# Properties

 Label 650.2.c.d.649.1 Level $650$ Weight $2$ Character 650.649 Analytic conductor $5.190$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$650 = 2 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 650.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.19027613138$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 26) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 649.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 650.649 Dual form 650.2.c.d.649.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +3.00000 q^{7} +1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +3.00000 q^{7} +1.00000 q^{8} +2.00000 q^{9} -1.00000i q^{12} +(-3.00000 + 2.00000i) q^{13} +3.00000 q^{14} +1.00000 q^{16} -3.00000i q^{17} +2.00000 q^{18} +6.00000i q^{19} -3.00000i q^{21} -6.00000i q^{23} -1.00000i q^{24} +(-3.00000 + 2.00000i) q^{26} -5.00000i q^{27} +3.00000 q^{28} +1.00000 q^{32} -3.00000i q^{34} +2.00000 q^{36} +3.00000 q^{37} +6.00000i q^{38} +(2.00000 + 3.00000i) q^{39} -3.00000i q^{42} -1.00000i q^{43} -6.00000i q^{46} +3.00000 q^{47} -1.00000i q^{48} +2.00000 q^{49} -3.00000 q^{51} +(-3.00000 + 2.00000i) q^{52} -6.00000i q^{53} -5.00000i q^{54} +3.00000 q^{56} +6.00000 q^{57} +6.00000i q^{59} -8.00000 q^{61} +6.00000 q^{63} +1.00000 q^{64} -12.0000 q^{67} -3.00000i q^{68} -6.00000 q^{69} +15.0000i q^{71} +2.00000 q^{72} -6.00000 q^{73} +3.00000 q^{74} +6.00000i q^{76} +(2.00000 + 3.00000i) q^{78} -10.0000 q^{79} +1.00000 q^{81} -6.00000 q^{83} -3.00000i q^{84} -1.00000i q^{86} +6.00000i q^{89} +(-9.00000 + 6.00000i) q^{91} -6.00000i q^{92} +3.00000 q^{94} -1.00000i q^{96} -12.0000 q^{97} +2.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 2 q^{4} + 6 q^{7} + 2 q^{8} + 4 q^{9}+O(q^{10})$$ 2 * q + 2 * q^2 + 2 * q^4 + 6 * q^7 + 2 * q^8 + 4 * q^9 $$2 q + 2 q^{2} + 2 q^{4} + 6 q^{7} + 2 q^{8} + 4 q^{9} - 6 q^{13} + 6 q^{14} + 2 q^{16} + 4 q^{18} - 6 q^{26} + 6 q^{28} + 2 q^{32} + 4 q^{36} + 6 q^{37} + 4 q^{39} + 6 q^{47} + 4 q^{49} - 6 q^{51} - 6 q^{52} + 6 q^{56} + 12 q^{57} - 16 q^{61} + 12 q^{63} + 2 q^{64} - 24 q^{67} - 12 q^{69} + 4 q^{72} - 12 q^{73} + 6 q^{74} + 4 q^{78} - 20 q^{79} + 2 q^{81} - 12 q^{83} - 18 q^{91} + 6 q^{94} - 24 q^{97} + 4 q^{98}+O(q^{100})$$ 2 * q + 2 * q^2 + 2 * q^4 + 6 * q^7 + 2 * q^8 + 4 * q^9 - 6 * q^13 + 6 * q^14 + 2 * q^16 + 4 * q^18 - 6 * q^26 + 6 * q^28 + 2 * q^32 + 4 * q^36 + 6 * q^37 + 4 * q^39 + 6 * q^47 + 4 * q^49 - 6 * q^51 - 6 * q^52 + 6 * q^56 + 12 * q^57 - 16 * q^61 + 12 * q^63 + 2 * q^64 - 24 * q^67 - 12 * q^69 + 4 * q^72 - 12 * q^73 + 6 * q^74 + 4 * q^78 - 20 * q^79 + 2 * q^81 - 12 * q^83 - 18 * q^91 + 6 * q^94 - 24 * q^97 + 4 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$$.

