	1.34918i	−0.0949283	−	0.0949283i
$203$	1.28465			0.0901650
$204$	−7.85615	−	3.60198i	−0.550041	−	0.252189i
$205$	9.61170			0.671311
$206$	1.16315	+	1.16315i	0.0810408	+	0.0810408i
$207$	−0.968106	+	0.401002i	−0.0672880	+	0.0278716i
$208$			3.10869i			0.215549i
$209$	0.132792	+	0.320588i	0.00918541	+	0.0221755i
$210$	2.20099	+	0.911680i	0.151883	+	0.0629119i
$211$	−2.91050	+	7.02656i	−0.200367	+	0.483728i	−0.991842	−	0.127473i	$-0.959313\pi$
$211$	−2.91050	+	7.02656i	−0.200367	+	0.483728i	0.791475	+	0.611201i	$0.209313\pi$
$212$	9.25847	−	9.25847i	0.635875	−	0.635875i
$213$	3.77257	−	3.77257i	0.258492	−	0.258492i
$214$	4.48481	−	10.8273i	0.306575	−	0.740139i
$215$	−6.70329	−	2.77660i	−0.457161	−	0.189362i
$216$	−1.28847	−	3.11065i	−0.0876694	−	0.211653i
$217$		−	1.06203i		−	0.0720951i
$218$	1.92407	−	0.796977i	0.130315	−	0.0539781i
$219$	−14.7540	−	14.7540i	−0.996986	−	0.996986i
$220$	−0.252299			−0.0170100
$221$	8.72001	+	9.39405i	0.586571	+	0.631912i
$222$	10.3039			0.691550
$223$	1.91171	+	1.91171i	0.128017	+	0.128017i	0.768212	−	0.640195i	$-0.221146\pi$
$223$	1.91171	+	1.91171i	0.128017	+	0.128017i	−0.640195	+	0.768212i	$0.721146\pi$
$224$	1.05003	−	0.434936i	0.0701580	−	0.0290604i
$225$			1.39373i			0.0929153i
$226$	−3.38057	−	8.16143i	−0.224872	−	0.542890i
$227$	−8.71853	−	3.61134i	−0.578669	−	0.239693i	0.0740982	−	0.997251i	$-0.476392\pi$
$227$	−8.71853	−	3.61134i	−0.578669	−	0.239693i	−0.652768	+	0.757558i	$0.726392\pi$
$228$	1.10324	−	2.66347i	0.0730642	−	0.176392i
$229$	−6.37289	+	6.37289i	−0.421133	+	0.421133i	−0.885594	−	0.464461i	$-0.846248\pi$
$229$	−6.37289	+	6.37289i	−0.421133	+	0.421133i	0.464461	+	0.885594i	$0.346248\pi$
$230$	−0.531635	+	0.531635i	−0.0350550	+	0.0350550i
$231$	0.230016	−	0.555309i	0.0151340	−	0.0365366i
$232$	1.04428	+	0.432553i	0.0685601	+	0.0283985i
$233$	5.08986	+	12.2880i	0.333448	+	0.805015i	0.998314	+	0.0580517i	$0.0184888\pi$
$233$	5.08986	+	12.2880i	0.333448	+	0.805015i	−0.664866	+	0.746963i	$0.731511\pi$
$234$		−	4.33267i		−	0.283235i
$235$	−8.97582	+	3.71790i	−0.585518	+	0.242529i
$236$	1.67839	+	1.67839i	0.109254	+	0.109254i
$237$	29.3978			1.90959
$238$	1.95304	−	4.25970i	0.126597	−	0.276116i
$239$	−2.66720			−0.172527			−0.0862633	−	0.996272i	$-0.527493\pi$
$239$	−2.66720			−0.172527			−0.0862633	+	0.996272i	$0.527493\pi$
$240$	1.48218	+	1.48218i	0.0956745	+	0.0956745i
$241$	−0.493333	+	0.204345i	−0.0317784	+	0.0131630i	−0.398516	−	0.917161i	$-0.630475\pi$
$241$	−0.493333	+	0.204345i	−0.0317784	+	0.0131630i	0.366738	+	0.930324i	$0.380475\pi$
$242$		−	10.9363i		−	0.703015i
$243$	5.14973	+	12.4325i	0.330355	+	0.797548i
$244$	−6.79001	−	2.81251i	−0.434686	−	0.180053i
$245$	2.18446	−	5.27375i	0.139560	−	0.336928i
$246$	−14.2463	+	14.2463i	−0.908311	+	0.908311i
$247$	−3.02327	+	3.02327i	−0.192366	+	0.192366i
$248$	0.357593	−	0.863307i	0.0227072	−	0.0548200i
$249$	30.1600	+	12.4927i	1.91131	+	0.791691i
$250$	0.382683	+	0.923880i	0.0242030	+	0.0584313i
$251$			13.3789i			0.844468i	0.906487	+	0.422234i	$0.138754\pi$
$251$			13.3789i			0.844468i	−0.906487	+	0.422234i	$0.861246\pi$
$252$	−1.46346	+	0.606184i	−0.0921892	+	0.0381860i
$253$	0.134131	+	0.134131i	0.00843276	+	0.00843276i
$254$	10.4420			0.655191
$255$	8.63656	+	0.321375i	0.540842	+	0.0201253i
$256$	1.00000			0.0625000
$257$	−13.6909	−	13.6909i	−0.854013	−	0.854013i	0.136612	−	0.990625i	$-0.456379\pi$
$257$	−13.6909	−	13.6909i	−0.854013	−	0.854013i	−0.990625	+	0.136612i	$0.956379\pi$
$258$	14.0509	−	5.82008i	0.874773	−	0.362343i
$259$			5.58688i			0.347152i
$260$	−1.18964	−	2.87205i	−0.0737785	−	0.178117i
$261$	−1.45544	−	0.602863i	−0.0900894	−	0.0373163i
$262$	3.71255	−	8.96288i	0.229362	−	0.553728i
$263$	8.55368	−	8.55368i	0.527442	−	0.527442i	−0.392367	−	0.919809i	$-0.628344\pi$
$263$	8.55368	−	8.55368i	0.527442	−	0.527442i	0.919809	+	0.392367i	$0.128344\pi$
$264$	0.373954	−	0.373954i	0.0230153	−	0.0230153i
$265$	−5.01065	+	12.0968i	−0.307802	+	0.743099i
$266$	1.44417	+	0.598193i	0.0885474	+	0.0366776i
$267$	9.56581	+	23.0939i	0.585418	+	1.41332i
$268$			15.8174i			0.966201i
$269$	18.4733	−	7.65189i	1.12634	−	0.466544i	0.259802	−	0.965662i	$-0.416343\pi$
$269$	18.4733	−	7.65189i	1.12634	−	0.466544i	0.866534	+	0.499118i	$0.166343\pi$
$270$	2.38079	+	2.38079i	0.144890	+	0.144890i
$271$	−3.67946			−0.223511			−0.111756	−	0.993736i	$-0.535647\pi$
$271$	−3.67946			−0.223511			−0.111756	+	0.993736i	$0.535647\pi$
$272$	3.02187	−	2.80505i	0.183228	−	0.170081i
$273$	7.40593			0.448227
$274$	−3.21888	−	3.21888i	−0.194460	−	0.194460i
$275$	0.233094	−	0.0965508i	0.0140561	−	0.00582223i
$276$		−	1.57596i		−	0.0948617i
$277$	5.03180	+	12.1478i	0.302331	+	0.729892i	0.999910	+	0.0133845i	$0.00426055\pi$
$277$	5.03180	+	12.1478i	0.302331	+	0.729892i	−0.697579	+	0.716508i	$0.745739\pi$
$278$	−11.5541	−	4.78586i	−0.692967	−	0.287037i
$279$	−0.498389	+	1.20322i	−0.0298377	+	0.0720347i
$280$	−0.803658	+	0.803658i	−0.0480277	+	0.0480277i
$281$	6.24669	−	6.24669i	0.372646	−	0.372646i	−0.495794	−	0.868440i	$-0.665123\pi$
$281$	6.24669	−	6.24669i	0.372646	−	0.372646i	0.868440	+	0.495794i	$0.165123\pi$
$282$	7.79318	−	18.8144i	0.464077	−	1.12038i
$283$	5.15384	+	2.13479i	0.306364	+	0.126900i	0.530569	−	0.847642i	$-0.321978\pi$
$283$	5.15384	+	2.13479i	0.306364	+	0.126900i	−0.224205	+	0.974542i	$0.571978\pi$
$284$	0.974036	+	2.35153i	0.0577984	+	0.139538i
$285$			2.88292i			0.170769i
$286$	−0.724617	+	0.300146i	−0.0428475	+	0.0177480i
$287$	−7.72452	−	7.72452i	−0.455964	−	0.455964i
$288$	−1.39373			−0.0821263
$289$	1.26343	−	16.9530i	0.0743192	−	0.997235i
$290$	−1.13032			−0.0663745
$291$	23.3275	+	23.3275i	1.36748	+	1.36748i
$292$	9.19654	−	3.80933i	0.538187	−	0.222924i
$293$			23.5631i			1.37657i	0.725439	+	0.688286i	$0.241637\pi$
$293$			23.5631i			1.37657i	−0.725439	+	0.688286i	$0.758363\pi$
$294$	4.57890	+	11.0544i	0.267047	+	0.644708i
$295$	−2.19293	−	0.908340i	−0.127677	−	0.0528856i
$296$	−1.88115	+	4.54149i	−0.109339	+	0.263969i
$297$	0.600671	−	0.600671i	0.0348545	−	0.0348545i
$298$	−15.7407	+	15.7407i	−0.911835	+	0.911835i
$299$	−0.894428	+	2.15934i	−0.0517261	+	0.124878i
$300$	−1.93656	−	0.802151i	−0.111808	−	0.0463122i
$301$	3.15572	+	7.61859i	0.181893	+	0.439128i
$302$		−	10.0882i		−	0.580509i
$303$	−3.69503	+	1.53053i	−0.212274	+	0.0879268i
$304$	0.972524	+	0.972524i	0.0557781	+	0.0557781i
$305$	7.34945			0.420828
$306$	−4.21167	+	3.90948i	−0.240765	+	0.223490i
$307$	−13.7608			−0.785371			−0.392686	−	0.919673i	$-0.628454\pi$
$307$	−13.7608			−0.785371			−0.392686	+	0.919673i	$0.628454\pi$
$308$	0.202762	+	0.202762i	0.0115535	+	0.0115535i
$309$	3.18555	−	1.31950i	0.181220	−	0.0750636i