 $$n$$ $$27$$ $$301$$ $$\chi(n)$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 1.00000i 0.577350i −0.957427 0.288675i $$-0.906785\pi$$
0.957427 0.288675i $$-0.0932147\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 1.00000i 0.408248i
$$7$$ 3.00000 1.13389 0.566947 0.823754i $$-0.308125\pi$$
0.566947 + 0.823754i $$0.308125\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 2.00000 0.666667
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ −3.00000 + 2.00000i −0.832050 + 0.554700i
$$14$$ 3.00000 0.801784
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 3.00000i 0.727607i −0.931476 0.363803i $$-0.881478\pi$$
0.931476 0.363803i $$-0.118522\pi$$
$$18$$ 2.00000 0.471405
$$19$$ 6.00000i 1.37649i 0.725476 + 0.688247i $$0.241620\pi$$
−0.725476 + 0.688247i $$0.758380\pi$$
$$20$$ 0 0
$$21$$ 3.00000i 0.654654i
$$22$$ 0 0
$$23$$ 6.00000i 1.25109i −0.780189 0.625543i $$-0.784877\pi$$
0.780189 0.625543i $$-0.215123\pi$$
$$24$$ 1.00000i 0.204124i
$$25$$ 0 0
$$26$$ −3.00000 + 2.00000i −0.588348 + 0.392232i
$$27$$ 5.00000i 0.962250i
$$28$$ 3.00000 0.566947
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 3.00000i 0.514496i
$$35$$ 0 0
$$36$$ 2.00000 0.333333
$$37$$ 3.00000 0.493197 0.246598 0.969118i $$-0.420687\pi$$
0.246598 + 0.969118i $$0.420687\pi$$
$$38$$ 6.00000i 0.973329i
$$39$$ 2.00000 + 3.00000i 0.320256 + 0.480384i
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 3.00000i 0.462910i
$$43$$ 1.00000i 0.152499i −0.997089 0.0762493i $$-0.975706\pi$$
0.997089 0.0762493i $$-0.0242945\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 6.00000i 0.884652i
$$47$$ 3.00000 0.437595 0.218797 0.975770i $$-0.429787\pi$$
0.218797 + 0.975770i $$0.429787\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ 2.00000 0.285714
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ −3.00000 + 2.00000i −0.416025 + 0.277350i
$$53$$ 6.00000i 0.824163i −0.911147 0.412082i $$-0.864802\pi$$
0.911147 0.412082i $$-0.135198\pi$$
$$54$$ 5.00000i 0.680414i
$$55$$ 0 0
$$56$$ 3.00000 0.400892
$$57$$ 6.00000 0.794719
$$58$$ 0 0
$$59$$ 6.00000i 0.781133i 0.920575 + 0.390567i $$0.127721\pi$$
−0.920575 + 0.390567i $$0.872279\pi$$
$$60$$ 0 0
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 0 0
$$63$$ 6.00000 0.755929
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −12.0000 −1.46603 −0.733017 0.680211i $$-0.761888\pi$$
−0.733017 + 0.680211i $$0.761888\pi$$
$$68$$ 3.00000i 0.363803i
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 15.0000i 1.78017i 0.455792 + 0.890086i $$0.349356\pi$$
−0.455792 + 0.890086i $$0.650644\pi$$
$$72$$ 2.00000 0.235702
$$73$$ −6.00000 −0.702247 −0.351123 0.936329i $$-0.614200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ 3.00000 0.348743
$$75$$ 0 0
$$76$$ 6.00000i 0.688247i
$$77$$ 0 0
$$78$$ 2.00000 + 3.00000i 0.226455 + 0.339683i
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ 3.00000i 0.327327i
$$85$$ 0 0
$$86$$ 1.00000i 0.107833i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 6.00000i 0.635999i 0.948091 + 0.317999i $$0.103011\pi$$
−0.948091 + 0.317999i $$0.896989\pi$$
$$90$$ 0 0
$$91$$ −9.00000 + 6.00000i −0.943456 + 0.628971i
$$92$$ 6.00000i 0.625543i
$$93$$ 0 0
$$94$$ 3.00000 0.309426
$$95$$ 0 0
$$96$$ 1.00000i 0.102062i
$$97$$ −12.0000 −1.21842 −0.609208 0.793011i $$-0.708512\pi$$
−0.609208 + 0.793011i $$0.708512\pi$$
$$98$$ 2.00000 0.202031
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ −3.00000 −0.297044
$$103$$ 14.0000i 1.37946i 0.724066 + 0.689730i $$0.242271\pi$$
−0.724066 + 0.689730i $$0.757729\pi$$
$$104$$ −3.00000 + 2.00000i −0.294174 + 0.196116i
$$105$$ 0 0
$$106$$ 6.00000i 0.582772i
$$107$$ 12.0000i 1.16008i 0.814587 + 0.580042i $$0.196964\pi$$
−0.814587 + 0.580042i $$0.803036\pi$$
$$108$$ 5.00000i 0.481125i
$$109$$ 9.00000i 0.862044i −0.902342 0.431022i $$-0.858153\pi$$
0.902342 0.431022i $$-0.141847\pi$$
$$110$$ 0 0
$$111$$ 3.00000i 0.284747i
$$112$$ 3.00000 0.283473
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 6.00000 0.561951
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −6.00000 + 4.00000i −0.554700 + 0.369800i
$$118$$ 6.00000i 0.552345i
$$119$$ 9.00000i 0.825029i
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ −8.00000 −0.724286
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 6.00000 0.534522
$$127$$ 2.00000i 0.177471i 0.996055 + 0.0887357i $$0.0282826\pi$$
−0.996055 + 0.0887357i $$0.971717\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −1.00000 −0.0880451
$$130$$ 0 0
$$131$$ −3.00000 −0.262111 −0.131056 0.991375i $$-0.541837\pi$$
−0.131056 + 0.991375i $$0.541837\pi$$
$$132$$ 0 0
$$133$$ 18.0000i 1.56080i
$$134$$ −12.0000 −1.03664
$$135$$ 0 0
$$136$$ 3.00000i 0.257248i
$$137$$ 18.0000 1.53784 0.768922 0.639343i $$-0.220793\pi$$
0.768922 + 0.639343i $$0.220793\pi$$
$$138$$ −6.00000 −0.510754
$$139$$ −5.00000 −0.424094 −0.212047 0.977259i $$-0.568013\pi$$
−0.212047 + 0.977259i $$0.568013\pi$$
$$140$$ 0 0
$$141$$ 3.00000i 0.252646i
$$142$$ 15.0000i 1.25877i
$$143$$ 0 0
$$144$$ 2.00000 0.166667
$$145$$ 0 0
$$146$$ −6.00000 −0.496564
$$147$$ 2.00000i 0.164957i
$$148$$ 3.00000 0.246598
$$149$$ 6.00000i 0.491539i 0.969328 + 0.245770i $$0.0790407\pi$$
−0.969328 + 0.245770i $$0.920959\pi$$
$$150$$ 0 0
$$151$$ 15.0000i 1.22068i −0.792139 0.610341i $$-0.791032\pi$$
0.792139 0.610341i $$-0.208968\pi$$
$$152$$ 6.00000i 0.486664i
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 2.00000 + 3.00000i 0.160128 + 0.240192i
$$157$$ 22.0000i 1.75579i 0.478852 + 0.877896i $$0.341053\pi$$
−0.478852 + 0.877896i $$0.658947\pi$$
$$158$$ −10.0000 −0.795557
$$159$$ −6.00000 −0.475831
$$160$$ 0 0
$$161$$ 18.0000i 1.41860i
$$162$$ 1.00000 0.0785674
$$163$$ −6.00000 −0.469956 −0.234978 0.972001i $$-0.575502\pi$$
−0.234978 + 0.972001i $$0.575502\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −6.00000 −0.465690
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 3.00000i 0.231455i
$$169$$ 5.00000 12.0000i 0.384615 0.923077i
$$170$$ 0 0
$$171$$ 12.0000i 0.917663i
$$172$$ 1.00000i 0.0762493i
$$173$$ 6.00000i 0.456172i −0.973641 0.228086i $$-0.926753\pi$$
0.973641 0.228086i $$-0.0732467\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 6.00000 0.450988
$$178$$ 6.00000i 0.449719i
$$179$$ −15.0000 −1.12115 −0.560576 0.828103i $$-0.689420\pi$$
−0.560576 + 0.828103i $$0.689420\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ −9.00000 + 6.00000i −0.667124 + 0.444750i
$$183$$ 8.00000i 0.591377i
$$184$$ 6.00000i 0.442326i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 3.00000 0.218797
$$189$$ 15.0000i 1.09109i
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 1.00000i 0.0721688i
$$193$$ −6.00000 −0.431889 −0.215945 0.976406i $$-0.569283\pi$$
−0.215945 + 0.976406i $$0.569283\pi$$
$$194$$ −12.0000 −0.861550
$$195$$ 0 0
$$196$$ 2.00000 0.142857
$$197$$ 3.00000 0.213741 0.106871 0.994273i $$-0.465917\pi$$
0.106871 + 0.994273i $$0.465917\pi$$
$$198$$ 0 0
$$199$$ 20.0000 1.41776 0.708881 0.705328i $$-0.249200\pi$$
0.708881 + 0.705328i $$0.249200\pi$$
$$200$$ 0 0
$$201$$ 12.0000i 0.846415i
$$202$$ 12.0000 0.844317
$$203$$ 0 0
$$204$$ −3.00000 −0.210042
$$205$$ 0 0
$$206$$ 14.0000i 0.975426i
$$207$$ 12.0000i 0.834058i
$$208$$ −3.00000 + 2.00000i −0.208013 + 0.138675i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −23.0000 −1.58339 −0.791693 0.610920i $$-0.790800\pi$$
−0.791693 + 0.610920i $$0.790800\pi$$
$$212$$ 6.00000i 0.412082i
$$213$$ 15.0000 1.02778
$$214$$ 12.0000i 0.820303i
$$215$$ 0 0
$$216$$ 5.00000i 0.340207i
$$217$$ 0 0
$$218$$ 9.00000i 0.609557i
$$219$$ 6.00000i 0.405442i
$$220$$ 0 0
$$221$$ 6.00000 + 9.00000i 0.403604 + 0.605406i
$$222$$ 3.00000i 0.201347i
$$223$$ 9.00000 0.602685 0.301342 0.953516i $$-0.402565\pi$$
0.301342 + 0.953516i $$0.402565\pi$$
$$224$$ 3.00000 0.200446
$$225$$ 0 0
$$226$$ 6.00000i 0.399114i