$310$			0.934437i			0.0530724i
$311$	−7.91601	−	19.1109i	−0.448876	−	1.08368i	−0.972744	−	0.231882i	$-0.925512\pi$
$311$	−7.91601	−	19.1109i	−0.448876	−	1.08368i	0.523868	−	0.851799i	$-0.324488\pi$
$312$	6.02017	+	2.49364i	0.340825	+	0.141174i
$313$	9.54896	−	23.0532i	0.539739	−	1.30305i	−0.385166	−	0.922847i	$-0.625856\pi$
$313$	9.54896	−	23.0532i	0.539739	−	1.30305i	0.924905	−	0.380198i	$-0.124144\pi$
$314$	11.6895	−	11.6895i	0.659678	−	0.659678i
$315$	1.12008	−	1.12008i	0.0631095	−	0.0631095i
$316$	−5.36708	+	12.9573i	−0.301922	+	0.728904i
$317$	−8.04517	−	3.33242i	−0.451862	−	0.187167i	0.145133	−	0.989412i	$-0.453639\pi$
$317$	−8.04517	−	3.33242i	−0.451862	−	0.187167i	−0.596995	+	0.802245i	$0.703639\pi$
$318$	−10.5029	−	25.3563i	−0.588975	−	1.42191i
$319$			0.285178i			0.0159669i
$320$	−0.923880	+	0.382683i	−0.0516464	+	0.0213927i
$321$	−17.3703	−	17.3703i	−0.969513	−	0.969513i
$322$	0.854505			0.0476197
$323$	5.66682	+	0.210868i	0.315310	+	0.0117330i
$324$	−11.2387			−0.624373
$325$	2.19817	+	2.19817i	0.121933	+	0.121933i
$326$	1.72641	−	0.715103i	0.0956171	−	0.0396059i
$327$		−	4.36539i		−	0.241407i
$328$	−3.67824	−	8.88006i	−0.203097	−	0.490319i
$329$	10.2014	+	4.22556i	0.562422	+	0.232963i
$330$	−0.202382	+	0.488594i	−0.0111408	+	0.0268962i
$331$	−14.5302	+	14.5302i	−0.798649	+	0.798649i	−0.982883	−	0.184233i	$-0.941020\pi$
$331$	−14.5302	+	14.5302i	−0.798649	+	0.798649i	0.184233	+	0.982883i	$0.441020\pi$
$332$	−11.0125	+	11.0125i	−0.604387	+	0.604387i
$333$	2.62181	−	6.32962i	0.143674	−	0.346861i
$334$	−21.9273	−	9.08260i	−1.19981	−	0.496978i
$335$	−6.05306	−	14.6134i	−0.330714	−	0.798414i
$336$		−	2.38233i		−	0.129967i
$337$	−28.2402	+	11.6975i	−1.53834	+	0.637202i	−0.981161	−	0.193191i	$-0.938116\pi$
$337$	−28.2402	+	11.6975i	−1.53834	+	0.637202i	−0.557179	+	0.830392i	$0.688116\pi$
$338$	2.35896	+	2.35896i	0.128310	+	0.128310i
$339$	−18.5169			−1.00570
$340$	−1.71840	+	3.74795i	−0.0931934	+	0.203261i
$341$	0.235758			0.0127670
$342$	−1.35544	−	1.35544i	−0.0732936	−	0.0732936i
$343$	−13.3441	+	5.52729i	−0.720511	+	0.298446i
$344$			7.25559i			0.391195i
$345$	0.603094	+	1.45600i	0.0324695	+	0.0783883i
$346$	−3.84503	−	1.59266i	−0.206710	−	0.0856221i
$347$	−6.49858	+	15.6890i	−0.348862	+	0.842228i	0.647893	+	0.761731i	$0.275650\pi$
$347$	−6.49858	+	15.6890i	−0.348862	+	0.842228i	−0.996755	+	0.0804961i	$0.974350\pi$
$348$	1.67534	−	1.67534i	0.0898074	−	0.0898074i
$349$	−15.8641	+	15.8641i	−0.849188	+	0.849188i	−0.990032	−	0.140844i	$-0.955018\pi$
$349$	−15.8641	+	15.8641i	−0.849188	+	0.849188i	0.140844	+	0.990032i	$0.455018\pi$
$350$	0.434936	−	1.05003i	0.0232483	−	0.0561264i
$351$	9.67002	+	4.00545i	0.516148	+	0.213795i
$352$	0.0965508	+	0.233094i	0.00514618	+	0.0124240i
$353$		−	22.5509i		−	1.20026i	−0.799902	−	0.600131i	$-0.795115\pi$
$353$		−	22.5509i		−	1.20026i	0.799902	−	0.600131i	$-0.204885\pi$
$354$	4.59664	−	1.90399i	0.244309	−	0.101196i
$355$	−1.79978	−	1.79978i	−0.0955226	−	0.0955226i
$356$	−11.9252			−0.632034
$357$	−6.68256	−	7.19911i	−0.353679	−	0.381017i
$358$	13.3292			0.704468
$359$	−7.45653	−	7.45653i	−0.393540	−	0.393540i	0.482407	−	0.875947i	$-0.339763\pi$
$359$	−7.45653	−	7.45653i	−0.393540	−	0.393540i	−0.875947	+	0.482407i	$0.839763\pi$
$360$	1.28764	−	0.533357i	0.0678645	−	0.0281104i
$361$		−	17.1084i		−	0.900442i
$362$	−3.20731	−	7.74313i	−0.168573	−	0.406970i
$363$	−21.1789	−	8.77260i	−1.11161	−	0.460442i
$364$	−1.35208	+	3.26421i	−0.0708683	+	0.171091i
$365$	−7.03873	+	7.03873i	−0.368424	+	0.368424i
$366$	−10.8932	+	10.8932i	−0.569398	+	0.569398i
$367$	−11.9104	+	28.7544i	−0.621720	+	1.50097i	0.227962	+	0.973670i	$0.426794\pi$
$367$	−11.9104	+	28.7544i	−0.621720	+	1.50097i	−0.849682	+	0.527296i	$0.823206\pi$
$368$	0.694615	+	0.287719i	0.0362093	+	0.0149984i
$369$	5.12647	+	12.3764i	0.266874	+	0.644290i
$370$		−	4.91568i		−	0.255554i
$371$	13.7485	−	5.69482i	0.713787	−	0.295660i
$372$	−1.38501	−	1.38501i	−0.0718092	−	0.0718092i
$373$	−21.7151			−1.12437			−0.562183	−	0.827013i	$-0.690038\pi$
$373$	−21.7151			−1.12437			−0.562183	+	0.827013i	$0.690038\pi$
$374$	0.945605	+	0.433552i	0.0488961	+	0.0224184i
$375$	2.09612			0.108243
$376$	6.86979	+	6.86979i	0.354282	+	0.354282i
$377$	−3.24633	+	1.34467i	−0.167194	+	0.0692542i
$378$		−	3.82667i		−	0.196823i
$379$	9.02028	+	21.7769i	0.463341	+	1.11860i	0.967017	+	0.254711i	$0.0819803\pi$
$379$	9.02028	+	21.7769i	0.463341	+	1.11860i	−0.503677	+	0.863892i	$0.668020\pi$
$380$	−1.27066	−	0.526326i	−0.0651837	−	0.0270000i
$381$	8.37608	−	20.2217i	0.429120	−	1.03599i
$382$	5.91957	−	5.91957i	0.302872	−	0.302872i
$383$	22.8956	−	22.8956i	1.16991	−	1.16991i	0.187683	−	0.982230i	$-0.439902\pi$
$383$	22.8956	−	22.8956i	1.16991	−	1.16991i	0.982230	−	0.187683i	$-0.0600976\pi$
$384$	0.802151	−	1.93656i	0.0409346	−	0.0988249i
$385$	−0.264922	−	0.109734i	−0.0135017	−	0.00559257i
$386$	−3.01064	−	7.26832i	−0.153237	−	0.369948i
$387$		−	10.1123i		−	0.514039i
$388$	−14.5406	+	6.02292i	−0.738188	+	0.305767i
$389$	5.57424	+	5.57424i	0.282625	+	0.282625i	0.834155	−	0.551530i	$-0.185956\pi$
$389$	5.57424	+	5.57424i	0.282625	+	0.282625i	−0.551530	+	0.834155i	$0.685956\pi$
$390$	−6.51619			−0.329960
$391$	2.90610	−	1.07898i	0.146968	−	0.0545662i
$392$	−5.70827			−0.288311
$393$	−14.3792	−	14.3792i	−0.725333	−	0.725333i
$394$	−0.420971	+	0.174372i	−0.0212082	+	0.00878472i
$395$		−	14.0249i		−	0.705667i
$396$	−0.134566	−	0.324871i	−0.00676219	−	0.0163254i
$397$	33.1614	+	13.7359i	1.66432	+	0.689386i	0.998395	−	0.0566296i	$-0.0180354\pi$
$397$	33.1614	+	13.7359i	1.66432	+	0.689386i	0.665929	+	0.746015i	$0.268035\pi$
$398$	3.51474	−	8.48532i	0.176178	−	0.425331i
$399$	2.31688	−	2.31688i	0.115989	−	0.115989i
$400$	0.707107	−	0.707107i	0.0353553	−	0.0353553i
$401$	−10.1715	+	24.5561i	−0.507940	+	1.22627i	0.437128	+	0.899399i	$0.355996\pi$
$401$	−10.1715	+	24.5561i	−0.507940	+	1.22627i	−0.945067	+	0.326875i	$0.894004\pi$
$402$	30.6314	+	12.6879i	1.52776	+	0.632817i
$403$	1.11165	+	2.68375i	0.0553750	+	0.133687i
$404$		−	1.90803i		−	0.0949283i
$405$	10.3832	−	4.30087i	0.515946	−	0.213712i
$406$	0.908387	+	0.908387i	0.0450825	+	0.0450825i
$407$	−1.24022			−0.0614756
$408$	−3.00816	−	8.10212i	−0.148926	−	0.401115i
$409$	10.6807			0.528128			0.264064	−	0.964505i	$-0.414937\pi$
$409$	10.6807			0.528128			0.264064	+	0.964505i	$0.414937\pi$
$410$	6.79650	+	6.79650i	0.335655	+	0.335655i
$411$	−8.81560	+	3.65154i	−0.434841	+	0.180117i
$412$			1.64495i			0.0810408i
$413$	1.03237	+	2.49236i	0.0507995	+	0.122641i
$414$	−0.968106	−	0.401002i	−0.0475798	−	0.0197082i
$415$	5.95990	−	14.3885i	0.292560	−	0.706302i
$416$	−2.19817	+	2.19817i	−0.107774	+	0.107774i
$417$	−18.5362	+	18.5362i	−0.907723	+	0.907723i
$418$	−0.132792	+	0.320588i	−0.00649506	+	0.0156805i
$419$	26.3201	+	10.9021i	1.28582	+	0.532604i	0.917737	−	0.397189i	$-0.130014\pi$
$419$	26.3201	+	10.9021i	1.28582	+	0.532604i	0.368083	+	0.929793i	$0.380014\pi$
$420$	0.911680	+	2.20099i	0.0444854	+	0.107397i
$421$		−	9.11011i		−	0.444000i	−0.975047	−	0.222000i	$-0.928742\pi$
$421$		−	9.11011i		−	0.444000i	0.975047	−	0.222000i	$-0.0712584\pi$
$422$	−7.02656	+	2.91050i	−0.342048	+	0.141681i
$423$	−9.57464	−	9.57464i	−0.465535	−	0.465535i
$424$	13.0935			0.635875
$425$	0.153319	−	4.12025i	0.00743706	−	0.199862i
$426$	5.33522			0.258492
$427$	−5.90644	−	5.90644i	−0.285833	−	0.285833i
$428$	10.8273	−	4.48481i	0.523357	−	0.216782i
$429$			1.64403i			0.0793746i
$430$	−2.77660	−	6.70329i	−0.133899	−	0.323262i
$431$	35.6926	+	14.7843i	1.71925	+	0.712137i	0.999846	+	0.0175458i	$0.00558529\pi$
$431$	35.6926	+	14.7843i	1.71925	+	0.712137i	0.719405	+	0.694591i	$0.244415\pi$
$432$	1.28847	−	3.11065i	0.0619916	−	0.149661i
$433$	4.09685	−	4.09685i	0.196882	−	0.196882i	−0.601780	−	0.798662i	$-0.705542\pi$
$433$	4.09685	−	4.09685i	0.196882	−	0.196882i	0.798662	+	0.601780i	$0.205542\pi$
$434$	0.750967	−	0.750967i	0.0360476	−	0.0360476i
$435$	−0.906685	+	2.18893i	−0.0434722	+	0.104951i
$436$	1.92407	+	0.796977i	0.0921464	+	0.0381683i
$437$	0.395716	+	0.955343i	0.0189297	+	0.0457003i
$438$		−	20.8654i		−	0.996986i
$439$	−29.9651	+	12.4119i	−1.43015	+	0.592390i	−0.957390	−	0.288799i	$-0.906744\pi$
$439$	−29.9651	+	12.4119i	−1.43015	+	0.592390i	−0.472765	+	0.881188i	$0.656744\pi$
$440$	−0.178403	−	0.178403i	−0.00850501	−	0.00850501i
$441$	7.95579			0.378847
$442$	−0.476621	+	12.8086i	−0.0226705	+	0.609242i
$443$	−10.1719			−0.483280			−0.241640	−	0.970366i	$-0.577685\pi$
$443$	−10.1719			−0.483280			−0.241640	+	0.970366i	$0.577685\pi$
$444$	7.28593	+	7.28593i	0.345775	+	0.345775i
$445$	11.0174	−	4.56357i	0.522277	−	0.216334i
$446$			2.70356i			0.128017i
$447$	17.8565	+	43.1094i	0.844582	+	2.03900i
$448$	1.05003	+	0.434936i	0.0496092	+	0.0205488i
$449$	1.99926	−	4.82665i	0.0943510	−	0.227783i	−0.869657	−	0.493656i	$-0.835660\pi$
$449$	1.99926	−	4.82665i	0.0943510	−	0.227783i	0.964008	+	0.265873i	$0.0856601\pi$
$450$	−0.985516	+	0.985516i	−0.0464577	+	0.0464577i
$451$	1.71475	−	1.71475i	0.0807446	−	0.0807446i
$452$	3.38057	−	8.16143i	0.159009	−	0.383881i
$453$	−19.5364	−	8.09224i	−0.917899	−	0.380206i
$454$	−3.61134	−	8.71853i	−0.169488	−	0.409181i
$455$		−	3.53316i		−	0.165637i
$456$	2.66347	−	1.10324i	0.124728	−	0.0516642i
$457$	−0.312397	−	0.312397i	−0.0146133	−	0.0146133i	0.699762	−	0.714376i	$-0.253289\pi$
$457$	−0.312397	−	0.312397i	−0.0146133	−	0.0146133i	−0.714376	+	0.699762i	$0.753289\pi$
$458$	−9.01263			−0.421133
$459$	−4.83191	−	13.0142i	−0.225534	−	0.607451i
$460$	−0.751846			−0.0350550
$461$	2.56589	+	2.56589i	0.119505	+	0.119505i	0.764330	−	0.644825i	$-0.223070\pi$
$461$	2.56589	+	2.56589i	0.119505	+	0.119505i	−0.644825	+	0.764330i	$0.723070\pi$
$462$	0.555309	−	0.230016i	0.0258353	−	0.0107013i
$463$		−	12.2323i		−	0.568483i	−0.958753	−	0.284241i	$-0.908258\pi$
$463$		−	12.2323i		−	0.568483i	0.958753	−	0.284241i	$-0.0917417\pi$
$464$	0.432553	+	1.04428i	0.0200808	+	0.0484793i
$465$	1.80960	+	0.749560i	0.0839180	+	0.0347600i
$466$	−5.08986	+	12.2880i	−0.235783	+	0.569231i
$467$	22.0816	−	22.0816i	1.02182	−	1.02182i	0.0220584	−	0.999757i	$-0.492978\pi$
$467$	22.0816	−	22.0816i	1.02182	−	1.02182i	0.999757	−	0.0220584i	$-0.00702196\pi$
$468$	3.06366	−	3.06366i	0.141618	−	0.141618i
$469$	−6.87956	+	16.6087i	−0.317669	+	0.766920i
$470$	−8.97582	−	3.71790i	−0.414024	−	0.171494i
$471$	−13.2607	−	32.0143i	−0.611023	−	1.47514i
$472$			2.37361i			0.109254i
$473$	−1.69124	+	0.700534i	−0.0777632	+	0.0322106i
$474$	20.7874	+	20.7874i	0.954797	+	0.954797i
$475$	1.37536			0.0631057
$476$	4.39307	−	1.63106i	0.201356	−	0.0747595i
$477$	−18.2487			−0.835553
$478$	−1.88599	−	1.88599i	−0.0862633	−	0.0862633i
$479$	−3.32393	+	1.37682i	−0.151874	+	0.0629084i	−0.457326	−	0.889299i	$-0.651193\pi$
$479$	−3.32393	+	1.37682i	−0.151874	+	0.0629084i	0.305451	+	0.952208i	$0.401193\pi$
$480$			2.09612i			0.0956745i
$481$	−5.84790	−	14.1181i	−0.266641	−	0.643729i
$482$	−0.493333	−	0.204345i	−0.0224707	−	0.00930766i
$483$	0.685443	−	1.65480i	0.0311887	−	0.0752962i
$484$	7.73316	−	7.73316i	0.351507	−	0.351507i
$485$	11.1289	−	11.1289i	0.505337	−	0.505337i
$486$	−5.14973	+	12.4325i	−0.233596	+	0.563952i
$487$	19.9459	+	8.26188i	0.903837	+	0.374381i	0.785694	−	0.618615i	$-0.212306\pi$
$487$	19.9459	+	8.26188i	0.903837	+	0.374381i	0.118143	+	0.992997i	$0.462306\pi$
$488$	−2.81251	−	6.79001i	−0.127316	−	0.307369i
$489$		−	3.91693i		−	0.177130i
$490$	5.27375	−	2.18446i	0.238244	−	0.0986838i
$491$	26.3349	+	26.3349i	1.18848	+	1.18848i	0.977488	+	0.210992i	$0.0676693\pi$
$491$	26.3349	+	26.3349i	1.18848	+	1.18848i	0.210992	+	0.977488i	$0.432331\pi$
$492$	−20.1473			−0.908311
$493$	4.23636	+	1.94234i	0.190796	+	0.0874785i
$494$	−4.27555			−0.192366
$495$	0.248645	+	0.248645i	0.0111758	+	0.0111758i
$496$	0.863307	−	0.357593i	0.0387636	−	0.0160564i
$497$			2.89282i			0.129761i
$498$	12.4927	+	30.1600i	0.559810	+	1.35150i
$499$	14.3055	+	5.92555i	0.640404	+	0.265264i	0.679166	−	0.733984i	$-0.262341\pi$
$499$	14.3055	+	5.92555i	0.640404	+	0.265264i	−0.0387621	+	0.999248i	$0.512341\pi$
$500$	−0.382683	+	0.923880i	−0.0171141	+	0.0413171i
$501$	−35.1781	+	35.1781i	−1.57164	+	1.57164i
$502$	−9.46030	+	9.46030i	−0.422234	+	0.422234i
$503$	0.469717	−	1.13400i	0.0209436	−	0.0505624i	−0.913062	−	0.407821i	$-0.866289\pi$
$503$	0.469717	−	1.13400i	0.0209436	−	0.0505624i	0.934005	+	0.357259i	$0.116289\pi$
$504$	−1.46346	−	0.606184i	−0.0651876	−	0.0270016i
$505$	0.730173	+	1.76279i	0.0324923	+	0.0784433i
$506$			0.189690i			0.00843276i
$507$	6.46052	−	2.67603i	0.286922	−	0.118847i
$508$	7.38362	+	7.38362i	0.327595	+	0.327595i
$509$	−25.8063			−1.14384			−0.571922	−	0.820308i	$-0.693802\pi$
$509$	−25.8063			−1.14384			−0.571922	+	0.820308i	$0.693802\pi$
$510$	5.87972	+	6.33422i	0.260358	+	0.280484i
$511$	11.3135			0.500478
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	4.27825	−	1.77211i	0.188889	−	0.0782405i
$514$		−	19.3618i		−	0.854013i
$515$	−0.629495	−	1.51973i	−0.0277388	−	0.0669675i
$516$	14.0509	+	5.82008i	0.618558	+	0.256215i
$517$	−0.938025	+	2.26459i	−0.0412543	+	0.0995967i
$518$	−3.95052	+	3.95052i	−0.173576	+	0.173576i
$519$	−6.16859	+	6.16859i	−0.270771	+	0.270771i
$520$	1.18964	−	2.87205i	0.0521693	−	0.125948i