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 6.00000 0.397360
$$229$$ 9.00000i 0.594737i −0.954763 0.297368i $$-0.903891\pi$$
0.954763 0.297368i $$-0.0961089\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 21.0000i 1.37576i −0.725826 0.687878i $$-0.758542\pi$$
0.725826 0.687878i $$-0.241458\pi$$
$$234$$ −6.00000 + 4.00000i −0.392232 + 0.261488i
$$235$$ 0 0
$$236$$ 6.00000i 0.390567i
$$237$$ 10.0000i 0.649570i
$$238$$ 9.00000i 0.583383i
$$239$$ 9.00000i 0.582162i −0.956698 0.291081i $$-0.905985\pi$$
0.956698 0.291081i $$-0.0940149\pi$$
$$240$$ 0 0
$$241$$ 30.0000i 1.93247i −0.257663 0.966235i $$-0.582952\pi$$
0.257663 0.966235i $$-0.417048\pi$$
$$242$$ 11.0000 0.707107
$$243$$ 16.0000i 1.02640i
$$244$$ −8.00000 −0.512148
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −12.0000 18.0000i −0.763542 1.14531i
$$248$$ 0 0
$$249$$ 6.00000i 0.380235i
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 6.00000 0.377964
$$253$$ 0 0
$$254$$ 2.00000i 0.125491i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 3.00000i 0.187135i −0.995613 0.0935674i $$-0.970173\pi$$
0.995613 0.0935674i $$-0.0298271\pi$$
$$258$$ −1.00000 −0.0622573
$$259$$ 9.00000 0.559233
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −3.00000 −0.185341
$$263$$ 24.0000i 1.47990i 0.672660 + 0.739952i $$0.265152\pi$$
−0.672660 + 0.739952i $$0.734848\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 18.0000i 1.10365i
$$267$$ 6.00000 0.367194
$$268$$ −12.0000 −0.733017
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 15.0000i 0.911185i 0.890188 + 0.455593i $$0.150573\pi$$
−0.890188 + 0.455593i $$0.849427\pi$$
$$272$$ 3.00000i 0.181902i
$$273$$ 6.00000 + 9.00000i 0.363137 + 0.544705i
$$274$$ 18.0000 1.08742
$$275$$ 0 0
$$276$$ −6.00000 −0.361158
$$277$$ 8.00000i 0.480673i −0.970690 0.240337i $$-0.922742\pi$$
0.970690 0.240337i $$-0.0772579\pi$$
$$278$$ −5.00000 −0.299880
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 30.0000i 1.78965i −0.446417 0.894825i $$-0.647300\pi$$
0.446417 0.894825i $$-0.352700\pi$$
$$282$$ 3.00000i 0.178647i
$$283$$ 4.00000i 0.237775i 0.992908 + 0.118888i $$0.0379328\pi$$
−0.992908 + 0.118888i $$0.962067\pi$$
$$284$$ 15.0000i 0.890086i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 2.00000 0.117851
$$289$$ 8.00000 0.470588
$$290$$ 0 0
$$291$$ 12.0000i 0.703452i
$$292$$ −6.00000 −0.351123
$$293$$ 9.00000 0.525786 0.262893 0.964825i $$-0.415323\pi$$
0.262893 + 0.964825i $$0.415323\pi$$
$$294$$ 2.00000i 0.116642i
$$295$$ 0 0
$$296$$ 3.00000 0.174371
$$297$$ 0 0
$$298$$ 6.00000i 0.347571i
$$299$$ 12.0000 + 18.0000i 0.693978 + 1.04097i
$$300$$ 0 0
$$301$$ 3.00000i 0.172917i
$$302$$ 15.0000i 0.863153i
$$303$$ 12.0000i 0.689382i
$$304$$ 6.00000i 0.344124i
$$305$$ 0 0
$$306$$ 6.00000i 0.342997i
$$307$$ 18.0000 1.02731 0.513657 0.857996i $$-0.328290\pi$$
0.513657 + 0.857996i $$0.328290\pi$$
$$308$$ 0 0
$$309$$ 14.0000 0.796432
$$310$$ 0 0
$$311$$ −18.0000 −1.02069 −0.510343 0.859971i $$-0.670482\pi$$
−0.510343 + 0.859971i $$0.670482\pi$$
$$312$$ 2.00000 + 3.00000i 0.113228 + 0.169842i
$$313$$ 19.0000i 1.07394i 0.843600 + 0.536972i $$0.180432\pi$$
−0.843600 + 0.536972i $$0.819568\pi$$
$$314$$ 22.0000i 1.24153i
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ −6.00000 −0.336463
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 18.0000i 1.00310i
$$323$$ 18.0000 1.00155
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −6.00000 −0.332309
$$327$$ −9.00000 −0.497701
$$328$$ 0 0
$$329$$ 9.00000 0.496186
$$330$$ 0 0
$$331$$ 30.0000i 1.64895i 0.565899 + 0.824475i $$0.308529\pi$$
−0.565899 + 0.824475i $$0.691471\pi$$
$$332$$ −6.00000 −0.329293
$$333$$ 6.00000 0.328798
$$334$$ −12.0000 −0.656611
$$335$$ 0 0
$$336$$ 3.00000i 0.163663i
$$337$$ 13.0000i 0.708155i −0.935216 0.354078i $$-0.884795\pi$$
0.935216 0.354078i $$-0.115205\pi$$
$$338$$ 5.00000 12.0000i 0.271964 0.652714i
$$339$$ −6.00000 −0.325875
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 12.0000i 0.648886i