$521$	−26.9444	−	11.1607i	−1.18046	−	0.488961i	−0.295820	−	0.955244i	$-0.595593\pi$
$521$	−26.9444	−	11.1607i	−1.18046	−	0.488961i	−0.884636	+	0.466283i	$0.845593\pi$
$522$	−0.602863	−	1.45544i	−0.0263866	−	0.0637028i
$523$		−	33.4958i		−	1.46467i	−0.680946	−	0.732334i	$-0.738431\pi$
$523$		−	33.4958i		−	1.46467i	0.680946	−	0.732334i	$-0.261569\pi$
$524$	8.96288	−	3.71255i	0.391545	−	0.162183i
$525$	−1.68456	−	1.68456i	−0.0735204	−	0.0735204i
$526$	12.0967			0.527442
$527$	1.60574	−	3.50222i	0.0699470	−	0.152559i
$528$	0.528851			0.0230153
$529$	−15.8637	−	15.8637i	−0.689728	−	0.689728i
$530$	−12.0968	+	5.01065i	−0.525450	+	0.217649i
$531$		−	3.30817i		−	0.143562i
$532$	0.598193	+	1.44417i	0.0259349	+	0.0626125i
$533$	27.6053	+	11.4345i	1.19572	+	0.495283i
$534$	−9.56581	+	23.0939i	−0.413953	+	0.999371i
$535$	−8.28685	+	8.28685i	−0.358272	+	0.358272i
$536$	−11.1846	+	11.1846i	−0.483101	+	0.483101i
$537$	10.6920	−	25.8128i	0.461394	−	1.11390i
$538$	18.4733	+	7.65189i	0.796440	+	0.329896i
$539$	−0.551138	−	1.33057i	−0.0237392	−	0.0573115i
$540$			3.36694i			0.144890i
$541$	38.3693	−	15.8931i	1.64962	−	0.683297i	0.652409	−	0.757867i	$-0.273759\pi$
$541$	38.3693	−	15.8931i	1.64962	−	0.683297i	0.997216	+	0.0745705i	$0.0237586\pi$
$542$	−2.60177	−	2.60177i	−0.111756	−	0.111756i
$543$	−17.5678			−0.753908
$544$	4.12025	+	0.153319i	0.176654	+	0.00657350i
$545$	−2.08260			−0.0892088
$546$	5.23678	+	5.23678i	0.224114	+	0.224114i
$547$	11.2756	−	4.67049i	0.482109	−	0.199696i	−0.128374	−	0.991726i	$-0.540976\pi$
$547$	11.2756	−	4.67049i	0.482109	−	0.199696i	0.610482	+	0.792030i	$0.290976\pi$
$548$		−	4.55218i		−	0.194460i
$549$	3.91988	+	9.46344i	0.167297	+	0.403890i
$550$	0.233094	+	0.0965508i	0.00993918	+	0.00411694i
$551$	−0.594915	+	1.43625i	−0.0253442	+	0.0611864i
$552$	1.11437	−	1.11437i	0.0474308	−	0.0474308i
$553$	−11.2712	+	11.2712i	−0.479299	+	0.479299i
$554$	−5.03180	+	12.1478i	−0.213780	+	0.516112i
$555$	−9.51953	−	3.94312i	−0.404081	−	0.167376i
$556$	−4.78586	−	11.5541i	−0.202965	−	0.490002i
$557$		−	11.7983i		−	0.499909i	−0.968258	−	0.249954i	$-0.919584\pi$
$557$		−	11.7983i		−	0.499909i	0.968258	−	0.249954i	$-0.0804156\pi$
$558$	−1.20322	+	0.498389i	−0.0509362	+	0.0210985i
$559$	−15.9491	−	15.9491i	−0.674573	−	0.674573i
$560$	−1.13654			−0.0480277
$561$	1.59812	−	1.48345i	0.0674726	−	0.0626313i
$562$	8.83415			0.372646
$563$	24.1004	+	24.1004i	1.01571	+	1.01571i	0.999875	+	0.0158341i	$0.00504037\pi$
$563$	24.1004	+	24.1004i	1.01571	+	1.01571i	0.0158341	+	0.999875i	$0.494960\pi$
$564$	18.8144	−	7.79318i	0.792230	−	0.328152i
$565$			8.83387i			0.371644i
$566$	2.13479	+	5.15384i	0.0897319	+	0.216632i
$567$	−11.8010	−	4.88812i	−0.495594	−	0.205282i
$568$	−0.974036	+	2.35153i	−0.0408697	+	0.0986681i
$569$	20.1508	−	20.1508i	0.844766	−	0.844766i	−0.144708	−	0.989474i	$-0.546224\pi$
$569$	20.1508	−	20.1508i	0.844766	−	0.844766i	0.989474	+	0.144708i	$0.0462244\pi$
$570$	−2.03853	+	2.03853i	−0.0853846	+	0.0853846i
$571$	−11.0538	+	26.6863i	−0.462589	+	1.11679i	0.504742	+	0.863270i	$0.331588\pi$
$571$	−11.0538	+	26.6863i	−0.462589	+	1.11679i	−0.967331	+	0.253518i	$0.918412\pi$
$572$	−0.724617	−	0.300146i	−0.0302978	−	0.0125497i
$573$	−6.71524	−	16.2120i	−0.280533	−	0.677267i
$574$		−	10.9241i		−	0.455964i
$575$	0.694615	−	0.287719i	0.0289674	−	0.0119987i
$576$	−0.985516	−	0.985516i	−0.0410632	−	0.0410632i
$577$	−3.90595			−0.162607			−0.0813033	−	0.996689i	$-0.525908\pi$
$577$	−3.90595			−0.162607			−0.0813033	+	0.996689i	$0.525908\pi$
$578$	12.8809	−	11.0942i	0.535777	−	0.461458i
$579$	−16.4906			−0.685324
$580$	−0.799254	−	0.799254i	−0.0331872	−	0.0331872i
$581$	−16.3531	+	6.77368i	−0.678441	+	0.281020i
$582$			32.9901i			1.36748i
$583$	1.26418	+	3.05201i	0.0523572	+	0.126401i
$584$	9.19654	+	3.80933i	0.380556	+	0.157631i
$585$	−1.65804	+	4.00287i	−0.0685516	+	0.165498i
$586$	−16.6616	+	16.6616i	−0.688286	+	0.688286i
$587$	28.0684	−	28.0684i	1.15851	−	1.15851i	0.173712	−	0.984797i	$-0.444424\pi$
$587$	28.0684	−	28.0684i	1.15851	−	1.15851i	0.984797	−	0.173712i	$-0.0555761\pi$
$588$	−4.57890	+	11.0544i	−0.188830	+	0.455877i
$589$	1.18736	+	0.491819i	0.0489241	+	0.0202650i
$590$	−0.908340	−	2.19293i	−0.0373957	−	0.0902813i
$591$			0.955110i			0.0392880i
$592$	−4.54149	+	1.88115i	−0.186654	+	0.0773147i
$593$	24.5468	+	24.5468i	1.00802	+	1.00802i	0.999968	+	0.00804758i	$0.00256165\pi$
$593$	24.5468	+	24.5468i	1.00802	+	1.00802i	0.00804758	+	0.999968i	$0.497438\pi$
$594$	0.849477			0.0348545
$595$	−3.43449	+	3.18806i	−0.140800	+	0.130698i
$596$	−22.2607			−0.911835
$597$	−13.6130	−	13.6130i	−0.557144	−	0.557144i
$598$	−2.15934	+	0.894428i	−0.0883020	+	0.0365759i
$599$		−	2.16423i		−	0.0884281i	−0.999022	−	0.0442140i	$-0.985922\pi$
$599$		−	2.16423i		−	0.0884281i	0.999022	−	0.0442140i	$-0.0140784\pi$
$600$	−0.802151	−	1.93656i	−0.0327477	−	0.0790599i
$601$	19.5522	+	8.09879i	0.797551	+	0.330356i	0.743975	−	0.668207i	$-0.232938\pi$
$601$	19.5522	+	8.09879i	0.797551	+	0.330356i	0.0535758	+	0.998564i	$0.482938\pi$
$602$	−3.15572	+	7.61859i	−0.128618	+	0.310510i
$603$	15.5883	−	15.5883i	0.634805	−	0.634805i
$604$	7.13341	−	7.13341i	0.290254	−	0.290254i
$605$	−4.18516	+	10.1039i	−0.170151	+	0.410781i
$606$	−3.69503	−	1.53053i	−0.150100	−	0.0621736i
$607$	−6.25210	−	15.0939i	−0.253765	−	0.612642i	0.744737	−	0.667358i	$-0.232575\pi$
$607$	−6.25210	−	15.0939i	−0.253765	−	0.612642i	−0.998502	+	0.0547155i	$0.982575\pi$
$608$			1.37536i			0.0557781i
$609$	2.48782	−	1.03049i	0.100811	−	0.0417574i
$610$	5.19685	+	5.19685i	0.210414	+	0.210414i
$611$	−30.2020			−1.22184
$612$	−5.74252	−	0.213685i	−0.232128	−	0.00863771i
$613$	−19.6808			−0.794900			−0.397450	−	0.917624i	$-0.630105\pi$
$613$	−19.6808			−0.794900			−0.397450	+	0.917624i	$0.630105\pi$
$614$	−9.73037	−	9.73037i	−0.392686	−	0.392686i
$615$	18.6137	−	7.71004i	0.750576	−	0.310899i
$616$			0.286749i			0.0115535i
$617$	15.1106	+	36.4803i	0.608331	+	1.46864i	0.864814	+	0.502092i	$0.167436\pi$
$617$	15.1106	+	36.4803i	0.608331	+	1.46864i	−0.256483	+	0.966549i	$0.582564\pi$
$618$	3.18555	+	1.31950i	0.128142	+	0.0530780i
$619$	15.9641	−	38.5407i	0.641650	−	1.54908i	−0.182803	−	0.983150i	$-0.558517\pi$
$619$	15.9641	−	38.5407i	0.641650	−	1.54908i	0.824453	−	0.565930i	$-0.191483\pi$
$620$	−0.660746	+	0.660746i	−0.0265362	+	0.0265362i
$621$	1.78998	−	1.78998i	0.0718295	−	0.0718295i
$622$	7.91601	−	19.1109i	0.317403	−	0.766278i
$623$	−12.5218	−	5.18670i	−0.501675	−	0.207801i
$624$	2.49364	+	6.02017i	0.0998254	+	0.241000i
$625$		−	1.00000i		−	0.0400000i
$626$	23.0532	−	9.54896i	0.921392	−	0.381653i
$627$	0.514320	+	0.514320i	0.0205400	+	0.0205400i
$628$	16.5315			0.659678
$629$	−8.44710	+	18.4237i	−0.336808	+	0.734601i
$630$	1.58403			0.0631095
$631$	27.0298	+	27.0298i	1.07604	+	1.07604i	0.996861	+	0.0791769i	$0.0252292\pi$
$631$	27.0298	+	27.0298i	1.07604	+	1.07604i	0.0791769	+	0.996861i	$0.474771\pi$
$632$	−12.9573	+	5.36708i	−0.515413	+	0.213491i
$633$			15.9421i			0.633640i
$634$	−3.33242	−	8.04517i	−0.132347	−	0.319515i
$635$	−9.64717	−	3.99599i	−0.382836	−	0.158576i
$636$	10.5029	−	25.3563i	0.416469	−	1.00544i
$637$	12.5478	−	12.5478i	0.497160	−	0.497160i
$638$	−0.201651	+	0.201651i	−0.00798346	+	0.00798346i
$639$	1.35754	−	3.27740i	0.0537036	−	0.129652i
$640$	−0.923880	−	0.382683i	−0.0365195	−	0.0151269i
$641$	3.93638	+	9.50327i	0.155478	+	0.375356i	0.982355	−	0.187026i	$-0.0598849\pi$
$641$	3.93638	+	9.50327i	0.155478	+	0.375356i	−0.826877	+	0.562382i	$0.809885\pi$
$642$		−	24.5653i		−	0.969513i
$643$	−1.11434	+	0.461573i	−0.0439451	+	0.0182027i	−0.404548	−	0.914517i	$-0.632571\pi$
$643$	−1.11434	+	0.461573i	−0.0439451	+	0.0182027i	0.360603	+	0.932720i	$0.382571\pi$
$644$	0.604226	+	0.604226i	0.0238099	+	0.0238099i
$645$	−15.2086			−0.598839
$646$	3.85794	+	4.15615i	0.151789	+	0.163522i
$647$	−40.9502			−1.60992			−0.804958	−	0.593331i	$-0.797812\pi$
$647$	−40.9502			−1.60992			−0.804958	+	0.593331i	$0.797812\pi$
$648$	−7.94697	−	7.94697i	−0.312186	−	0.312186i
$649$	−0.553274	+	0.229174i	−0.0217179	+	0.00899585i
$650$			3.10869i			0.121933i
$651$	−0.851907	−	2.05669i	−0.0333889	−	0.0806079i
$652$	1.72641	+	0.715103i	0.0676115	+	0.0280056i
$653$	−5.10972	+	12.3360i	−0.199959	+	0.482743i	−0.991771	−	0.128021i	$-0.959138\pi$
$653$	−5.10972	+	12.3360i	−0.199959	+	0.482743i	0.791813	+	0.610764i	$0.209138\pi$
$654$	3.08680	−	3.08680i	0.120703	−	0.120703i
$655$	−6.85989	+	6.85989i	−0.268038	+	0.268038i
$656$	3.67824	−	8.88006i	0.143611	−	0.346708i
$657$	−12.8175	−	5.30918i	−0.500058	−	0.207131i
$658$	4.22556	+	10.2014i	0.164729	+	0.397692i
$659$		−	25.9742i		−	1.01181i	−0.862589	−	0.505905i	$-0.831159\pi$
$659$		−	25.9742i		−	1.01181i	0.862589	−	0.505905i	$-0.168841\pi$
$660$	−0.488594	+	0.202382i	−0.0190185	+	0.00787772i
$661$	−18.2918	−	18.2918i	−0.711470	−	0.711470i	0.255372	−	0.966843i	$-0.417802\pi$
$661$	−18.2918	−	18.2918i	−0.711470	−	0.711470i	−0.966843	+	0.255372i	$0.917802\pi$
$662$	−20.5487			−0.798649
$663$	24.4223	+	11.1974i	0.948484	+	0.434872i
$664$	−15.5740			−0.604387
$665$	−1.10532	−	1.10532i	−0.0428623	−	0.0428623i
$666$	6.32962	−	2.62181i	0.245268	−	0.101593i
$667$			0.849823i			0.0329053i
$668$	−9.08260	−	21.9273i	−0.351416	−	0.848394i
$669$	5.23562	+	2.16866i	0.202421	+	0.0838454i
$670$	6.05306	−	14.6134i	0.233850	−	0.564564i
$671$	1.31116	−	1.31116i	0.0506168	−	0.0506168i
$672$	1.68456	−	1.68456i	0.0649835	−	0.0649835i
$673$	1.77044	−	4.27421i	0.0682453	−	0.164759i	−0.886077	−	0.463538i	$-0.846580\pi$
$673$	1.77044	−	4.27421i	0.0682453	−	0.164759i	0.954322	+	0.298780i	$0.0965796\pi$
$674$	−28.2402	−	11.6975i	−1.08777	−	0.450570i
$675$	−1.28847	−	3.11065i	−0.0495933	−	0.119729i
$676$			3.33607i			0.128310i
$677$	23.6515	−	9.79677i	0.909001	−	0.376521i	0.121327	−	0.992613i	$-0.461285\pi$
$677$	23.6515	−	9.79677i	0.909001	−	0.376521i	0.787674	+	0.616092i	$0.211285\pi$
$678$	−13.0934	−	13.0934i	−0.502849	−	0.502849i
$679$	−17.8877			−0.686465
$680$	−3.86529	+	1.43510i	−0.148227	+	0.0550338i
$681$	−19.7808			−0.758004
$682$	0.166706	+	0.166706i	0.00638350	+	0.00638350i
$683$	−19.9779	+	8.27510i	−0.764431	+	0.316638i	−0.730614	−	0.682790i	$-0.760766\pi$
$683$	−19.9779	+	8.27510i	−0.764431	+	0.316638i	−0.0338169	+	0.999428i	$0.510766\pi$
$684$		−	1.91688i		−	0.0732936i
$685$	1.74205	+	4.20567i	0.0665601	+	0.160690i
$686$	−13.3441	−	5.52729i	−0.509478	−	0.211033i
$687$	−7.22949	+	17.4535i	−0.275822	+	0.665894i
$688$	−5.13048	+	5.13048i	−0.195598	+	0.195598i
$689$	−28.7817	+	28.7817i	−1.09650	+	1.09650i
$690$	−0.603094	+	1.45600i	−0.0229594	+	0.0554289i
$691$	−25.4956	−	10.5606i	−0.969899	−	0.401745i	−0.159224	−	0.987242i	$-0.550899\pi$
$691$	−25.4956	−	10.5606i	−0.969899	−	0.401745i	−0.810674	+	0.585497i	$0.800899\pi$
$692$	−1.59266	−	3.84503i	−0.0605439	−	0.146166i
$693$		−	0.399651i		−	0.0151815i
$694$	−15.6890	+	6.49858i	−0.595545	+	0.246683i
$695$	8.84311	+	8.84311i	0.335438	+	0.335438i
$696$	2.36928			0.0898074
$697$	−13.7938	−	37.1520i	−0.522478	−	1.40723i
$698$	−22.4353			−0.849188
$699$	19.7137	+	19.7137i	0.745641	+	0.745641i
$700$	1.05003	−	0.434936i	0.0396874	−	0.0164390i
$701$			11.3549i			0.428868i	0.976739	+	0.214434i	$0.0687906\pi$
$701$			11.3549i			0.428868i	−0.976739	+	0.214434i	$0.931209\pi$
$702$	4.00545	+	9.67002i	0.151176	+	0.364971i
$703$	−6.24617	−	2.58725i	−0.235579	−	0.0975800i
$704$	−0.0965508	+	0.233094i	−0.00363890	+	0.00878507i
$705$	−14.3999	+	14.3999i	−0.542333	+	0.542333i
$706$	15.9459	−	15.9459i	0.600131	−	0.600131i
$707$	0.829874	−	2.00349i	0.0312106	−	0.0753491i
$708$	4.59664	+	1.90399i	0.172752	+	0.0715564i
$709$	−3.45727	−	8.34658i	−0.129840	−	0.313462i	0.845568	−	0.533868i	$-0.179262\pi$
$709$	−3.45727	−	8.34658i	−0.129840	−	0.313462i	−0.975408	+	0.220405i	$0.929262\pi$
$710$		−	2.54528i		−	0.0955226i
$711$	18.0589	−	7.48026i	0.677263	−	0.280532i
$712$	−8.43238	−	8.43238i	−0.316017	−	0.316017i
$713$	0.702552			0.0263108
$714$	0.365257	−	9.81582i	0.0136694	−	0.367348i
$715$	0.784320			0.0293319
$716$	9.42514	+	9.42514i	0.352234	+	0.352234i
$717$	−5.16520	+	2.13950i	−0.192898	+	0.0799010i
$718$		−	10.5451i		−	0.393540i
$719$	−1.58656	−	3.83030i	−0.0591688	−	0.142846i	0.891530	−	0.452961i	$-0.149632\pi$
$719$	−1.58656	−	3.83030i	−0.0591688	−	0.142846i	−0.950699	+	0.310115i	$0.899632\pi$
$720$	1.28764	+	0.533357i	0.0479875	+	0.0198771i
$721$	−0.715448	+	1.72724i	−0.0266447	+	0.0643259i
$722$	12.0975	−	12.0975i	0.450221	−	0.450221i
$723$	−0.791455	+	0.791455i	−0.0294345	+	0.0294345i
$724$	3.20731	−	7.74313i	0.119199	−	0.287771i
$725$	1.04428	+	0.432553i	0.0387834	+	0.0160646i
$726$	−8.77260	−	21.1789i	−0.325582	−	0.786024i
$727$			5.28370i			0.195961i	0.995188	+	0.0979807i	$0.0312383\pi$
$727$			5.28370i			0.195961i	−0.995188	+	0.0979807i	$0.968762\pi$
$728$	−3.26421	+	1.35208i	−0.120980	+	0.0501114i
$729$	−3.89533	−	3.89533i	−0.144271	−	0.144271i
$730$	−9.95427			−0.368424
$731$	−1.11242	+	29.8949i	−0.0411443	+	1.10570i
$732$	−15.4054			−0.569398
$733$	15.0917	+	15.0917i	0.557424	+	0.557424i	0.928573	−	0.371149i	$-0.121036\pi$
$733$	15.0917	+	15.0917i	0.557424	+	0.557424i	−0.371149	+	0.928573i	$0.621036\pi$
$734$	−28.7544	+	11.9104i	−1.06134	+	0.439623i
$735$		−	11.9652i		−	0.441344i
$736$	0.287719	+	0.694615i	0.0106055	+	0.0256038i
$737$	−3.68695	−	1.52718i	−0.135810	−	0.0562545i