$$343$$ −15.0000 −0.809924
$$344$$ 1.00000i 0.0539164i
$$345$$ 0 0
$$346$$ 6.00000i 0.322562i
$$347$$ 33.0000i 1.77153i −0.464131 0.885766i $$-0.653633\pi$$
0.464131 0.885766i $$-0.346367\pi$$
$$348$$ 0 0
$$349$$ 21.0000i 1.12410i 0.827102 + 0.562052i $$0.189988\pi$$
−0.827102 + 0.562052i $$0.810012\pi$$
$$350$$ 0 0
$$351$$ 10.0000 + 15.0000i 0.533761 + 0.800641i
$$352$$ 0 0
$$353$$ −6.00000 −0.319348 −0.159674 0.987170i $$-0.551044\pi$$
−0.159674 + 0.987170i $$0.551044\pi$$
$$354$$ 6.00000 0.318896
$$355$$ 0 0
$$356$$ 6.00000i 0.317999i
$$357$$ −9.00000 −0.476331
$$358$$ −15.0000 −0.792775
$$359$$ 24.0000i 1.26667i −0.773877 0.633336i $$-0.781685\pi$$
0.773877 0.633336i $$-0.218315\pi$$
$$360$$ 0 0
$$361$$ −17.0000 −0.894737
$$362$$ 2.00000 0.105118
$$363$$ 11.0000i 0.577350i
$$364$$ −9.00000 + 6.00000i −0.471728 + 0.314485i
$$365$$ 0 0
$$366$$ 8.00000i 0.418167i
$$367$$ 8.00000i 0.417597i −0.977959 0.208798i $$-0.933045\pi$$
0.977959 0.208798i $$-0.0669552\pi$$
$$368$$ 6.00000i 0.312772i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 18.0000i 0.934513i
$$372$$ 0 0
$$373$$ 4.00000i 0.207112i 0.994624 + 0.103556i $$0.0330221\pi$$
−0.994624 + 0.103556i $$0.966978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 3.00000 0.154713
$$377$$ 0 0
$$378$$ 15.0000i 0.771517i
$$379$$ 6.00000i 0.308199i 0.988055 + 0.154100i $$0.0492477\pi$$
−0.988055 + 0.154100i $$0.950752\pi$$
$$380$$ 0 0
$$381$$ 2.00000 0.102463
$$382$$ 12.0000 0.613973
$$383$$ 9.00000 0.459879 0.229939 0.973205i $$-0.426147\pi$$
0.229939 + 0.973205i $$0.426147\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ 0 0
$$386$$ −6.00000 −0.305392
$$387$$ 2.00000i 0.101666i
$$388$$ −12.0000 −0.609208
$$389$$ 30.0000 1.52106 0.760530 0.649303i $$-0.224939\pi$$
0.760530 + 0.649303i $$0.224939\pi$$
$$390$$ 0 0
$$391$$ −18.0000 −0.910299
$$392$$ 2.00000 0.101015
$$393$$ 3.00000i 0.151330i
$$394$$ 3.00000 0.151138
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 18.0000 0.903394 0.451697 0.892171i $$-0.350819\pi$$
0.451697 + 0.892171i $$0.350819\pi$$
$$398$$ 20.0000 1.00251
$$399$$ 18.0000 0.901127
$$400$$ 0 0
$$401$$ 30.0000i 1.49813i 0.662497 + 0.749064i $$0.269497\pi$$
−0.662497 + 0.749064i $$0.730503\pi$$
$$402$$ 12.0000i 0.598506i
$$403$$ 0 0
$$404$$ 12.0000 0.597022
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ −3.00000 −0.148522
$$409$$ 6.00000i 0.296681i 0.988936 + 0.148340i $$0.0473931\pi$$
−0.988936 + 0.148340i $$0.952607\pi$$
$$410$$ 0 0
$$411$$ 18.0000i 0.887875i
$$412$$ 14.0000i 0.689730i
$$413$$ 18.0000i 0.885722i
$$414$$ 12.0000i 0.589768i
$$415$$ 0 0
$$416$$ −3.00000 + 2.00000i −0.147087 + 0.0980581i
$$417$$ 5.00000i 0.244851i
$$418$$ 0 0
$$419$$ −15.0000 −0.732798 −0.366399 0.930458i $$-0.619409\pi$$
−0.366399 + 0.930458i $$0.619409\pi$$
$$420$$ 0 0
$$421$$ 15.0000i 0.731055i −0.930800 0.365528i $$-0.880889\pi$$
0.930800 0.365528i $$-0.119111\pi$$
$$422$$ −23.0000 −1.11962
$$423$$ 6.00000 0.291730
$$424$$ 6.00000i 0.291386i
$$425$$ 0 0
$$426$$ 15.0000 0.726752
$$427$$ −24.0000 −1.16144
$$428$$ 12.0000i 0.580042i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 15.0000i 0.722525i −0.932464 0.361262i $$-0.882346\pi$$
0.932464 0.361262i $$-0.117654\pi$$
$$432$$ 5.00000i 0.240563i
$$433$$ 11.0000i 0.528626i −0.964437 0.264313i $$-0.914855\pi$$
0.964437 0.264313i $$-0.0851452\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 9.00000i 0.431022i
$$437$$ 36.0000 1.72211
$$438$$ 6.00000i 0.286691i
$$439$$ 10.0000 0.477274 0.238637 0.971109i $$-0.423299\pi$$
0.238637 + 0.971109i $$0.423299\pi$$
$$440$$ 0 0
$$441$$ 4.00000 0.190476
$$442$$ 6.00000 + 9.00000i 0.285391 + 0.428086i
$$443$$ 21.0000i 0.997740i −0.866677 0.498870i $$-0.833748\pi$$
0.866677 0.498870i $$-0.166252\pi$$
$$444$$ 3.00000i 0.142374i
$$445$$ 0 0
$$446$$ 9.00000 0.426162
$$447$$ 6.00000 0.283790
$$448$$ 3.00000 0.141737
$$449$$ 24.0000i 1.13263i −0.824189 0.566315i $$-0.808369\pi$$
0.824189 0.566315i $$-0.191631\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 6.00000i 0.282216i
$$453$$ −15.0000 −0.704761
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ 6.00000 0.280976
$$457$$ 18.0000 0.842004 0.421002 0.907060i $$-0.361678\pi$$
0.421002 + 0.907060i $$0.361678\pi$$
$$458$$ 9.00000i 0.420542i
$$459$$ −15.0000 −0.700140
$$460$$ 0 0
$$461$$ 15.0000i 0.698620i −0.937007 0.349310i $$-0.886416\pi$$
0.937007 0.349310i $$-0.113584\pi$$
$$462$$ 0 0
$$463$$ 24.0000 1.11537 0.557687 0.830051i $$-0.311689\pi$$
0.557687 + 0.830051i $$0.311689\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 21.0000i 0.972806i
$$467$$ 12.0000i 0.555294i 0.960683 + 0.277647i $$0.0895545\pi$$
−0.960683 + 0.277647i $$0.910445\pi$$
$$468$$ −6.00000 + 4.00000i −0.277350 + 0.184900i
$$469$$ −36.0000 −1.66233
$$470$$ 0 0
$$471$$ 22.0000 1.01371
$$472$$ 6.00000i 0.276172i
$$473$$ 0 0
$$474$$ 10.0000i 0.459315i
$$475$$ 0 0
$$476$$ 9.00000i 0.412514i
$$477$$ 12.0000i 0.549442i
$$478$$ 9.00000i 0.411650i
$$479$$ 39.0000i 1.78196i −0.454047 0.890978i $$-0.650020\pi$$
0.454047 0.890978i $$-0.349980\pi$$
$$480$$ 0 0
$$481$$ −9.00000 + 6.00000i −0.410365 + 0.273576i
$$482$$ 30.0000i 1.36646i
$$483$$ −18.0000 −0.819028
$$484$$ 11.0000 0.500000
$$485$$ 0 0
$$486$$ 16.0000i 0.725775i
$$487$$ −12.0000 −0.543772 −0.271886 0.962329i $$-0.587647\pi$$
−0.271886 + 0.962329i $$0.587647\pi$$
$$488$$ −8.00000 −0.362143
$$489$$ 6.00000i 0.271329i
$$490$$ 0 0
$$491$$ 27.0000 1.21849 0.609246 0.792981i $$-0.291472\pi$$
0.609246 + 0.792981i $$0.291472\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −12.0000 18.0000i −0.539906 0.809858i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 45.0000i 2.01853i
$$498$$ 6.00000i 0.268866i
$$499$$ 36.0000i 1.61158i 0.592200 + 0.805791i $$0.298259\pi$$
−0.592200 + 0.805791i $$0.701741\pi$$
$$500$$ 0 0
$$501$$ 12.0000i 0.536120i
$$502$$ 12.0000 0.535586
$$503$$ 6.00000i 0.267527i −0.991013 0.133763i $$-0.957294\pi$$
0.991013 0.133763i $$-0.0427062\pi$$
$$504$$ 6.00000 0.267261
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −12.0000 5.00000i −0.532939 0.222058i
$$508$$ 2.00000i 0.0887357i
$$509$$ 6.00000i 0.265945i 0.991120 + 0.132973i $$0.0424523\pi$$
−0.991120 + 0.132973i $$0.957548\pi$$
$$510$$ 0 0
$$511$$ −18.0000 −0.796273
$$512$$ 1.00000 0.0441942
$$513$$ 30.0000 1.32453
$$514$$ 3.00000i 0.132324i
$$515$$ 0 0
$$516$$ −1.00000 −0.0440225
$$517$$ 0 0
$$518$$ 9.00000 0.395437
$$519$$ −6.00000 −0.263371
$$520$$ 0 0
$$521$$ 27.0000 1.18289 0.591446 0.806345i $$-0.298557\pi$$
0.591446 + 0.806345i $$0.298557\pi$$
$$522$$ 0 0
$$523$$ 16.0000i 0.699631i −0.936819 0.349816i $$-0.886244\pi$$
0.936819 0.349816i $$-0.113756\pi$$
$$524$$ −3.00000 −0.131056
$$525$$ 0 0
$$526$$ 24.0000i 1.04645i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −13.0000 −0.565217
$$530$$ 0 0
$$531$$ 12.0000i 0.520756i
$$532$$ 18.0000i 0.780399i
$$533$$ 0 0
$$534$$ 6.00000 0.259645
$$535$$ 0 0
$$536$$ −12.0000 −0.518321
$$537$$ 15.0000i 0.647298i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 15.0000i 0.644900i −0.946586 0.322450i $$-0.895494\pi$$
0.946586 0.322450i $$-0.104506\pi$$
$$542$$ 15.0000i 0.644305i
$$543$$ 2.00000i 0.0858282i
$$544$$ 3.00000i 0.128624i
$$545$$ 0 0
$$546$$ 6.00000 + 9.00000i 0.256776 + 0.385164i
$$547$$ 37.0000i 1.58201i 0.611812 + 0.791003i $$0.290441\pi$$
−0.611812 + 0.791003i $$0.709559\pi$$
$$548$$ 18.0000 0.768922
$$549$$ −16.0000 −0.682863
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −6.00000 −0.255377
$$553$$ −30.0000 −1.27573
$$554$$ 8.00000i 0.339887i
$$555$$ 0 0
$$556$$ −5.00000 −0.212047
$$557$$ −27.0000 −1.14403 −0.572013 0.820244i $$-0.693837\pi$$
−0.572013 + 0.820244i $$0.693837\pi$$
$$558$$ 0 0
$$559$$ 2.00000 + 3.00000i 0.0845910 + 0.126886i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 30.0000i 1.26547i