$738$	−5.12647	+	12.3764i	−0.188708	+	0.455582i
$739$	10.3591	−	10.3591i	0.381065	−	0.381065i	−0.490420	−	0.871486i	$-0.663157\pi$
$739$	10.3591	−	10.3591i	0.381065	−	0.381065i	0.871486	+	0.490420i	$0.163157\pi$
$740$	3.47591	−	3.47591i	0.127777	−	0.127777i
$741$	−3.42964	+	8.27989i	−0.125991	+	0.304169i
$742$	13.7485	+	5.69482i	0.504724	+	0.209063i
$743$	13.9748	+	33.7382i	0.512687	+	1.23774i	0.942314	+	0.334730i	$0.108645\pi$
$743$	13.9748	+	33.7382i	0.512687	+	1.23774i	−0.429627	+	0.903006i	$0.641355\pi$
$744$		−	1.95869i		−	0.0718092i
$745$	20.5662	−	8.51881i	0.753489	−	0.312105i
$746$	−15.3549	−	15.3549i	−0.562183	−	0.562183i
$747$	21.7059			0.794177
$748$	0.362076	+	0.975211i	0.0132388	+	0.0356572i
$749$	13.3196			0.486687
$750$	1.48218	+	1.48218i	0.0541217	+	0.0541217i
$751$	17.6508	−	7.31120i	0.644087	−	0.266790i	−0.0366379	−	0.999329i	$-0.511665\pi$
$751$	17.6508	−	7.31120i	0.644087	−	0.266790i	0.680725	+	0.732539i	$0.261665\pi$
$752$			9.71535i			0.354282i
$753$	10.7319	+	25.9091i	0.391092	+	0.944180i
$754$	−3.24633	−	1.34467i	−0.118224	−	0.0489701i
$755$	−3.86057	+	9.32025i	−0.140501	+	0.339199i
$756$	2.70587	−	2.70587i	0.0984114	−	0.0984114i
$757$	−14.2078	+	14.2078i	−0.516390	+	0.516390i	−0.916477	−	0.400087i	$-0.868980\pi$
$757$	−14.2078	+	14.2078i	−0.516390	+	0.516390i	0.400087	+	0.916477i	$0.368980\pi$
$758$	−9.02028	+	21.7769i	−0.327631	+	0.790972i
$759$	0.367347	+	0.152160i	0.0133339	+	0.00552307i
$760$	−0.526326	−	1.27066i	−0.0190919	−	0.0460918i
$761$		−	12.0122i		−	0.435441i	−0.976011	−	0.217721i	$-0.930138\pi$
$761$		−	12.0122i		−	0.435441i	0.976011	−	0.217721i	$-0.0698622\pi$
$762$	20.2217	−	8.37608i	0.732553	−	0.303433i
$763$	1.67370	+	1.67370i	0.0605920	+	0.0605920i
$764$	8.37154			0.302872
$765$	5.38717	−	2.00015i	0.194774	−	0.0723155i
$766$	32.3793			1.16991
$767$	−5.21760	−	5.21760i	−0.188396	−	0.188396i
$768$	1.93656	−	0.802151i	0.0698798	−	0.0289451i
$769$			28.5106i			1.02812i	0.857755	+	0.514059i	$0.171859\pi$
$769$			28.5106i			1.02812i	−0.857755	+	0.514059i	$0.828141\pi$
$770$	−0.109734	−	0.264922i	−0.00395455	−	0.00954712i
$771$	−37.4954	−	15.5311i	−1.35036	−	0.559339i
$772$	3.01064	−	7.26832i	0.108355	−	0.261593i
$773$	−16.8373	+	16.8373i	−0.605596	+	0.605596i	−0.941792	−	0.336196i	$-0.890859\pi$
$773$	−16.8373	+	16.8373i	−0.605596	+	0.605596i	0.336196	+	0.941792i	$0.390859\pi$
$774$	7.15050	−	7.15050i	0.257020	−	0.257020i
$775$	0.357593	−	0.863307i	0.0128451	−	0.0310109i
$776$	−14.5406	−	6.02292i	−0.521977	−	0.216210i
$777$	4.48152	+	10.8194i	0.160774	+	0.388142i
$778$			7.88317i			0.282625i
$779$	12.2132	−	5.05889i	0.437585	−	0.181254i
$780$	−4.60764	−	4.60764i	−0.164980	−	0.164980i
$781$	−0.642173			−0.0229787
$782$	2.81788	+	1.29197i	0.100767	+	0.0462008i
$783$	3.80571			0.136005
$784$	−4.03636	−	4.03636i	−0.144156	−	0.144156i
$785$	−15.2731	+	6.32632i	−0.545120	+	0.225796i
$786$		−	20.3352i		−	0.725333i
$787$	9.12132	+	22.0208i	0.325140	+	0.784958i	0.998939	+	0.0460433i	$0.0146612\pi$
$787$	9.12132	+	22.0208i	0.325140	+	0.784958i	−0.673799	+	0.738914i	$0.735339\pi$
$788$	−0.420971	−	0.174372i	−0.0149965	−	0.00621174i
$789$	9.70341	−	23.4261i	0.345450	−	0.833991i
$790$	9.91707	−	9.91707i	0.352834	−	0.352834i
$791$	7.09940	−	7.09940i	0.252426	−	0.252426i
$792$	0.134566	−	0.324871i	0.00478159	−	0.0115438i
$793$	21.1080	+	8.74322i	0.749567	+	0.310481i
$794$	13.7359	+	33.1614i	0.487469	+	1.17685i
$795$			27.4455i			0.973391i
$796$	8.48532	−	3.51474i	0.300754	−	0.124577i
$797$	28.2603	+	28.2603i	1.00103	+	1.00103i	0.999999	+	0.00103330i	$0.000328910\pi$
$797$	28.2603	+	28.2603i	1.00103	+	1.00103i	0.00103330	+	0.999999i	$0.499671\pi$
$798$	3.27656			0.115989
$799$	27.2520	+	29.3586i	0.964107	+	1.03863i
$800$	1.00000			0.0353553
$801$	11.7525	+	11.7525i	0.415253	+	0.415253i
$802$	−24.5561	+	10.1715i	−0.867107	+	0.359168i
$803$			2.51146i			0.0886274i
$804$	12.6879	+	30.6314i	0.447469	+	1.08029i
$805$	−0.789460	−	0.327005i	−0.0278248	−	0.0115254i
$806$	−1.11165	+	2.68375i	−0.0391560	+	0.0945311i
$807$	29.6368	−	29.6368i	1.04326	−	1.04326i
$808$	1.34918	−	1.34918i	0.0474641	−	0.0474641i
$809$	17.1684	−	41.4483i	0.603610	−	1.45724i	−0.266230	−	0.963910i	$-0.585778\pi$
$809$	17.1684	−	41.4483i	0.603610	−	1.45724i	0.869840	−	0.493334i	$-0.164222\pi$
$810$	10.3832	+	4.30087i	0.364829	+	0.151117i
$811$	−11.6694	−	28.1724i	−0.409768	−	0.989266i	−0.985199	−	0.171416i	$-0.945166\pi$
$811$	−11.6694	−	28.1724i	−0.409768	−	0.989266i	0.575431	−	0.817850i	$-0.304834\pi$
$812$			1.28465i			0.0450825i
$813$	−7.12551	+	2.95148i	−0.249902	+	0.103513i
$814$	−0.876970	−	0.876970i	−0.0307378	−	0.0307378i
$815$	−1.86865			−0.0654561
$816$	3.60198	−	7.85615i	0.126095	−	0.275020i
$817$	−9.97903			−0.349122
$818$	7.55242	+	7.55242i	0.264064	+	0.264064i
$819$	4.54943	−	1.88444i	0.158970	−	0.0658475i
$820$			9.61170i			0.335655i
$821$	−18.7827	−	45.3455i	−0.655522	−	1.58257i	−0.804648	−	0.593752i	$-0.797646\pi$
$821$	−18.7827	−	45.3455i	−0.655522	−	1.58257i	0.149126	−	0.988818i	$-0.452354\pi$
$822$	−8.81560	−	3.65154i	−0.307479	−	0.127362i
$823$	−1.69527	+	4.09274i	−0.0590933	+	0.142664i	−0.950668	−	0.310209i	$-0.899601\pi$
$823$	−1.69527	+	4.09274i	−0.0590933	+	0.142664i	0.891575	+	0.452873i	$0.149601\pi$
$824$	−1.16315	+	1.16315i	−0.0405204	+	0.0405204i
$825$	0.373954	−	0.373954i	0.0130194	−	0.0130194i
$826$	−1.03237	+	2.49236i	−0.0359207	+	0.0867201i
$827$	5.92635	+	2.45477i	0.206079	+	0.0853609i	0.483336	−	0.875435i	$-0.339425\pi$
$827$	5.92635	+	2.45477i	0.206079	+	0.0853609i	−0.277256	+	0.960796i	$0.589425\pi$
$828$	−0.401002	−	0.968106i	−0.0139358	−	0.0336440i
$829$		−	24.9754i		−	0.867432i	−0.901050	−	0.433716i	$-0.857202\pi$
$829$		−	24.9754i		−	0.867432i	0.901050	−	0.433716i	$-0.142798\pi$
$830$	14.3885	−	5.95990i	0.499431	−	0.206871i
$831$	19.4888	+	19.4888i	0.676059	+	0.676059i
$832$	−3.10869			−0.107774
$833$	−23.5195	−	0.875186i	−0.814903	−	0.0303234i
$834$	−26.2142			−0.907723
$835$	16.7825	+	16.7825i	0.580781	+	0.580781i
$836$	−0.320588	+	0.132792i	−0.0110878	+	0.00459270i
$837$		−	3.14619i		−	0.108748i
$838$	10.9021	+	26.3201i	0.376608	+	0.909212i
$839$	5.83303	+	2.41612i	0.201379	+	0.0834138i	0.481093	−	0.876669i	$-0.340240\pi$
$839$	5.83303	+	2.41612i	0.201379	+	0.0834138i	−0.279715	+	0.960083i	$0.590240\pi$
$840$	−0.911680	+	2.20099i	−0.0314559	+	0.0759414i
$841$	19.6027	−	19.6027i	0.675955	−	0.675955i
$842$	6.44182	−	6.44182i	0.222000	−	0.222000i
$843$	7.08633	−	17.1079i	0.244066	−	0.589227i
$844$	−7.02656	−	2.91050i	−0.241864	−	0.100183i
$845$	−1.27666	−	3.08213i	−0.0439184	−	0.106028i
$846$		−	13.5406i		−	0.465535i