$$563$$ 39.0000i 1.64365i 0.569737 + 0.821827i $$0.307045\pi$$
−0.569737 + 0.821827i $$0.692955\pi$$
$$564$$ 3.00000i 0.126323i
$$565$$ 0 0
$$566$$ 4.00000i 0.168133i
$$567$$ 3.00000 0.125988
$$568$$ 15.0000i 0.629386i
$$569$$ −45.0000 −1.88650 −0.943249 0.332086i $$-0.892248\pi$$
−0.943249 + 0.332086i $$0.892248\pi$$
$$570$$ 0 0
$$571$$ −23.0000 −0.962520 −0.481260 0.876578i $$-0.659821\pi$$
−0.481260 + 0.876578i $$0.659821\pi$$
$$572$$ 0 0
$$573$$ 12.0000i 0.501307i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 2.00000 0.0833333
$$577$$ −42.0000 −1.74848 −0.874241 0.485491i $$-0.838641\pi$$
−0.874241 + 0.485491i $$0.838641\pi$$
$$578$$ 8.00000 0.332756
$$579$$ 6.00000i 0.249351i
$$580$$ 0 0
$$581$$ −18.0000 −0.746766
$$582$$ 12.0000i 0.497416i
$$583$$ 0 0
$$584$$ −6.00000 −0.248282
$$585$$ 0 0
$$586$$ 9.00000 0.371787
$$587$$ 18.0000 0.742940 0.371470 0.928445i $$-0.378854\pi$$
0.371470 + 0.928445i $$0.378854\pi$$
$$588$$ 2.00000i 0.0824786i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 3.00000i 0.123404i
$$592$$ 3.00000 0.123299
$$593$$ −36.0000 −1.47834 −0.739171 0.673517i $$-0.764783\pi$$
−0.739171 + 0.673517i $$0.764783\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6.00000i 0.245770i
$$597$$ 20.0000i 0.818546i
$$598$$ 12.0000 + 18.0000i 0.490716 + 0.736075i
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 0 0
$$601$$ 37.0000 1.50926 0.754631 0.656150i $$-0.227816\pi$$
0.754631 + 0.656150i $$0.227816\pi$$
$$602$$ 3.00000i 0.122271i
$$603$$ −24.0000 −0.977356
$$604$$ 15.0000i 0.610341i
$$605$$ 0 0
$$606$$ 12.0000i 0.487467i
$$607$$ 22.0000i 0.892952i 0.894795 + 0.446476i $$0.147321\pi$$
−0.894795 + 0.446476i $$0.852679\pi$$
$$608$$ 6.00000i 0.243332i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −9.00000 + 6.00000i −0.364101 + 0.242734i
$$612$$ 6.00000i 0.242536i
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ 18.0000 0.726421
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −12.0000 −0.483102 −0.241551 0.970388i $$-0.577656\pi$$
−0.241551 + 0.970388i $$0.577656\pi$$
$$618$$ 14.0000 0.563163
$$619$$ 24.0000i 0.964641i −0.875995 0.482321i $$-0.839794\pi$$
0.875995 0.482321i $$-0.160206\pi$$
$$620$$ 0 0
$$621$$ −30.0000 −1.20386
$$622$$ −18.0000 −0.721734
$$623$$ 18.0000i 0.721155i
$$624$$ 2.00000 + 3.00000i 0.0800641 + 0.120096i
$$625$$ 0 0
$$626$$ 19.0000i 0.759393i
$$627$$ 0 0
$$628$$ 22.0000i 0.877896i
$$629$$ 9.00000i 0.358854i
$$630$$ 0 0
$$631$$ 15.0000i 0.597141i −0.954388 0.298570i $$-0.903490\pi$$
0.954388 0.298570i $$-0.0965097\pi$$
$$632$$ −10.0000 −0.397779
$$633$$ 23.0000i 0.914168i
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ −6.00000 + 4.00000i −0.237729 + 0.158486i
$$638$$ 0 0
$$639$$ 30.0000i 1.18678i
$$640$$ 0 0
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 12.0000 0.473602
$$643$$ −36.0000 −1.41970 −0.709851 0.704352i $$-0.751238\pi$$
−0.709851 + 0.704352i $$0.751238\pi$$
$$644$$ 18.0000i 0.709299i
$$645$$ 0 0
$$646$$ 18.0000 0.708201
$$647$$ 42.0000i 1.65119i 0.564263 + 0.825595i $$0.309160\pi$$
−0.564263 + 0.825595i $$0.690840\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −6.00000 −0.234978
$$653$$ 36.0000i 1.40879i −0.709809 0.704394i $$-0.751219\pi$$
0.709809 0.704394i $$-0.248781\pi$$
$$654$$ −9.00000 −0.351928
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −12.0000 −0.468165
$$658$$ 9.00000 0.350857
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 30.0000i 1.16686i 0.812162 + 0.583432i $$0.198291\pi$$
−0.812162 + 0.583432i $$0.801709\pi$$
$$662$$ 30.0000i 1.16598i
$$663$$ 9.00000 6.00000i 0.349531 0.233021i
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ 0 0
$$668$$ −12.0000 −0.464294
$$669$$ 9.00000i 0.347960i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 3.00000i 0.115728i
$$673$$ 1.00000i 0.0385472i −0.999814 0.0192736i $$-0.993865\pi$$
0.999814 0.0192736i $$-0.00613535\pi$$
$$674$$ 13.0000i 0.500741i
$$675$$ 0 0