$847$	11.4835	−	4.75661i	0.394577	−	0.163439i
$848$	9.25847	+	9.25847i	0.317937	+	0.317937i
$849$	11.6932			0.401309
$850$	3.02187	−	2.80505i	0.103649	−	0.0962123i
$851$	−3.69583			−0.126691
$852$	3.77257	+	3.77257i	0.129246	+	0.129246i
$853$	5.80811	−	2.40580i	0.198866	−	0.0823730i	−0.281028	−	0.959700i	$-0.590675\pi$
$853$	5.80811	−	2.40580i	0.198866	−	0.0823730i	0.479894	+	0.877327i	$0.340675\pi$
$854$		−	8.35297i		−	0.285833i
$855$	0.733557	+	1.77096i	0.0250871	+	0.0605657i
$856$	10.8273	+	4.48481i	0.370069	+	0.153288i
$857$	−17.4626	+	42.1583i	−0.596510	+	1.44010i	0.280607	+	0.959823i	$0.409464\pi$
$857$	−17.4626	+	42.1583i	−0.596510	+	1.44010i	−0.877116	+	0.480278i	$0.840536\pi$
$858$	−1.16251	+	1.16251i	−0.0396873	+	0.0396873i
$859$	−20.4579	+	20.4579i	−0.698015	+	0.698015i	−0.963982	−	0.265967i	$-0.914309\pi$
$859$	−20.4579	+	20.4579i	−0.698015	+	0.698015i	0.265967	+	0.963982i	$0.414309\pi$
$860$	2.77660	−	6.70329i	0.0946811	−	0.228580i
$861$	−21.1553	−	8.76280i	−0.720970	−	0.298635i
$862$	14.7843	+	35.6926i	0.503557	+	1.21569i
$863$			7.31084i			0.248864i	0.992228	+	0.124432i	$0.0397109\pi$
$863$			7.31084i			0.248864i	−0.992228	+	0.124432i	$0.960289\pi$
$864$	3.11065	−	1.28847i	0.105826	−	0.0438347i
$865$	2.94286	+	2.94286i	0.100060	+	0.100060i
$866$	5.79382			0.196882
$867$	−11.1522	−	33.8440i	−0.378747	−	1.14940i
$868$	1.06203			0.0360476
$869$	−2.50207	−	2.50207i	−0.0848770	−	0.0848770i
$870$	−2.18893	+	0.906685i	−0.0742117	+	0.0307395i
$871$		−	49.1713i		−	1.66611i
$872$	0.796977	+	1.92407i	0.0269890	+	0.0651573i
$873$	20.2657	+	8.39432i	0.685890	+	0.284105i
$874$	−0.395716	+	0.955343i	−0.0133853	+	0.0323150i
$875$	−0.803658	+	0.803658i	−0.0271686	+	0.0271686i
$876$	14.7540	−	14.7540i	0.498493	−	0.498493i
$877$	13.4790	−	32.5412i	0.455153	−	1.09884i	−0.515184	−	0.857080i	$-0.672276\pi$
$877$	13.4790	−	32.5412i	0.455153	−	1.09884i	0.970337	−	0.241757i	$-0.0777237\pi$
$878$	−29.9651	−	12.4119i	−1.01127	−	0.418883i
$879$	18.9012	+	45.6315i	0.637521	+	1.53911i
$880$		−	0.252299i		−	0.00850501i
$881$	−11.8515	+	4.90905i	−0.399287	+	0.165390i	−0.573285	−	0.819356i	$-0.694331\pi$
$881$	−11.8515	+	4.90905i	−0.399287	+	0.165390i	0.173998	+	0.984746i	$0.444331\pi$
$882$	5.62559	+	5.62559i	0.189423	+	0.189423i
$883$	25.2939			0.851208			0.425604	−	0.904910i	$-0.360062\pi$
$883$	25.2939			0.851208			0.425604	+	0.904910i	$0.360062\pi$
$884$	−9.39405	+	8.72001i	−0.315956	+	0.293286i
$885$	−4.97537			−0.167245
$886$	−7.19260	−	7.19260i	−0.241640	−	0.241640i
$887$	−21.6520	+	8.96853i	−0.727001	+	0.301134i	−0.715319	−	0.698798i	$-0.753719\pi$
$887$	−21.6520	+	8.96853i	−0.727001	+	0.301134i	−0.0116823	+	0.999932i	$0.503719\pi$
$888$			10.3039i			0.345775i
$889$	4.54161	+	10.9644i	0.152321	+	0.367735i
$890$	11.0174	+	4.56357i	0.369305	+	0.152971i
$891$	1.08511	−	2.61968i	0.0363524	−	0.0877625i
$892$	−1.91171	+	1.91171i	−0.0640086	+	0.0640086i
$893$	−9.44842	+	9.44842i	−0.316179	+	0.316179i
$894$	−17.8565	+	43.1094i	−0.597210	+	1.44179i
$895$	−12.3145	−	5.10085i	−0.411630	−	0.170503i
$896$	0.434936	+	1.05003i	0.0145302	+	0.0350790i
$897$			4.89917i			0.163578i
$898$	4.82665	−	1.99926i	0.161067	−	0.0667162i
$899$	0.746852	+	0.746852i	0.0249089	+	0.0249089i
$900$	−1.39373			−0.0464577
$901$	53.9484	+	2.00748i	1.79728	+	0.0668787i
$902$	2.42503			0.0807446
$903$	12.2225	+	12.2225i	0.406740	+	0.406740i
$904$	8.16143	−	3.38057i	0.271445	−	0.112436i
$905$			8.38111i			0.278597i
$906$	−8.09224	−	19.5364i	−0.268847	−	0.649053i
$907$	−46.1626	−	19.1212i	−1.53280	−	0.634908i	−0.552697	−	0.833382i	$-0.686401\pi$
$907$	−46.1626	−	19.1212i	−1.53280	−	0.634908i	−0.980106	+	0.198474i	$0.936401\pi$
$908$	3.61134	−	8.71853i	0.119846	−	0.289335i
$909$	−1.88040	+	1.88040i	−0.0623689	+	0.0623689i
$910$	2.49832	−	2.49832i	0.0828185	−	0.0828185i
$911$	14.9768	−	36.1572i	0.496204	−	1.19794i	−0.455309	−	0.890334i	$-0.650471\pi$
$911$	14.9768	−	36.1572i	0.496204	−	1.19794i	0.951513	−	0.307609i	$-0.0995289\pi$
$912$	2.66347	+	1.10324i	0.0881962	+	0.0365321i
$913$	−1.50368	−	3.63020i	−0.0497645	−	0.120142i
$914$		−	0.441796i		−	0.0146133i
$915$	14.2327	−	5.89537i	0.470518	−	0.194895i
$916$	−6.37289	−	6.37289i	−0.210566	−	0.210566i
$917$	11.0260			0.364111
$918$	5.78575	−	12.6191i	0.190958	−	0.416492i
$919$	34.5751			1.14053			0.570263	−	0.821462i	$-0.306841\pi$
$919$	34.5751			1.14053			0.570263	+	0.821462i	$0.306841\pi$
$920$	−0.531635	−	0.531635i	−0.0175275	−	0.0175275i
$921$	−26.6487	+	11.0383i	−0.878105	+	0.363723i
$922$			3.62872i			0.119505i
$923$	−3.02797	−	7.31017i	−0.0996670	−	0.240617i
$924$	0.555309	+	0.230016i	0.0182683	+	0.00756698i
$925$	−1.88115	+	4.54149i	−0.0618518	+	0.149323i
$926$	8.64954	−	8.64954i	0.284241	−	0.284241i
$927$	1.62112	−	1.62112i	0.0532447	−	0.0532447i
$928$	−0.432553	+	1.04428i	−0.0141993	+	0.0342800i
$929$	−17.4963	−	7.24720i	−0.574035	−	0.237773i	0.0767308	−	0.997052i	$-0.475552\pi$
$929$	−17.4963	−	7.24720i	−0.574035	−	0.237773i	−0.650765	+	0.759279i	$0.725552\pi$
$930$	0.749560	+	1.80960i	0.0245790	+	0.0593390i
$931$		−	7.85091i		−	0.257303i
$932$	−12.2880	+	5.08986i	−0.402507	+	0.166724i
$933$	−30.6597	−	30.6597i	−1.00375	−	1.00375i
$934$	31.2281			1.02182
$935$	−0.707712	−	0.762417i	−0.0231447	−	0.0249337i
$936$	4.33267			0.141618
$937$	−10.1161	−	10.1161i	−0.330478	−	0.330478i	0.522290	−	0.852768i	$-0.325078\pi$
$937$	−10.1161	−	10.1161i	−0.330478	−	0.330478i	−0.852768	+	0.522290i	$0.825078\pi$
$938$	−16.6087	+	6.87956i	−0.542294	+	0.224626i
$939$		−	52.3038i		−	1.70687i
$940$	−3.71790	−	8.97582i	−0.121265	−	0.292759i
$941$	13.0487	+	5.40494i	0.425375	+	0.176196i	0.585092	−	0.810967i	$-0.301058\pi$
$941$	13.0487	+	5.40494i	0.425375	+	0.176196i	−0.159717	+	0.987163i	$0.551058\pi$
$942$	13.2607	−	32.0143i	0.432058	−	1.04308i
$943$	5.10992	−	5.10992i	0.166402	−	0.166402i
$944$	−1.67839	+	1.67839i	−0.0546270	+	0.0546270i
$945$	−1.46440	+	3.53538i	−0.0476371	+	0.115006i
$946$	−1.69124	−	0.700534i	−0.0549869	−	0.0227763i
$947$	−11.2228	−	27.0944i	−0.364694	−	0.880448i	−0.994601	−	0.103778i	$-0.966907\pi$
$947$	−11.2228	−	27.0944i	−0.364694	−	0.880448i	0.629907	−	0.776671i	$-0.283093\pi$
$948$			29.3978i			0.954797i
$949$	−28.5892	+	11.8420i	−0.928044	+	0.384408i
$950$	0.972524	+	0.972524i	0.0315529	+	0.0315529i
$951$	−18.2531			−0.591897
$952$	4.25970	+	1.95304i	0.138058	+	0.0632983i
$953$	−11.5308			−0.373521			−0.186760	−	0.982406i	$-0.559799\pi$
$953$	−11.5308			−0.373521			−0.186760	+	0.982406i	$0.559799\pi$
$954$	−12.9038	−	12.9038i	−0.417776	−	0.417776i
$955$	−7.73429	+	3.20365i	−0.250276	+	0.103668i
$956$		−	2.66720i		−	0.0862633i