$$676$$ 5.00000 12.0000i 0.192308 0.461538i
$$677$$ 18.0000i 0.691796i −0.938272 0.345898i $$-0.887574\pi$$
0.938272 0.345898i $$-0.112426\pi$$
$$678$$ −6.00000 −0.230429
$$679$$ −36.0000 −1.38155
$$680$$ 0 0
$$681$$ 12.0000i 0.459841i
$$682$$ 0 0
$$683$$ −6.00000 −0.229584 −0.114792 0.993390i $$-0.536620\pi$$
−0.114792 + 0.993390i $$0.536620\pi$$
$$684$$ 12.0000i 0.458831i
$$685$$ 0 0
$$686$$ −15.0000 −0.572703
$$687$$ −9.00000 −0.343371
$$688$$ 1.00000i 0.0381246i
$$689$$ 12.0000 + 18.0000i 0.457164 + 0.685745i
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 6.00000i 0.228086i
$$693$$ 0 0
$$694$$ 33.0000i 1.25266i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 21.0000i 0.794862i
$$699$$ −21.0000 −0.794293
$$700$$ 0 0
$$701$$ 42.0000 1.58632 0.793159 0.609015i $$-0.208435\pi$$
0.793159 + 0.609015i $$0.208435\pi$$
$$702$$ 10.0000 + 15.0000i 0.377426 + 0.566139i
$$703$$ 18.0000i 0.678883i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −6.00000 −0.225813
$$707$$ 36.0000 1.35392
$$708$$ 6.00000 0.225494
$$709$$ 6.00000i 0.225335i 0.993633 + 0.112667i $$0.0359394\pi$$
−0.993633 + 0.112667i $$0.964061\pi$$
$$710$$ 0 0
$$711$$ −20.0000 −0.750059
$$712$$ 6.00000i 0.224860i
$$713$$ 0 0
$$714$$ −9.00000 −0.336817
$$715$$ 0 0
$$716$$ −15.0000 −0.560576
$$717$$ −9.00000 −0.336111
$$718$$ 24.0000i 0.895672i
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 42.0000i 1.56416i
$$722$$ −17.0000 −0.632674
$$723$$ −30.0000 −1.11571
$$724$$ 2.00000 0.0743294
$$725$$ 0 0
$$726$$ 11.0000i 0.408248i
$$727$$ 28.0000i 1.03846i −0.854634 0.519231i $$-0.826218\pi$$
0.854634 0.519231i $$-0.173782\pi$$
$$728$$ −9.00000 + 6.00000i −0.333562 + 0.222375i
$$729$$ −13.0000 −0.481481
$$730$$ 0 0
$$731$$ −3.00000 −0.110959
$$732$$ 8.00000i 0.295689i
$$733$$ 9.00000 0.332423 0.166211 0.986090i $$-0.446847\pi$$
0.166211 + 0.986090i $$0.446847\pi$$
$$734$$ 8.00000i 0.295285i
$$735$$ 0 0
$$736$$ 6.00000i 0.221163i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 36.0000i 1.32428i 0.749380 + 0.662141i $$0.230352\pi$$
−0.749380 + 0.662141i $$0.769648\pi$$
$$740$$ 0 0
$$741$$ −18.0000 + 12.0000i −0.661247 + 0.440831i
$$742$$ 18.0000i 0.660801i
$$743$$ 39.0000 1.43077 0.715386 0.698730i $$-0.246251\pi$$
0.715386 + 0.698730i $$0.246251\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 4.00000i 0.146450i
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ 36.0000i 1.31541i
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 3.00000 0.109399
$$753$$ 12.0000i 0.437304i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 15.0000i 0.545545i
$$757$$ 2.00000i 0.0726912i 0.999339 + 0.0363456i $$0.0115717\pi$$
−0.999339 + 0.0363456i $$0.988428\pi$$
$$758$$ 6.00000i 0.217930i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 30.0000i 1.08750i −0.839248 0.543750i $$-0.817004\pi$$
0.839248 0.543750i $$-0.182996\pi$$
$$762$$ 2.00000 0.0724524
$$763$$ 27.0000i 0.977466i
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ 9.00000 0.325183
$$767$$ −12.0000 18.0000i −0.433295 0.649942i
$$768$$ 1.00000i 0.0360844i
$$769$$ 24.0000i 0.865462i −0.901523 0.432731i $$-0.857550\pi$$
0.901523 0.432731i $$-0.142450\pi$$
$$770$$ 0 0
$$771$$ −3.00000 −0.108042
$$772$$ −6.00000 −0.215945
$$773$$ −21.0000 −0.755318 −0.377659 0.925945i $$-0.623271\pi$$
−0.377659 + 0.925945i $$0.623271\pi$$
$$774$$ 2.00000i 0.0718885i
$$775$$ 0 0
$$776$$ −12.0000 −0.430775
$$777$$ 9.00000i 0.322873i
$$778$$ 30.0000 1.07555
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −18.0000 −0.643679
$$783$$ 0 0
$$784$$ 2.00000 0.0714286
$$785$$ 0 0
$$786$$ 3.00000i 0.107006i
$$787$$ −12.0000 −0.427754 −0.213877 0.976861i $$-0.568609\pi$$
−0.213877 + 0.976861i $$0.568609\pi$$
$$788$$ 3.00000 0.106871
$$789$$ 24.0000 0.854423
$$790$$ 0 0
$$791$$ 18.0000i 0.640006i
$$792$$ 0 0
$$793$$ 24.0000 16.0000i 0.852265 0.568177i
$$794$$ 18.0000 0.638796
$$795$$ 0 0
$$796$$ 20.0000 0.708881
$$797$$ 18.0000i