$957$	0.228756	+	0.552266i	0.00739464	+	0.0178522i
$958$	−3.32393	−	1.37682i	−0.107391	−	0.0444829i
$959$	1.97991	−	4.77993i	0.0639346	−	0.154352i
$960$	−1.48218	+	1.48218i	−0.0478372	+	0.0478372i
$961$	−21.3029	+	21.3029i	−0.687190	+	0.687190i
$962$	5.84790	−	14.1181i	0.188544	−	0.455185i
$963$	−15.0903	−	6.25062i	−0.486279	−	0.201423i
$964$	−0.204345	−	0.493333i	−0.00658151	−	0.0158892i
$965$			7.86718i			0.253253i
$966$	1.65480	−	0.685443i	0.0532425	−	0.0220538i
$967$	30.1392	+	30.1392i	0.969211	+	0.969211i	0.999540	−	0.0303294i	$-0.00965562\pi$
$967$	30.1392	+	30.1392i	0.969211	+	0.969211i	−0.0303294	+	0.999540i	$0.509656\pi$
$968$	10.9363			0.351507
$969$	11.1433	−	4.13729i	0.357975	−	0.132909i
$970$	15.7386			0.505337
$971$	11.6594	+	11.6594i	0.374167	+	0.374167i	0.868993	−	0.494825i	$-0.164768\pi$
$971$	11.6594	+	11.6594i	0.374167	+	0.374167i	−0.494825	+	0.868993i	$0.664768\pi$
$972$	−12.4325	+	5.14973i	−0.398774	+	0.165178i
$973$		−	14.2137i		−	0.455669i
$974$	8.26188	+	19.9459i	0.264728	+	0.639109i
$975$	6.02017	+	2.49364i	0.192800	+	0.0798603i
$976$	2.81251	−	6.79001i	0.0900264	−	0.217343i
$977$	13.4637	−	13.4637i	0.430741	−	0.430741i	−0.458139	−	0.888880i	$-0.651484\pi$
$977$	13.4637	−	13.4637i	0.430741	−	0.430741i	0.888880	+	0.458139i	$0.151484\pi$
$978$	2.76969	−	2.76969i	0.0885648	−	0.0885648i
$979$	1.15139	−	2.77969i	0.0367985	−	0.0888394i
$980$	5.27375	+	2.18446i	0.168464	+	0.0697800i
$981$	−1.11077	−	2.68164i	−0.0354642	−	0.0856181i
$982$			37.2432i			1.18848i
$983$	2.07283	−	0.858595i	0.0661131	−	0.0273849i	−0.349382	−	0.936980i	$-0.613608\pi$
$983$	2.07283	−	0.858595i	0.0661131	−	0.0273849i	0.415495	+	0.909595i	$0.363608\pi$
$984$	−14.2463	−	14.2463i	−0.454155	−	0.454155i
$985$	0.455655			0.0145184
$986$	1.62212	+	4.36900i	0.0516589	+	0.139137i
$987$	23.1452			0.736721
$988$	−3.02327	−	3.02327i	−0.0961831	−	0.0961831i
$989$	−5.03984	+	2.08757i	−0.160258	+	0.0663809i
$990$			0.351637i			0.0111758i
$991$	6.12684	+	14.7915i	0.194625	+	0.469867i	0.990822	−	0.135170i	$-0.0431581\pi$
$991$	6.12684	+	14.7915i	0.194625	+	0.469867i	−0.796197	+	0.605038i	$0.793158\pi$
$992$	0.863307	+	0.357593i	0.0274100	+	0.0113536i
$993$	−16.4832	+	39.7940i	−0.523079	+	1.26282i
$994$	−2.04553	+	2.04553i	−0.0648804	+	0.0648804i
$995$	−6.49439	+	6.49439i	−0.205886	+	0.205886i
$996$	−12.4927	+	30.1600i	−0.395846	+	0.955656i
$997$	−22.0338	−	9.12670i	−0.697818	−	0.289046i	0.00543534	−	0.999985i	$-0.498270\pi$
$997$	−22.0338	−	9.12670i	−0.697818	−	0.289046i	−0.703253	+	0.710940i	$0.748270\pi$
$998$	5.92555	+	14.3055i	0.187570	+	0.452834i
$999$			16.5508i			0.523643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.b.121.4	yes	16
5.2	odd	4		850.2.o.g.699.1		16
5.3	odd	4		850.2.o.j.699.4		16
5.4	even	2		850.2.l.e.801.1		16
17.3	odd	16		2890.2.a.bj.1.6		8
17.5	odd	16		2890.2.b.r.2311.13		16
17.9	even	8	inner	170.2.k.b.111.4	✓	16
17.12	odd	16		2890.2.b.r.2311.4		16
17.14	odd	16		2890.2.a.bi.1.3		8
85.9	even	8		850.2.l.e.451.1		16
85.43	odd	8		850.2.o.g.349.1		16
85.77	odd	8		850.2.o.j.349.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.111.4	✓	16	17.9	even	8	inner
170.2.k.b.121.4	yes	16	1.1	even	1	trivial
850.2.l.e.451.1		16	85.9	even	8
850.2.l.e.801.1		16	5.4	even	2
850.2.o.g.349.1		16	85.43	odd	8
850.2.o.g.699.1		16	5.2	odd	4
850.2.o.j.349.4		16	85.77	odd	8
850.2.o.j.699.4		16	5.3	odd	4
2890.2.a.bi.1.3		8	17.14	odd	16
2890.2.a.bj.1.6		8	17.3	odd	16
2890.2.b.r.2311.4		16	17.12	odd	16
2890.2.b.r.2311.13		16	17.5	odd	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.k (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.93656 - 0.802151i) q^{3} +1.00000i q^{4} +(-0.382683 - 0.923880i) q^{5} +(1.93656 + 0.802151i) q^{6} +(-0.434936 + 1.05003i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.985516 - 0.985516i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.93656 - 0.802151i) q^{3} +1.00000i q^{4} +(-0.382683 - 0.923880i) q^{5} +(1.93656 + 0.802151i) q^{6} +(-0.434936 + 1.05003i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.985516 - 0.985516i) q^{9} +(0.382683 - 0.923880i) q^{10} +(-0.233094 - 0.0965508i) q^{11} +(0.802151 + 1.93656i) q^{12} -3.10869i q^{13} +(-1.05003 + 0.434936i) q^{14} +(-1.48218 - 1.48218i) q^{15} -1.00000 q^{16} +(-3.02187 + 2.80505i) q^{17} +1.39373 q^{18} +(-0.972524 - 0.972524i) q^{19} +(0.923880 - 0.382683i) q^{20} +2.38233i q^{21} +(-0.0965508 - 0.233094i) q^{22} +(-0.694615 - 0.287719i) q^{23} +(-0.802151 + 1.93656i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(2.19817 - 2.19817i) q^{26} +(-1.28847 + 3.11065i) q^{27} +(-1.05003 - 0.434936i) q^{28} +(-0.432553 - 1.04428i) q^{29} -2.09612i q^{30} +(-0.863307 + 0.357593i) q^{31} +(-0.707107 - 0.707107i) q^{32} -0.528851 q^{33} +(-4.12025 - 0.153319i) q^{34} +1.13654 q^{35} +(0.985516 + 0.985516i) q^{36} +(4.54149 - 1.88115i) q^{37} -1.37536i q^{38} +(-2.49364 - 6.02017i) q^{39} +(0.923880 + 0.382683i) q^{40} +(-3.67824 + 8.88006i) q^{41} +(-1.68456 + 1.68456i) q^{42} +(5.13048 - 5.13048i) q^{43} +(0.0965508 - 0.233094i) q^{44} +(-1.28764 - 0.533357i) q^{45} +(-0.287719 - 0.694615i) q^{46} -9.71535i q^{47} +(-1.93656 + 0.802151i) q^{48} +(4.03636 + 4.03636i) q^{49} -1.00000 q^{50} +(-3.60198 + 7.85615i) q^{51} +3.10869 q^{52} +(-9.25847 - 9.25847i) q^{53} +(-3.11065 + 1.28847i) q^{54} +0.252299i q^{55} +(-0.434936 - 1.05003i) q^{56} +(-2.66347 - 1.10324i) q^{57} +(0.432553 - 1.04428i) q^{58} +(1.67839 - 1.67839i) q^{59} +(1.48218 - 1.48218i) q^{60} +(-2.81251 + 6.79001i) q^{61} +(-0.863307 - 0.357593i) q^{62} +(0.606184 + 1.46346i) q^{63} -1.00000i q^{64} +(-2.87205 + 1.18964i) q^{65} +(-0.373954 - 0.373954i) q^{66} +15.8174 q^{67} +(-2.80505 - 3.02187i) q^{68} -1.57596 q^{69} +(0.803658 + 0.803658i) q^{70} +(2.35153 - 0.974036i) q^{71} +1.39373i q^{72} +(-3.80933 - 9.19654i) q^{73} +(4.54149 + 1.88115i) q^{74} +(-0.802151 + 1.93656i) q^{75} +(0.972524 - 0.972524i) q^{76} +(0.202762 - 0.202762i) q^{77} +(2.49364 - 6.02017i) q^{78} +(12.9573 + 5.36708i) q^{79} +(0.382683 + 0.923880i) q^{80} +11.2387i q^{81} +(-8.88006 + 3.67824i) q^{82} +(11.0125 + 11.0125i) q^{83} -2.38233 q^{84} +(3.74795 + 1.71840i) q^{85} +7.25559 q^{86} +(-1.67534 - 1.67534i) q^{87} +(0.233094 - 0.0965508i) q^{88} +11.9252i q^{89} +(-0.533357 - 1.28764i) q^{90} +(3.26421 + 1.35208i) q^{91} +(0.287719 - 0.694615i) q^{92} +(-1.38501 + 1.38501i) q^{93} +(6.86979 - 6.86979i) q^{94} +(-0.526326 + 1.27066i) q^{95} +(-1.93656 - 0.802151i) q^{96} +(6.02292 + 14.5406i) q^{97} +5.70827i q^{98} +(-0.324871 + 0.134566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

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